diff --git "a/data/test-all.jsonl" "b/data/test-all.jsonl"
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+++ /dev/null
@@ -1,3725 +0,0 @@
-{"premise":"There are two 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 Alice'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)","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":"Alice can now know whether Christine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alice","Christine"],"index":35351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994251728,"difficulty":0.0005748272}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Lauren can now know that Tracy can know that Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debbie","Tracy","Lauren","Johnnie"],"index":49417,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982271791,"difficulty":0.0017728209}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Winifred 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 (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":"Freddie can now know that Amanda can know that Freddie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Freddie","Amanda","Winifred","Kathy"],"index":66799,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8635368943,"difficulty":0.1364631057}
-{"premise":"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 Michael knows whether or not nobody'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 (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] (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 (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Phillip"],"index":12191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9109317064,"difficulty":0.0890682936}
-{"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 Nathaniel. Raymond's card is shown to Raymond. Andrew's card is shown to Willie. Willie'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 Willie does not know whether Willie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Andrew can now know whether Willie can know that Willie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nathaniel","Raymond","Willie","Andrew"],"index":55199,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9405223131,"difficulty":0.0594776869}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc knows whether 2) ] 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 2) ] 0","hypothesis":"Margaret can now know that Jennifer can know that Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Jennifer","Howard"],"index":2974,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985671043,"difficulty":0.0014328957}
-{"premise":"There are four persons. Everyone is visible 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 knows whether or not nobody's forehead is muddy. It is publicly announced that Esther knows whether Esther's forehead is muddy. It is publicly announced that Maranda's forehead is muddy. It is publicly announced that Melissa knows whether Maranda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (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":"Jennifer can now know whether Esther can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maranda","Esther","Melissa","Jennifer"],"index":12924,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
-{"premise":"There are four persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Joyce knows whether Joyce's forehead is muddy. It is publicly announced that Chad's forehead is muddy. It is publicly announced that Shawn knows whether Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Joyce can now know whether Brian can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chad","Joyce","Shawn","Brian"],"index":53967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997524619,"difficulty":0.0002475381}
-{"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 Joseph. Joseph's card is shown to Sally. It is publicly announced that someone picked a red card. It is publicly announced that Sally does not know whether Sally picked a red card. It is publicly announced that Sally does not know whether Sally picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb 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 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joseph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Sally","Donna"],"index":52384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
-{"premise":"There are three persons. Everyone is visible 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 Dorothy 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) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (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) ] 0","hypothesis":"Max can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Max","Dorothy","Thomas"],"index":36339,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983114004,"difficulty":0.0016885996}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Vanessa 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 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 (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Vanessa can now know that Catherine can know whether Vanessa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vanessa","Catherine"],"index":25024,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991545677,"difficulty":0.0008454323}
-{"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 Michael. Michael's card is shown to Michael. Thomas's card is shown to Dani. Michael's card is shown to Dani. Dani's card is shown to Dani. 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 Thomas knows whether Michael 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 (~(1|2|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":"Michael can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Michael","Dani"],"index":58320,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! 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) ] [ ! 1 ] 0","hypothesis":"Austin can now know that Michael can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Austin","Esperanza"],"index":57961,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997013092,"difficulty":0.002986908}
-{"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 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) ] [ ! (Agentc knows whether 3) ] Agentb 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&2&3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Timothy can now know whether Margaret can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Felix","Timothy","Margaret"],"index":59151,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985899329,"difficulty":0.0014100671}
-{"premise":"There are three persons. Everyone is visible 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 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":"Myrtle can now know that Steven can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Myrtle","Steven","Ashli"],"index":27423,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996806383,"difficulty":0.0003193617}
-{"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 Raymond 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 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":"Raymond can now know whether Timothy can know whether Raymond is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Timothy"],"index":22804,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986045957,"difficulty":0.0013954043}
-{"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 Reginald is thirsty. It is publicly announced that Jill does not know whether Randy is 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 (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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Randy can now know that Reginald can know that Randy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Reginald","Jill","Randy"],"index":51378,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9930247068,"difficulty":0.0069752932}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rikki does not know whether Daryl is 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 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":"Billy can now know whether Rikki is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daryl","Allan","Rikki","Billy"],"index":5050,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9522816539,"difficulty":0.0477183461}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvester knows whether someone is thirsty. It is publicly announced that Sylvester knows whether Sylvester 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|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 2) ] [ ! (1&2) ] 0","hypothesis":"Sylvester can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jerry","Sylvester"],"index":66328,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997271895,"difficulty":0.0002728105}
-{"premise":"There are two persons. Everyone is visible 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 Kevin 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 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":"Kevin can now know that Harrison's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kevin","Harrison"],"index":8793,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8041531444,"difficulty":0.1958468556}
-{"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 Robert. Clyde's card is shown to Robert. Christina's card is shown to Nancee. Robert's card is shown to Christina. Clyde's card is shown to Christina. Robert'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 Nancee does not know whether Clyde 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 (1&2&3&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":"Christina can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Nancee","Christina","Clyde"],"index":36638,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998611331,"difficulty":0.001388669}
-{"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 or not everyone 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 (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":"David can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clarence","David","Richard","Micheal"],"index":62585,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997296929,"difficulty":0.0002703071}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harry's card is shown to Harry. Kay's card is shown to Harry. Harry's card is shown to Kay. 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 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":"Kay can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Kay"],"index":16860,"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. It is publicly announced that Liliana 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":"Rene can now know that Liliana can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rene","Liliana","Hilda"],"index":62523,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982565045,"difficulty":0.0017434955}
-{"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. Debora's card is shown to Patricia. Patricia's card is shown to William. William's card is shown to William. Clemente's card is shown to William. Debora's card is shown to William. Patricia's card is shown to Clemente. William's card is shown to Debora. 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 (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Debora can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","William","Clemente","Debora"],"index":34283,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997824192,"difficulty":0.002175808}
-{"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)","n_announcements":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":"Franklin can now know whether Assunta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Assunta","Marion","Franklin","Richard"],"index":6788,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951654673,"difficulty":0.0048345327}
-{"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 Laurie. Laurie'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:4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 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":"Jane can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laurie","Jane","Christopher","Gary"],"index":62431,"s-l":"explicit-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's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy. It is publicly announced that Elizabeth 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)","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":"Elizabeth can now know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kimberly","Elizabeth"],"index":36753,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940788746,"difficulty":0.0059211254}
-{"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 Agnes is thirsty. It is publicly announced that Agnes does not know whether Nancy 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 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Agnes can now know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Nancy","Agnes"],"index":64616,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6982142329,"difficulty":0.3017857671}
-{"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 or not everyone is thirsty. It is publicly announced that Brittany does not know whether Victor is thirsty. It is publicly announced that Brittany does not know whether Victor 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta 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: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":"Victor can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brittany","Paul","Victor"],"index":29145,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976765513,"difficulty":0.0023234487}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shon does not know whether Alta 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 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":"Mark can now know that Alta can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shon","Mark","Alta"],"index":35465,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984117746,"difficulty":0.0015882254}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zachary's card is shown to John. Zachary's card is shown to Zachary. Jason's card is shown to Zachary. Terry's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Zachary does not know whether Terry 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) ] [ ! ~(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:2 Agentb:2,3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Zachary can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Zachary","Jason","Terry"],"index":19259,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9814903736,"difficulty":0.0185096264}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin 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 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":"Joseph can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kevin","Joseph"],"index":41420,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985839128,"difficulty":0.0014160872}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Thomas 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)) ] Agentc 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)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know whether Thomas can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Rodney","William","Stephanie"],"index":32078,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9735162258,"difficulty":0.0264837742}
-{"premise":"There are two persons. Everyone is visible 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 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)","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":"Stephany can now know that Stephany's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephany","Samuel"],"index":666,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982606769,"difficulty":0.0017393231}
-{"premise":"There are three persons. Everyone is visible 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 1,2,3 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)","n_announcements":1,"pbcheck":"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":"Jose can now know that Tonya can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Tonya","Rachel"],"index":10542,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950435162,"difficulty":0.0049564838}
-{"premise":"There are three persons. Everyone is visible 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 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)) ] 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) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kelly 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":["Kelly","Michael","Roger"],"index":23190,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984896183,"difficulty":0.0015103817}
-{"premise":"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 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 (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 Kimberly can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Kimberly","Kevin"],"index":50622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9612755775,"difficulty":0.0387244225}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dean 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 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Douglas can now know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dean","Jennifer","Douglas","Robert"],"index":13885,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.5767472386,"difficulty":1.5767472386}
-{"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 Neil. Frankie's card is shown to Frankie. Jacob's card is shown to Frankie. Frankie's card is shown to Charlotte. Neil's card is shown to Jacob. It is publicly announced that someone picked a red card. It is publicly announced that Frankie picked a black card. It is publicly announced that Frankie does not know whether Neil picked a red card. It is publicly announced that Frankie knows whether someone picked a red card. It is publicly announced that Frankie does not know whether Neil 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) ] Agentb knows whether (Agentd knows that 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":"Frankie can now know whether Jacob can know that Jacob picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Neil","Frankie","Charlotte","Jacob"],"index":61026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9578191638,"difficulty":0.0421808362}
-{"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 Dexter is thirsty. It is publicly announced that Dexter 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) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (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 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Dexter can now know whether Helen can know that Howard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Howard","Helen","Dexter"],"index":56500,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9915130734,"difficulty":0.0084869266}
-{"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 Neva. Sarah's card is shown to Neva. Sarah's card is shown to William. Neva's card is shown to Sarah. 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 2)","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":"Sarah can now know that William can know whether William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Neva","William","Sarah"],"index":28416,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9279150367,"difficulty":1.9279150367}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louise 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 (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":"Anthony can now know that Sharon can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louise","Robert","Sharon","Anthony"],"index":52544,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985796213,"difficulty":0.0014203787}
-{"premise":"There are three persons. Everyone is visible 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 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)","n_announcements":1,"pbcheck":"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":"Etta can now know that Jeffrey can know that Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Etta","Ashley"],"index":17951,"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 Alfred knows whether Steve'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 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 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) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Steve can now know that Alfred can know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alfred","Sara","Steve","Willie"],"index":67681,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5743825436,"difficulty":0.4256174564}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Latasha's card is shown to Ida. Jack's card is shown to Latasha. Latasha'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:2 Agentb:3 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:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ida can now know whether Ida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ida","Latasha","Jack"],"index":57954,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9546145797,"difficulty":0.0453854203}
-{"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 Lupe. Henry's card is shown to Alexander. Alexander's card is shown to Henry. Henry's card is shown to Henry. It is publicly announced that someone picked a red card. It is publicly announced that Lupe 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)) ] Agenta knows that (Agentc knows whether (1&2&3))","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":"Lupe can now know that Henry can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lupe","Alexander","Henry"],"index":15349,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9870170951,"difficulty":0.0129829049}
-{"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":"Justin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Justin","Mark","Jeffrey"],"index":39374,"s-l":"forehead-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 is thirsty. It is publicly announced that Harvey is not thirsty. It is publicly announced that 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) ] [ ! ~(4) ] [ ! 1 ] 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) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Judy can now know that Harvey can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judy","William","Clinton","Harvey"],"index":24174,"s-l":"internal-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 James knows whether James's forehead is muddy. It is publicly announced that Donald 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) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (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) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know whether Donald can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Donald","James","Robert"],"index":9158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997182488,"difficulty":0.0002817512}
-{"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 George. Bruce's card is shown to George. George's card is shown to Tim. Tim's card is shown to Bruce. 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 (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":"Bruce can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Tim","Bruce"],"index":18534,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947792292,"difficulty":0.0052207708}
-{"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 Roy. Robert's card is shown to Robert. Robert's card is shown to Chad. Chad's card is shown to Chad. Chad's card is shown to Linda. 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 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] (Agenta knows that 4)","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":"Roy can now know that Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roy","Robert","Chad","Linda"],"index":63538,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977869987,"difficulty":0.0022130013}
-{"premise":"There are two persons. Everyone is visible 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 Melissa knows whether Melissa'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|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":"Melissa can now know whether Helen can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melissa","Helen"],"index":2387,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997448325,"difficulty":0.0002551675}
-{"premise":"There are two persons. Everyone is visible 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 Timothy'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 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":"James 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":["Timothy","James"],"index":39841,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983913302,"difficulty":0.0016086698}
-{"premise":"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 William knows whether Eric'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) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 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) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Marsha can now know that William can know that Marsha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marsha","William","Eric"],"index":19822,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958395958,"difficulty":0.0041604042}
-{"premise":"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)) ] 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 (1&2&3&4)) ] 0","hypothesis":"Dora can now know whether Thomas can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Eileen","Dora","Thomas"],"index":43067,"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 is thirsty. It is publicly announced that Carolyn does not know whether or not everyone is thirsty. It is publicly announced that Silvana does not know whether Ronald is thirsty. It is publicly announced that Carolyn 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 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)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ronald can now know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Carolyn","Silvana"],"index":33224,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7304099202,"difficulty":0.2695900798}
-{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Pok can now know that Joseph can know that Pok's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Pok"],"index":31668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982257485,"difficulty":0.0017742515}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deloise 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)","n_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":"Deloise can now know whether Deloise's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cody","Deloise","Jennifer"],"index":25937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.829285562,"difficulty":0.170714438}
-{"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 (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":"Bettie can now know whether Laurence can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laurence","Joann","Ricky","Bettie"],"index":27268,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995433092,"difficulty":0.0004566908}
-{"premise":"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 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":"Barbara can now know that Stephen can know that Stephen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Stephen","Tara"],"index":53062,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9960029721,"difficulty":0.0039970279}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose knows whether or not everyone is thirsty. It is publicly announced that Kyle knows whether Jose 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 (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&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Kyle can now know whether Jose can know that Jose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kyle","Jose","Thomas"],"index":49729,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9659089446,"difficulty":0.0340910554}
-{"premise":"There are two 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 Pamela knows whether or not nobody is thirsty. It is publicly announced that Pamela 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)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta 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) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Linda can now know that Pamela can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pamela","Linda"],"index":13183,"s-l":"internal-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). Howard's card is shown to Anna. Morgan's card is shown to Anna. Anna's card is shown to Howard. 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. It is publicly announced that Anna 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))) ] (Agentb knows that 1)","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":"Howard can now know that Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anna","Howard","Morgan"],"index":21449,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5774366856,"difficulty":1.5774366856}
-{"premise":"There are three persons. Everyone is visible 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'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 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":"Francisco can now know that Joni can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joni","Francisco","Jeanne"],"index":16921,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961944818,"difficulty":0.0038055182}
-{"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 Ronald. Jeanette's card is shown to Jeanette. Melissa's card is shown to Sharon. Jeanette'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:2 Agentb:3 Agentc: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:3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Melissa","Jeanette","Sharon"],"index":28453,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983389378,"difficulty":0.0016610622}
-{"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. Gerald's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Gerald picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gerald","David"],"index":20346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7212927938,"difficulty":0.2787072062}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Avelina knows whether someone's forehead is muddy. It is publicly announced that Avelina 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 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)) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jackson can now know that Avelina can know whether Avelina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Avelina","Jackson"],"index":61330,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996469021,"difficulty":0.0003530979}
-{"premise":"There are two 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.","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":"Phillip can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Phillip","Diana"],"index":59409,"s-l":"internal-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). Gina's card is shown to Gina. Gina's card is shown to Phyllis. Phyllis's card is shown to James. James's card is shown to Fredrick. Fredrick's card is shown to Fredrick. 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) ] (Agentd 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":"Fredrick can now know that Gina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gina","Phyllis","James","Fredrick"],"index":29971,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982433319,"difficulty":0.0017566681}
-{"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 Lisa knows 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) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (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) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lisa can now know whether Howard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Danielle","Howard","Robert"],"index":2972,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951430559,"difficulty":0.0048569441}
-{"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 Gordon. Tommie's card is shown to Gordon. Gordon's card is shown to Anna. Anna's card is shown to Anna. Anna's card is shown to Tommie. 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 that (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":"Anna can now know that Tommie can know that Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gordon","Anna","Tommie"],"index":16538,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960313439,"difficulty":0.0039686561}
-{"premise":"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 everyone's forehead is muddy. It is publicly announced that John'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) ] (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":"John can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Lee","Joann"],"index":34682,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Anita does not know 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) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 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) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Patricia can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexis","Patricia","Mario","Anita"],"index":31382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8408505321,"difficulty":0.1591494679}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agenta knows whether 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 3) ] 0","hypothesis":"Judith can now know whether Elizabeth can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Judith","Elizabeth"],"index":35896,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996750355,"difficulty":0.0003249645}
-{"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 James is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Maria 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) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Joseph can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Tabitha","Maria","Joseph"],"index":32763,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960266352,"difficulty":0.0039733648}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kellie's card is shown to Kellie. Kellie's card is shown to Alan. Alan'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 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:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kellie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kellie","Alan","Eric"],"index":29666,"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. 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) ] 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Patricia can now know that Ella can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Patricia","Ella","Larry"],"index":44644,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997519851,"difficulty":0.0002480149}
-{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Charles knows whether Susan's forehead is muddy. It is publicly announced that Charles'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 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) ] [ ! ~(1) ] 0","hypothesis":"Charles can now know whether Susan can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Susan"],"index":15364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997057319,"difficulty":0.0002942681}
-{"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) ] [ ! (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":"Melodie can now know whether George can know whether Tina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tina","George","Melodie","Ellen"],"index":19393,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989756346,"difficulty":0.0010243654}
-{"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 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":"Mark can now know that Taryn can know whether Sam's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Taryn","Mark","Sam","Dorothy"],"index":16620,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996221066,"difficulty":0.0003778934}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celestina 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Susan can now know that Sue can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Celestina","Sue","Judith"],"index":23493,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984301925,"difficulty":0.0015698075}
-{"premise":"There are three persons. Everyone is visible to others. 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:2,3 Agentb:1,3 Agentc:1,2 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: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 Kimberly can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","James","Danny"],"index":6061,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992602468,"difficulty":0.0007397532}
-{"premise":"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 Betty 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|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":"Betty can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frank","Betty"],"index":27958,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978913665,"difficulty":0.0021086335}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Anthony can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tina","Anthony","Beverly","Arthur"],"index":50900,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998210907,"difficulty":0.001789093}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luis knows whether 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) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jacqueline can now know that Sammie can know that Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Luis","Sammie","Nicole"],"index":63604,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980052114,"difficulty":0.0019947886}
-{"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 Larry is thirsty. It is publicly announced that Helen 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Larry can now know whether Leslie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lee","Leslie","Larry","Helen"],"index":24894,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994781613,"difficulty":0.0005218387}
-{"premise":"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 does not know whether Chad'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 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":"Nicholas can now know whether Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Chad","Richard","Nicholas"],"index":66864,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883298874,"difficulty":0.0116701126}
-{"premise":"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's forehead is not muddy. It is publicly announced that Francisco 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)","n_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":"Francisco can now know that Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joan","Francisco","Monty"],"index":8088,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992434144,"difficulty":0.007565856}
-{"premise":"There are four persons. Everyone is visible 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 Rita knows whether Jeri's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Rita can now know that Rita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Rita","Jeri","Jose"],"index":42119,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951967597,"difficulty":0.0048032403}
-{"premise":"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 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) ] [ ! (Agenta knows whether 1) ] 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that Jackie can know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Elizabeth","Jackie","Linda"],"index":15537,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996046424,"difficulty":0.0003953576}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christy knows whether someone's forehead is muddy. It is publicly announced that Carolyn knows whether Christy's forehead is muddy. It is publicly announced that Rob does not know whether Rob's forehead 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 (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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rob can now know whether Christy can know whether Christy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Rob","Christy"],"index":40039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5623679161,"difficulty":0.4376320839}
-{"premise":"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 John knows whether someone's forehead is muddy. It is publicly announced that Frank knows whether Dianne's forehead is muddy. It is publicly announced that Bryan does not know whether Bryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 whether (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) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Frank can now know whether John can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dianne","Frank","Bryan","John"],"index":3641,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997127652,"difficulty":0.0002872348}
-{"premise":"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 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":"Gina can now know whether Marta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janet","Marta","Gina","Donna"],"index":67422,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995583892,"difficulty":0.0004416108}
-{"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 Beth is thirsty. It is publicly announced that Beth does not know whether Terry is thirsty. It is publicly announced that Terry does not know whether Beth is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alexandria can now know that Beth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beth","Terry","Alexandria","Ryan"],"index":34622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997853637,"difficulty":0.0002146363}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Israel does not know whether Israel's forehead is muddy. It is publicly announced that Christian 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)) ] 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christian can now know that Israel can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Israel","Christian","Carolyn"],"index":60514,"s-l":"forehead-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). Claudia's card is shown to Heather. Suzanne's card is shown to Heather. Heather's card is shown to Claudia. Claudia's card is shown to Claudia. 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 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Heather can now know that Frank picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Heather","Claudia","Suzanne"],"index":1566,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982725382,"difficulty":0.0017274618}
-{"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 Olivia is thirsty. It is publicly announced that Olivia does not know whether Ruby is 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) ] 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ruby can now know whether Pedro can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olivia","Patricia","Ruby","Pedro"],"index":58742,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978147745,"difficulty":0.0021852255}
-{"premise":"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 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Mario can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Mario","Rose","Ardath"],"index":38195,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9718791842,"difficulty":1.9718791842}
-{"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 Bernard. Kristina's card is shown to Kristina. Kristina's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Kristina does not know whether or not everyone picked a red card. It is publicly announced that Kristina 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 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":"Bernard can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Bernard","Kristina","Karen"],"index":44456,"s-l":"explicit-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 is thirsty. It is publicly announced that David does not know whether Russell is thirsty. It is publicly announced that David 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)) ] (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) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Russell can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Russell","David"],"index":21241,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8562071919,"difficulty":0.1437928081}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 (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) ] [ ! ~(2) ] 0","hypothesis":"Fred can now know whether Clay can know whether Clay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Amy","Jeffrey","Clay"],"index":51612,"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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaac does not know whether Isaac'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":"Isaac can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Isaac"],"index":37831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997686744,"difficulty":0.0002313256}
-{"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 Tamika. Tamika's card is shown to Jacquelin. It is publicly announced that someone picked a red card. It is publicly announced that Tamika does not know whether or not everyone 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 (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:3 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jacquelin can now know that Tamika can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamika","Jacquelin","Matthew","Richard"],"index":58103,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.506816566,"difficulty":1.506816566}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alden's card is shown to David. David's card is shown to Alden. Jack's card is shown to Alden. Alden's card is shown to Alden. 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 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:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jack can now know that David can know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Jack","Alden"],"index":51834,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6564028859,"difficulty":0.3435971141}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Meghan does not know whether Rose is thirsty. It is publicly announced that Rose is thirsty. It is publicly announced that Rose 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 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) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"David can now know that Rose can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Meghan","Rose","David"],"index":20324,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997297585,"difficulty":0.002702415}
-{"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 Steven. Alicia's card is shown to Wilma. Steven's card is shown to Alicia. 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":"Steven can now know whether Alicia can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Wilma","Alicia"],"index":65294,"s-l":"explicit-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 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) ] [ ! ~(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":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carl","Edwin","Nikki","Michael"],"index":37156,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9760933518,"difficulty":0.0239066482}
-{"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 Marshall 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 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|2))) ] 0","hypothesis":"Marshall can now know that Tanya can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tanya","Marshall"],"index":57317,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984661341,"difficulty":0.0015338659}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carole knows whether Carole 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 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 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know that Carole can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carole","John"],"index":64890,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9551694989,"difficulty":0.0448305011}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Harold 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&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd 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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mary can now know that Harold can know that Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Keith","Jerry","Mary"],"index":36955,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5730167627,"difficulty":0.4269832373}
-{"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 James. James's card is shown to Gabrielle. James's card is shown to Jill. It is publicly announced that someone picked a red card. It is publicly announced that Jill does not know whether Jill picked a red card. It is publicly announced that Gabrielle knows whether or not everyone picked a red card. It is publicly announced that Gabrielle 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)","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":"Jill can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Gabrielle","Jill"],"index":29910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6182409525,"difficulty":0.3817590475}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Brian 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] (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|2|3|4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Brian can now know whether Tammy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Diana","Brian","Tammy"],"index":146,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997259974,"difficulty":0.0002740026}
-{"premise":"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) ] [ ! ~(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":"Laura can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Laura","Olive"],"index":30307,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9713094234,"difficulty":1.9713094234}
-{"premise":"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 Erin knows whether Sharon's forehead is muddy. It is publicly announced that 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 1) ] [ ! 1 ] 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Sharon can now know that Louis can know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Louis","Erin"],"index":15244,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6094961762,"difficulty":0.3905038238}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alberta's forehead is not muddy. It is publicly announced that Steven knows 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) ] [ ! ~(1) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Alberta can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alberta","Nathaniel","Steven","Rudolph"],"index":60861,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985166192,"difficulty":0.0014833808}
-{"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 Michael is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Dolores 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) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd 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) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Michael can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Sheila","Frank","Dolores"],"index":53469,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985900521,"difficulty":0.0014099479}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genevieve's card is shown to Blanche. Blanche's card is shown to Mary. Genevieve's card is shown to Mary. Blanche's card is shown to Genevieve. 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) ] (Agentc knows that (~(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":"Genevieve can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Blanche","Mary","Genevieve"],"index":19134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983640313,"difficulty":0.0016359687}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Esther knows whether Esther is thirsty. It is publicly announced that Jeffrey does not know whether Esther is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Lenard 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 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":"Esther can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Esther","Lenard","Darlene","Jeffrey"],"index":48814,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984647036,"difficulty":0.0015352964}
-{"premise":"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 Richard'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) ] (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 1) ] [ ! (1|2|3) ] 0","hypothesis":"Joyce can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Joyce","John"],"index":55155,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997457862,"difficulty":0.0002542138}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether or not everyone's forehead is muddy. It is publicly announced that John'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 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":"Beverly can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Beverly","John"],"index":40401,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8577531576,"difficulty":0.1422468424}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly 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 (1&2&3&4))","n_announcements":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":"Pamela can now know that Kelly can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Pamela","Matthew","Christopher"],"index":54876,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8580032587,"difficulty":1.8580032587}
-{"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 Xavier. Margaret's card is shown to Xavier. Xavier's card is shown to Joshua. Xavier's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Joshua does not know whether Joshua 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) ] (Agentb 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) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Xavier","Joshua","Margaret"],"index":53864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9741904736,"difficulty":0.0258095264}
-{"premise":"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 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 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Luther can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willie","Stephen","Luther","Timothy"],"index":7956,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995482564,"difficulty":0.0004517436}
-{"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 Phillip. Dane's card is shown to Dane. Robert's card is shown to Dane. Robert's card is shown to Justin. Justin'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:2,4 Agentc:4 Agentd: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:4 Agentb:2,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Dane can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phillip","Dane","Justin","Robert"],"index":37850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986153841,"difficulty":0.0013846159}
-{"premise":"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 John'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) ] 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) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"John can now know whether Nona can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nona","William","John"],"index":55644,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995383024,"difficulty":0.0004616976}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Misty is thirsty. It is publicly announced that Alison does not know whether or not everyone is thirsty. It is publicly announced that Alison does not know whether Chester is 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) ] (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) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Chester can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Chester","Misty","Alison"],"index":2020,"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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":"Henry can now know whether William can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Tracy","Wayne","Henry"],"index":61585,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99975878,"difficulty":0.00024122}
-{"premise":"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 Mary does not know whether Mary's forehead is muddy. It is publicly announced that John 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (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 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","John","Wanda","Georgina"],"index":37282,"s-l":"forehead-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 Maria's forehead is not muddy. It is publicly announced that Miguel 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 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":"Carrie can now know that Maria can know whether Miguel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Miguel","Joyce","Maria","Carrie"],"index":8529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996919632,"difficulty":0.0003080368}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clinton knows 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) ] [ ! (Agentb knows whether 2) ] (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 2) ] 0","hypothesis":"Monica can now know whether Monica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ruth","Clinton","Monica","Alex"],"index":6636,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9962112904,"difficulty":0.0037887096}
-{"premise":"There are three persons. Everyone is visible 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 Ruby knows whether Mike's forehead is muddy.","smcdel_problem":"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 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":"Mike can now know whether Ruby can know whether Ruby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Christopher","Mike"],"index":32797,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995926023,"difficulty":0.0004073977}
-{"premise":"There are two persons. Everyone is visible 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 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&2) ] 0","hypothesis":"Betty can now know whether Kevin can know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Betty"],"index":51452,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994112253,"difficulty":0.0005887747}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"John can now know that Brian can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","John","Mary","Brian"],"index":58794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972794652,"difficulty":0.0027205348}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karmen'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 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":"Betty can now know whether Evelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karmen","Evelyn","Betty"],"index":13799,"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's forehead is muddy. It is publicly announced that Ralph does not know whether Ralph'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) ] (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) ] [ ! (1|2|3) ] 0","hypothesis":"Kristen can now know that Kristen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristen","Ralph","Chad"],"index":66356,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971996546,"difficulty":0.0028003454}
-{"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. Ella's card is shown to Ella. Jessie'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 Max 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 whether 2)","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":"Ella can now know whether Ella picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jessie","Ella","Max"],"index":18643,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9451605678,"difficulty":0.0548394322}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bradley 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":"Bryan can now know that Aileen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aileen","Bradley","Bryan"],"index":2046,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99834764,"difficulty":0.00165236}
-{"premise":"There are two persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 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) ] [ ! 2 ] 0","hypothesis":"Heather can now know that Nora's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nora","Heather"],"index":41902,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9440824986,"difficulty":0.0559175014}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether or not nobody's forehead is muddy. It is publicly announced that Erin'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: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 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))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earl","Erin","Denise","Charles"],"index":40695,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8786183,"difficulty":0.1213817}
-{"premise":"There are two persons. Everyone is visible 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 Philip's forehead is muddy. It is publicly announced that Philip knows whether Sarah'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 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sarah can now know that Philip can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Philip","Sarah"],"index":25915,"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. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Benjamin's card is shown to Benjamin. Mary's card is shown to Carol. Benjamin's card is shown to Carol. Rena's card is shown to Carol. Mary's card is shown to Rena. Rena's card is shown to Rena. It is publicly announced that someone picked a red card. It is publicly announced that Carol does not know whether Carol picked a red card. It is publicly announced that Benjamin does not know whether Carol 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) ] (Agenta knows that 2)","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":"Mary can now know that Benjamin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Benjamin","Carol","Rena"],"index":34126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9853255153,"difficulty":0.0146744847}
-{"premise":"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 does not know whether Edna's forehead is muddy. It is publicly announced that Daisy'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 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":"Daisy can now know that Edna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daisy","Edna"],"index":32489,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985057116,"difficulty":0.0014942884}
-{"premise":"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 William knows whether 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: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))) ] 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 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Kevin can now know that William can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Kevin","William"],"index":57184,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977617264,"difficulty":0.0022382736}
-{"premise":"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 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 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":"Guadalupe can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicholas","Linda","Kent","Guadalupe"],"index":23603,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.997399807,"difficulty":1.997399807}
-{"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)","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":"Eric can now know that Sallie can know that Paulette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paulette","Mia","Eric","Sallie"],"index":50844,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985659719,"difficulty":0.0014340281}
-{"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 Harry is thirsty. It is publicly announced that Jamie does not know whether Harry 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 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jamie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jamie","Harry","Jack"],"index":34181,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.958996594,"difficulty":0.041003406}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miquel knows whether Evelyn's forehead is muddy. It is publicly announced that Miquel knows whether 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) ] [ ! (Agenta knows whether 2) ] [ ! (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:1,2,3,4 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":"William can now know that Evelyn can know that Evelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Miquel","Evelyn","Robert","William"],"index":60971,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962402582,"difficulty":0.0037597418}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luis's card is shown to Luis. Darrell's card is shown to Luis. Luis's card is shown to Mary. Luis's card is shown to Darrell. 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:1,3 Agentb:1 Agentc:1 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:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know whether Darrell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Luis","Mary","Darrell"],"index":57172,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8734334111,"difficulty":1.8734334111}
-{"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 Ophelia. Ophelia's card is shown to Todd. Julia's card is shown to Todd. Ophelia's card is shown to Julia. It is publicly announced that someone picked a red card. It is publicly announced that Ophelia does not know whether Ophelia 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 2)","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":"Julia can now know whether Todd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ophelia","Todd","Julia"],"index":6853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9103986621,"difficulty":0.0896013379}
-{"premise":"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 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) ] 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) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Virginia can now know whether Julie can know that Virginia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hector","Julie","Mark","Virginia"],"index":28504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9343715906,"difficulty":0.0656284094}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margarito's forehead is not muddy. It is publicly announced that Leroy knows whether Allyson's forehead is muddy.","smcdel_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 (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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Leroy can now know that Margarito can know that Leroy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Allyson","Leroy","Margarito"],"index":59816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9954598546,"difficulty":0.0045401454}
-{"premise":"There are three persons. Everyone is visible 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 Micheal 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":"Micheal can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Phyllis","Micheal"],"index":38279,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981753826,"difficulty":0.0018246174}
-{"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. It is publicly announced that Rebecca 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 (1|2|3|4)) ] [ ! ~(Agenta 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rebecca can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Thomas","Richard","Gary"],"index":13227,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979051352,"difficulty":0.0020948648}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Buford's card is shown to Alfred. Suzanne's card is shown to Alfred. Buford's card is shown to Paul. Suzanne's card is shown to Paul. Paul's card is shown to Suzanne. Suzanne's card is shown to Suzanne. 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) ] Agentb knows whether (Agentc knows whether 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":"Paul can now know whether Buford can know whether Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alfred","Paul","Buford","Suzanne"],"index":62846,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983536005,"difficulty":0.0016463995}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bertha's card is shown to Bertha. Bertha's card is shown to Rita. Tyson's card is shown to Rita. Rita's card is shown to Tyson. 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 that 2)","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":"Rita can now know that Bertha can know that Rita picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bertha","Rita","Tyson"],"index":42513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964283109,"difficulty":0.0035716891}
-{"premise":"There are two 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 Beryl. It is publicly announced that someone picked a red card. It is publicly announced that Beryl 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|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":"Anna can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anna","Beryl"],"index":18828,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983341098,"difficulty":0.0016658902}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beatriz knows whether Leona's forehead is muddy. It is publicly announced that Beatriz does not know whether or not everyone's forehead is muddy. It is publicly announced that Leona knows whether or not everyone's forehead is muddy. It is publicly announced that Leona knows whether Beatriz'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) ] (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 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Beatriz can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Beatriz","Leona"],"index":10939,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977904558,"difficulty":0.0022095442}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agenta knows whether 1) ] Agenta 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Heather can now know that Gregory can know whether Heather's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Gregory","Deborah","Robert"],"index":12540,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997332692,"difficulty":0.0002667308}
-{"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 Justin. Justin's card is shown to Mirta. Mirta's card is shown to Mirta. Justin's card is shown to Clifford. Mirta's card is shown to Clifford. Clifford's card is shown to Clifford. 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 whether (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":"Mirta can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Justin","Mirta","Clifford"],"index":28957,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.986803472,"difficulty":0.013196528}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annette does not know whether Jody is thirsty. It is publicly announced that Hector 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 3) ] [ ! ~(Agenta knows whether 4) ] Agentc 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Jody can now know that Annette can know whether Annette is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hector","Michael","Jody","Annette"],"index":18306,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990596175,"difficulty":0.0009403825}
-{"premise":"There are four persons. Everyone is visible 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 Bonnie's forehead is muddy. It is publicly announced that Keith knows whether 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) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ruthie can now know that Ethyl can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Bonnie","Ruthie","Ethyl"],"index":61100,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983294606,"difficulty":0.0016705394}
-{"premise":"There are two persons. Everyone is visible 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 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":"Donna can now know that Kristy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donna","Kristy"],"index":1870,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985049963,"difficulty":0.0014950037}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge does not know whether Jorge's forehead is muddy. It is publicly announced that Collette knows whether or not everyone's forehead is muddy. It is publicly announced that Jorge's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 ] (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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Collette can now know whether Collette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Collette","Jennifer","Erik","Jorge"],"index":18159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7250282764,"difficulty":0.2749717236}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jason 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":["Jason","Tim","Dwayne","Clarence"],"index":27894,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983034134,"difficulty":0.0016965866}
-{"premise":"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 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 (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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jason can now know that Joe can know that Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Sarah","Joe","Jason"],"index":64612,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5390765071,"difficulty":1.5390765071}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosie 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 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":"Bonnie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rodney","Rosie","Bonnie"],"index":11452,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967261553,"difficulty":0.0032738447}
-{"premise":"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 Kevin knows whether Kevin'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":"Mark can now know whether Kevin can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Mark"],"index":50700,"s-l":"forehead-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). Michael's card is shown to Michael. Michael's card is shown to Lisa. Michael's card is shown to Kira. It is publicly announced that someone picked a red card. It is publicly announced that Kira does not know whether Lisa 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) ] (Agentc knows that 3)","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":"Kira can now know that Kira picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Lisa","Kira"],"index":48231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949643612,"difficulty":0.0050356388}
-{"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 Patricia is thirsty. It is publicly announced that Kari does not know whether Martha is thirsty. It is publicly announced that Martha 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)","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":"Jessica can now know whether Kari is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kari","Martha","Patricia","Jessica"],"index":1518,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5284016132,"difficulty":1.5284016132}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dona's card is shown to Dona. Dona's card is shown to Leona. It is publicly announced that someone picked a red card. It is publicly announced that Leona 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)) ] 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) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Dona can now know whether Leona can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dona","Leona"],"index":65014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994997978,"difficulty":0.0005002022}
-{"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 Katherine 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) ] 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Reba can know whether Katherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Reba","Katherine","Mary","Veronica"],"index":2869,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9903202653,"difficulty":0.0096797347}
-{"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. Robert's card is shown to Robert. Patricia's card is shown to Robert. Robert's card is shown to Rita. Rita'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:2,4 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:2,4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rose","Robert","Rita","Patricia"],"index":5144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Damaris 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":["Damaris","Diana","Anne","Eric"],"index":38659,"s-l":"forehead_mirror-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 Joyce 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) ] [ ! ~(Agentd knows whether 3) ] (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":"Joyce can now know that Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Sherri","Lisa","Joyce"],"index":62973,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982182384,"difficulty":0.0017817616}
-{"premise":"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 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 Meredith can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Meredith","James"],"index":27601,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9143453836,"difficulty":1.9143453836}
-{"premise":"There are 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":"Hazel can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Connie","Hazel","Terrence"],"index":46460,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997504354,"difficulty":0.0002495646}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elisabeth does not know whether Ricardo is thirsty. It is publicly announced that Elisabeth does not know whether Ruby is thirsty. It is publicly announced that Elisabeth 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) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Ricardo can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ricardo","Ruby","Elisabeth"],"index":47395,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983366728,"difficulty":0.0016633272}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olga's card is shown to Olga. Michael's card is shown to Olga. 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:1,2 Agentb:2 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:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Olga can now know that Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Olga","Michael"],"index":25852,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983357787,"difficulty":0.0016642213}
-{"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 William. Karen's card is shown to Karen. Sergio's card is shown to Karen. Karen's card is shown to Sergio. William's card is shown to Antonio. Karen's card is shown to Antonio. Antonio's card is shown to Antonio. It is publicly announced that someone picked a red card. It is publicly announced that Antonio 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 ] (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 Agentc:2 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Karen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Karen","Sergio","Antonio"],"index":53830,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
-{"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 Lewis. Rosemary's card is shown to Lewis. Rosemary'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:3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Lewis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lewis","Thomas","Rosemary"],"index":11082,"s-l":"explicit-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 Christopher 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 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":"Katharine can now know that Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Katharine","Grace","John","Christopher"],"index":43382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998318553,"difficulty":0.001681447}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Estelle does not know whether Alex is thirsty. It is publicly announced that 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) ] [ ! ~(Agentb knows whether 1) ] [ ! 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 1) ] [ ! 3 ] 0","hypothesis":"Alex can now know whether Jonathan can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alex","Estelle","Jonathan","Luisa"],"index":59828,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997869134,"difficulty":0.0002130866}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brooke 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 (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":"Brooke can now know whether Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mathew","Brooke","Joseph"],"index":52852,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
-{"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 Sally. Bobby's card is shown to Billy. Dwight's card is shown to Dwight. 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 whether 3)","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":"Sally can now know that Dwight can know whether Dwight picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sally","Billy","Dwight","Bobby"],"index":11131,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9877564907,"difficulty":0.0122435093}
-{"premise":"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. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary knows whether Robbie's forehead 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 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) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know whether Robbie can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Robbie","Sandra"],"index":33862,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970818162,"difficulty":0.0029181838}
-{"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 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 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 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Angela can now know that Mary can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Angela","Mary","Jennifer"],"index":28060,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984428287,"difficulty":0.0015571713}
-{"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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] (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":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dorothy","Mary"],"index":58395,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999763906,"difficulty":0.000236094}
-{"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 Bobby. Monica's card is shown to Monica. Christian's card is shown to Christian. It is publicly announced that someone picked a red card. It is publicly announced that Monica does not know whether Bobby 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) ] Agentc knows that (Agentb knows that (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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Christian can now know that Monica can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","Monica","Christian"],"index":9132,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
-{"premise":"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) ] [ ! ~(Agenta knows whether 1) ] 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Catherine can now know that Richard can know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Richard","Catherine"],"index":22258,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995471835,"difficulty":0.0004528165}
-{"premise":"There are three persons. Everyone is visible 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 Irene's forehead is muddy.","smcdel_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":"Cynthia can now know that Irene can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cynthia","Irene","Laronda"],"index":9919,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997592568,"difficulty":0.0002407432}
-{"premise":"There are three persons. Everyone is visible 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 muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benito 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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Nathan can now know that Benito can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Nathan","Benito"],"index":14092,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996351004,"difficulty":0.0003648996}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is not muddy. It is publicly announced that Lee does not know whether Lee'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: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 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lee can now know whether John can know that Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christine","Lee","John"],"index":10989,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7927607298,"difficulty":1.7927607298}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Theodore can now know that Lonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lonnie","Theodore","Jessica","Kevin"],"index":58012,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793709517,"difficulty":0.0206290483}
-{"premise":"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 Cynthia's forehead is muddy. It is publicly announced that James 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) ] [ ! (Agentc knows whether 3) ] 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) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Eric can now know whether Dwayne can know that Dwayne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Dwayne","James","Cynthia"],"index":53836,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9356104136,"difficulty":0.0643895864}
-{"premise":"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 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 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 3) ] 0","hypothesis":"Jason can now know that Richard can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Jason","Richard"],"index":26886,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983801842,"difficulty":0.0016198158}
-{"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 Suzanne. Gary's card is shown to Gary. Gabriel's card is shown to Gary. Gary's card is shown to Gabriel. 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 Gabriel does not know whether Gabriel 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) ] (Agenta 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":"Suzanne can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Suzanne","Gary","Gabriel"],"index":51884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986363053,"difficulty":0.0013636947}
-{"premise":"There are 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)","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":"Edmund can now know whether John can know that Ivan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ivan","Edmund","Patrick","John"],"index":57663,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996809959,"difficulty":0.0003190041}
-{"premise":"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 Leroy'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":"Leroy can now know that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Leroy"],"index":21012,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997183681,"difficulty":0.0002816319}
-{"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 Ira. Danielle's card is shown to Danielle. Danielle'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 Agentb:2 Agentc: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 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ira can now know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ira","Danielle","Hazel"],"index":4515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9496871233,"difficulty":0.0503128767}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Debbie does not know whether Louise is thirsty. It is publicly announced that Debbie does not know whether Louise 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 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":"Louise can now know whether Louise is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louise","Debbie"],"index":36492,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988777041,"difficulty":0.0011222959}
-{"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 Leah. Shirley's card is shown to Leah. Leah's card is shown to Lynn. Richard's card is shown to Lynn. Shirley's card is shown to Lynn. Leah's card is shown to Richard. Lynn'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:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Shirley can know whether Leah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leah","Lynn","Richard","Shirley"],"index":57286,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5462184548,"difficulty":1.5462184548}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rogelio's forehead is not 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) ] [ ! (~(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) ] [ ! (~(1&2)) ] 0","hypothesis":"Rogelio can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rogelio","Willis"],"index":66798,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997314811,"difficulty":0.0002685189}
-{"premise":"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 Kimberly's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy. It is publicly announced that Lindsey knows whether 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agentb 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kimberly can now know whether Lindsey can know whether Lindsey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Kimberly","Lindsey","Thomas"],"index":20056,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.767677784,"difficulty":0.232322216}
-{"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 Shirley is thirsty. It is publicly announced that Shirley does not know whether Ethel is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Shirley can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lois","Michael","Ethel","Shirley"],"index":38159,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9917110205,"difficulty":0.0082889795}
-{"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 or not nobody is thirsty. It is publicly announced that Annie 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)) ] (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 (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Hubert can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annie","Maria","William","Hubert"],"index":45554,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9210917354,"difficulty":0.0789082646}
-{"premise":"There are three persons. Everyone is visible 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 Tom's forehead is muddy. It is publicly announced that Clara'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 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":"Johnny can now know whether Tom can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnny","Tom","Clara"],"index":55100,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995885491,"difficulty":0.0004114509}
-{"premise":"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 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 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":"Grace can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ignacio","David","Grace","Michael"],"index":33335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985060692,"difficulty":0.0014939308}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mattie 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)","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":"Clarence can now know that Mattie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mattie","Clarence"],"index":45086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972324967,"difficulty":0.0027675033}
-{"premise":"There are four persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 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":"Phillip can now know that Antoinette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samantha","Gina","Antoinette","Phillip"],"index":37841,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9691686034,"difficulty":0.0308313966}
-{"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 Linda. Jon's card is shown to Jon. Jennifer's card is shown to Jon. Joel's card is shown to Jon. Joel's card is shown to Jennifer. Jon's card is shown to Joel. Joel's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Linda 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) ] (Agentb knows that 3)","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":"Jon can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jon","Jennifer","Joel"],"index":22390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940152764,"difficulty":0.0059847236}
-{"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 or not everyone is thirsty. It is publicly announced that Toby 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 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)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Toby can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Toby","Lourdes","William"],"index":36395,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6538709402,"difficulty":1.6538709402}
-{"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 Delores. Joseph's card is shown to Janice. Delores's card is shown to Janice. William's card is shown to Janice. Delores's card is shown to William. Janice'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 Agentc:1,2,4 Agentd: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:1 Agentb:1 Agentc:1,2,4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Delores can know whether Janice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Delores","Janice","William"],"index":15120,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5185596943,"difficulty":1.5185596943}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bob 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 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":"Rebecca can now know whether Mark can know that Bob's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Mark","Bob","Jeffery"],"index":51310,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996564388,"difficulty":0.0003435612}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Julie. Julie's card is shown to Michael. Michael's card is shown to Joseph. Julie's card is shown to Jeff. Jeff's card is shown to Jeff. 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 Julie 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 1)","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":"Jeff can now know that Julie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Michael","Joseph","Jeff"],"index":2723,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6789783239,"difficulty":0.3210216761}
-{"premise":"There are three persons. Everyone is visible 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 knows whether Chris's forehead is muddy. It is publicly announced that Chris knows whether Evelyn's forehead is muddy. It is publicly announced that Elaine'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 (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":"Evelyn can now know that Elaine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evelyn","Chris","Elaine"],"index":31852,"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. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Richard. Richard's card is shown to Richard. Harold's card is shown to Richard. Ronald's card is shown to Harold. Alisa's card is shown to Harold. Alisa's card is shown to Alisa. It is publicly announced that someone picked a red card. It is publicly announced that Alisa 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 that (Agenta knows that 3)","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":"Harold can now know that Ronald can know that Harold picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Richard","Harold","Alisa"],"index":29950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9162185788,"difficulty":0.0837814212}
-{"premise":"There are two persons. Everyone is visible 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 Richard knows whether Debra'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) ] 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) ] [ ! (1&2) ] [ ! (Agenta knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Debra 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":["Richard","Debra"],"index":58040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997381568,"difficulty":0.0002618432}
-{"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.","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 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":"Rosetta can now know that Rosetta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosetta","Matthew","Willie","Linwood"],"index":24838,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8578053713,"difficulty":0.1421946287}
-{"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 Maria. Irma's card is shown to Maria. Irma's card is shown to Claretha. Richard's card is shown to Richard. Claretha's card is shown to Irma. Irma's card is shown to Irma. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether someone picked a red card. It is publicly announced that Maria picked a red card. It is publicly announced that Claretha does not know whether Richard 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 (Agentb knows whether 2)","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":"Richard can now know that Claretha can know whether Claretha picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Claretha","Richard","Irma"],"index":24412,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6484274268,"difficulty":0.3515725732}
-{"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 Dolly. Dolly's card is shown to Janice. Claudia's card is shown to Janice. Dolly's card is shown to Claudia. It is publicly announced that someone picked a red card. It is publicly announced that Dolly does not know whether Claudia 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) ] (Agentc knows that 2)","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":"Claudia can now know that Janice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dolly","Janice","Claudia"],"index":44076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949871302,"difficulty":0.0050128698}
-{"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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Daniel can now know that Aaron can know that Aaron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Daniel","Aaron"],"index":12909,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978804588,"difficulty":0.0021195412}
-{"premise":"There are two 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 John. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether John 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 (~(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":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","John"],"index":3580,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997224212,"difficulty":0.0002775788}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelton does not know whether or not everyone's forehead is muddy. It is publicly announced that Shelton does not know whether Shelton's forehead is muddy. It is publicly announced that Shelton 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 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":"Shelton can now know whether John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shelton","John"],"index":11123,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9164233208,"difficulty":0.0835766792}
-{"premise":"There are four persons. Everyone is visible 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 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":"Frances can now know that Lisa can know whether Glenn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Lisa","Glenn","Frances"],"index":56676,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997305274,"difficulty":0.0002694726}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna's forehead is not muddy. It is publicly announced that Howard'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) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 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 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Howard can now know that Ralph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edna","Howard","Ralph"],"index":2653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979788661,"difficulty":0.0020211339}
-{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that Curtis knows whether Kimberly's forehead is muddy. It is publicly announced that Irma does not know whether Irma's forehead 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) ] Agentc knows that (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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kimberly can now know that Irma can know whether Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Irma","Kimberly"],"index":57363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Constance 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|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":"Robert can now know that Constance can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Constance","Robert"],"index":15799,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983355403,"difficulty":0.0016644597}
-{"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. Jamie's card is shown to Cynthia. Charles's card is shown to Cynthia. Jamie's card is shown to Jamie. Charles's card is shown to Jamie. Cynthia's card is shown to Charles. Annette's card is shown to Annette. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether Annette 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) ] (Agentc knows whether 3)","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":"Charles can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Jamie","Charles","Annette"],"index":22427,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9414127469,"difficulty":1.9414127469}
-{"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 Brenda is thirsty. It is publicly announced that Charles 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 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) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ronald can now know that Brenda can know whether Brenda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brenda","Ronald","Charles"],"index":38999,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998794198,"difficulty":0.001205802}
-{"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 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":"Charles can now know whether Ruth can know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Ruth","Evelyn","Beatrice"],"index":33743,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9966558218,"difficulty":0.0033441782}
-{"premise":"There are three persons. Everyone is visible 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 ] (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":"Steven can now know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Catherine","Michael","Steven"],"index":37017,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9847772121,"difficulty":0.0152227879}
-{"premise":"There are two 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.","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 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":"Jennifer can now know that Elaine can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Elaine"],"index":16419,"s-l":"forehead-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 Carina's forehead is muddy.","smcdel_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 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":"Jesus can now know that Carina can know that Jesus's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gracie","Jesus","Carina"],"index":55604,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9680927396,"difficulty":0.0319072604}
-{"premise":"There are three persons. Everyone is visible 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 1,2,3 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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Victoria 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":["Victoria","Betty","Andrew"],"index":28485,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984513521,"difficulty":0.0015486479}
-{"premise":"There are four persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Kecia can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Otis","Terrence","Kecia"],"index":33082,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9978475571,"difficulty":0.0021524429}
-{"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 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 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":"Shirley can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","James","Kyle","Michel"],"index":5551,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984679818,"difficulty":0.0015320182}
-{"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 James. Mark's card is shown to James. Leslie's card is shown to Leslie. It is publicly announced that someone picked a red card. It is publicly announced that Leslie knows whether Leslie 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) ] (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) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Leslie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Leslie","Mark"],"index":35103,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984841943,"difficulty":0.0015158057}
-{"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 Donald is thirsty. It is publicly announced that Donald does not know whether Jeffrey is thirsty. It is publicly announced that Jeffrey is thirsty. It is publicly announced that Charity 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 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! 1 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jeffrey can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Donald","Charity","Nancy"],"index":31283,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9166817665,"difficulty":0.0833182335}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melinda 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 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":"Melinda can now know whether Karen can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Melinda","Karen"],"index":52443,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9462856054,"difficulty":0.0537143946}
-{"premise":"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))) ] (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":"Joan can now know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Robert","Joan","Joey"],"index":57596,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995737672,"difficulty":0.0004262328}
-{"premise":"There are four persons. Everyone is visible 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 Tanika's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 1) ] 0","hypothesis":"Bill can now know whether Rosemary can know whether Tanika's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tanika","Rosemary","Frank","Bill"],"index":47056,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997370839,"difficulty":0.0002629161}
-{"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 Hazel 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)) ] (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":"Hazel can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Hazel","Julie"],"index":24939,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9951049089,"difficulty":0.0048950911}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peter's card is shown to Peter. 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 Michael knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Peter"],"index":14039,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7689444423,"difficulty":1.7689444423}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robbie's card is shown to Robbie. Tammy's card is shown to Robbie. Aaron's card is shown to Tammy. Aaron'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:1,2 Agentb:3 Agentc: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 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robbie can now know that Tammy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robbie","Tammy","Aaron"],"index":52146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983640313,"difficulty":0.0016359687}
-{"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. Joan's card is shown to Leslie. Leslie's card is shown to Leslie. Leslie's card is shown to Ruth. Joan's card is shown to Emma. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Emma 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) ] (Agentd knows whether 1)","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":"Emma can now know whether Joan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joan","Leslie","Ruth","Emma"],"index":41747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8969265819,"difficulty":0.1030734181}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendell does not know whether Wendell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Omar can now know whether Wendell can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melissa","Omar","Joann","Wendell"],"index":48356,"s-l":"forehead-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 not everyone's forehead is muddy. It is publicly announced that Jessie 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 (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)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Crystal can now know that Jessie can know that Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irene","Sandra","Crystal","Jessie"],"index":4177,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9761903882,"difficulty":0.0238096118}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline 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) ] [ ! (Agenta knows whether 2) ] (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 2) ] 0","hypothesis":"Jacqueline can now know whether Louie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacqueline","Joseph","Louie","Miguel"],"index":13316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995318651,"difficulty":0.0004681349}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monika is thirsty. It is publicly announced that Rose 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)) ] 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) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Monika can now know whether Elizabeth can know whether Monika is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Rose","Monika"],"index":14381,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985027313,"difficulty":0.0014972687}
-{"premise":"There are two persons. Everyone is visible 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 not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(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) ] [ ! ~(2) ] 0","hypothesis":"Elizabeth can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Elizabeth"],"index":21756,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9952367544,"difficulty":1.9952367544}
-{"premise":"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) ] Agenta knows that (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":"Barbara can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Michael","Helen"],"index":17045,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942329526,"difficulty":0.0057670474}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (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":"Jeremy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Florence","Jeremy","Sherry"],"index":59612,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981864095,"difficulty":0.0018135905}
-{"premise":"There are four persons. Everyone is visible 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 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":"Teresa can now know that Viva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Viva","Teresa","Kathie"],"index":24429,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970163107,"difficulty":0.0029836893}
-{"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 Jerry. Jerry's card is shown to Jason. Jason's card is shown to Jason. Jeffrey's card is shown to Jason. Jason's card is shown to Nichole. 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) ] (Agenta knows that 3)","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":"Jerry can now know that Nichole picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Jason","Nichole","Jeffrey"],"index":24702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974370003,"difficulty":0.0025629997}
-{"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 Robert 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) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|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) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Kenny can now know that Anthony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenny","Michael","Anthony","Robert"],"index":31872,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998142004,"difficulty":0.001857996}
-{"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. Paul's card is shown to Stephen. Stephen'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:1,2 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:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Paul","Mark"],"index":66927,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997722507,"difficulty":0.0002277493}
-{"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 Beverly is thirsty. It is publicly announced that Ben does not know whether Lois is thirsty. It is publicly announced that Lois does not know whether Paul 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc 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) ] [ ! ~(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 Ben is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ben","Beverly","Paul","Lois"],"index":49845,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953166246,"difficulty":0.0046833754}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darius 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 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":"Darius can now know that Jacqueline can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darius","Mary","Jacqueline"],"index":44299,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997332692,"difficulty":0.0002667308}
-{"premise":"There are 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 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 whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucille","Raymond","Rena","Jason"],"index":63651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999741137,"difficulty":0.000258863}
-{"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 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":"Joshua can now know that George can know that Joshua is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Joshua","James"],"index":32072,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985571504,"difficulty":0.0014428496}
-{"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 Carolyn. Stephanie's card is shown to Carolyn. 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: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":"Carolyn can now know whether Stephanie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carolyn","Stephanie","Linda"],"index":12004,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9165451527,"difficulty":0.0834548473}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachelle'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 whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Rachelle can now know that Anita can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anita","Rachelle"],"index":21014,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7161663175,"difficulty":1.7161663175}
-{"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. Malena's card is shown to Richard. Malena's card is shown to Malena. Leon's card is shown to Malena. Malena's card is shown to Lisa. Lisa's card is shown to Lisa. Leon'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:1,2 Agentb:2,4 Agentc:2,3 Agentd:4 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:1,2 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Leon can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Malena","Lisa","Leon"],"index":59811,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999773562,"difficulty":0.000226438}
-{"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 Christopher 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 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Christopher","Joseph"],"index":3262,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7380641103,"difficulty":0.2619358897}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Moses 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 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":"Moses can now know that Colleen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Moses","Colleen"],"index":54513,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997659326,"difficulty":0.0002340674}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myrtle 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 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 2) ] 0","hypothesis":"Myrtle can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Myrtle","Mary"],"index":25324,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995580316,"difficulty":0.0004419684}
-{"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. Frank's card is shown to Mark. Rhonda'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:1,4 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:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mark","Dawn","Rhonda","Frank"],"index":42494,"s-l":"explicit-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 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 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":"John can now know that Ebonie can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ebonie","Francisco","John","Betty"],"index":11662,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968805313,"difficulty":0.0031194687}
-{"premise":"There are four persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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 someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Norma","Brian","George"],"index":47002,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Jessica. Samantha's card is shown to Jessica. Wallace's card is shown to Melissa. Melissa's card is shown to Melissa. Samantha's card is shown to Melissa. Jessica's card is shown to Samantha. Wallace's card is shown to Samantha. Samantha's card is shown to Samantha. It is publicly announced that someone picked a red card. It is publicly announced that Melissa 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 whether 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":"Melissa can now know whether Wallace can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Wallace","Melissa","Samantha"],"index":19050,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982950091,"difficulty":0.0017049909}
-{"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. Catherine's card is shown to Lisa. Bruce's card is shown to Bruce. Catherine's card is shown to Bruce. Bruce's card is shown to Michael. Michael's card is shown to Michael. Lisa's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Catherine picked a red card. It is publicly announced that Lisa does not know whether Bruce 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) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Bruce can now know whether Lisa can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Bruce","Michael","Catherine"],"index":45539,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9078022242,"difficulty":1.9078022242}
-{"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 Gary does not know whether Joan is thirsty. It is publicly announced that Joan 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 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":"Joan can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Joan","Gary"],"index":30320,"s-l":"internal-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 is thirsty. It is publicly announced that Rhett knows whether or not everyone is thirsty. It is publicly announced that Donald 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 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":"Donald can now know that Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Donald","Rhett"],"index":25890,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9833125472,"difficulty":0.0166874528}
-{"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 Michael is thirsty. It is publicly announced that Christine does not know whether 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"John can now know whether Michael can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","John","Allyson","Christine"],"index":34241,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9925898314,"difficulty":0.0074101686}
-{"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 (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":"April can now know that Terrence can know whether Carter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","April","Terrence","Carter"],"index":34906,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.958041966,"difficulty":0.041958034}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores 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 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":"Steven can now know that Dolores can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helena","Dolores","Judy","Steven"],"index":47765,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.968434751,"difficulty":1.968434751}
-{"premise":"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 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Norman can now know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gregory","Thomas","Melanie","Norman"],"index":22742,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993312359,"difficulty":0.0006687641}
-{"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 Christopher. Carol's card is shown to Carol. Marvin's card is shown to Marvin. 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) ] (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Carol","Marvin"],"index":38895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955588579,"difficulty":0.0044411421}
-{"premise":"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 or not everyone'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) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 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) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Anthony can now know that Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Louise","Thomas","Anthony"],"index":8259,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7192512155,"difficulty":0.2807487845}
-{"premise":"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 knows whether or not nobody's forehead is muddy. It is publicly announced that Scott does not know whether Scott'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 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":"Lillian can now know whether Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lillian","Scott"],"index":60157,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9663050175,"difficulty":1.9663050175}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelia's card is shown to Millicent. Leila's card is shown to Willie. Millicent's card is shown to Willie. Willie's card is shown to Angelia. It is publicly announced that someone picked a red card. It is publicly announced that Leila knows whether Angelia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta 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:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Willie can now know that Millicent can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leila","Millicent","Willie","Angelia"],"index":48600,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998457551,"difficulty":0.001542449}
-{"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 Laura. Geoffrey's card is shown to Laura. Laura's card is shown to Geoffrey. Alan's card is shown to Geoffrey. Laura'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:1,2 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":"Geoffrey can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Geoffrey","Alan"],"index":41081,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997252822,"difficulty":0.0002747178}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachell's forehead is muddy. It is publicly announced that Rachell knows whether Rachell's forehead is muddy.","smcdel_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 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) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Melissa can now know whether Charles can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Melissa","Rachell"],"index":55781,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997245669,"difficulty":0.0002754331}
-{"premise":"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 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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Brian can now know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["German","Kevin","Eugene","Brian"],"index":62948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929233789,"difficulty":0.0070766211}
-{"premise":"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 Shameka's forehead is muddy. It is publicly announced that Shameka does not know whether or not everyone's forehead is muddy. It is publicly announced that Stanley knows whether Dennis's forehead is muddy. It is publicly announced that Stanley 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) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agenta 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) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Stanley can now know whether Shameka's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stanley","Dennis","Esmeralda","Shameka"],"index":51932,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993533492,"difficulty":0.0006466508}
-{"premise":"There are four persons. Everyone is visible 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 Shari's forehead is muddy. It is publicly announced that Tim knows whether Violet's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Ruthe can now know whether Tim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Violet","Shari","Tim","Ruthe"],"index":48179,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999736011,"difficulty":0.000263989}
-{"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 Elizabeth. Debra's card is shown to Debra. Elizabeth'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 Debra does not know whether Elizabeth 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 (Agentb 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":"Maria can now know that Debra can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Debra","Maria"],"index":7302,"s-l":"explicit-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 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)) ] Agentc knows that (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)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know that John can know whether Doris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Walter","Doris"],"index":40296,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6669961214,"difficulty":1.6669961214}
-{"premise":"There are four persons. Everyone is visible 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|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Marilyn can now know whether Harriet can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","Amy","Margie","Harriet"],"index":17422,"s-l":"forehead_mirror-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 Brian does not know whether or not everyone'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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(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&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brian can now know whether Heather's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brian","Heather"],"index":26039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994268417,"difficulty":0.0005731583}
-{"premise":"There are three persons. Everyone is visible 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 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":"Darrell can now know that Bernice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darrell","Bernice","Steven"],"index":43558,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970296621,"difficulty":0.0029703379}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Billy's card is shown to Billy. Wesley's card is shown to Billy. Billy's card is shown to Wesley. 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","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":"Billy can now know that Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Billy","James","Wesley"],"index":55799,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9806720614,"difficulty":0.0193279386}
-{"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 Jeffery 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) ] [ ! ~(4) ] [ ! ~(Agentb 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) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Sharon can now know that Sharon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Jeffery","Anthony","Sharon"],"index":38265,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6319665909,"difficulty":0.3680334091}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hilda's card is shown to Lester. Jose's card is shown to Hilda. Lester's card is shown to Jose. Hilda'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 Hilda 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&2&3))","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":"Jose can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lester","Hilda","Jose"],"index":24896,"s-l":"explicit-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 Alberta 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 (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":"Daniel can now know whether Alberta can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dominick","Daniel","Alberta"],"index":30998,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997707009,"difficulty":0.0002292991}
-{"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 Brian. Reba's card is shown to James. James's card is shown to James. Brian's card is shown to Genevieve. James's card is shown to Genevieve. 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: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:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know that Reba picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Reba","Brian","James","Genevieve"],"index":38629,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981421232,"difficulty":0.0018578768}
-{"premise":"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) ] [ ! ~(Agentc knows whether 3) ] 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 3) ] 0","hypothesis":"Philip can now know that Nevada can know that Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Carolyn","Tracy","Nevada"],"index":44534,"s-l":"forehead-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 Heather does not know whether John is thirsty. It is publicly announced that Deborah does not know whether Ashley is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Deborah can now know whether Ashley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Heather","Ashley","John","Deborah"],"index":56757,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9833096862,"difficulty":0.0166903138}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adelaide's card is shown to Adelaide. Kevin's card is shown to Adelaide. Adelaide's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin does not know whether Kevin 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 red card. It is publicly announced that Kevin 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 whether (Agentb knows whether (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":"Adelaide can now know whether Kevin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Adelaide","Kevin"],"index":45659,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9865356088,"difficulty":0.0134643912}
-{"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 Arianne. Robert's card is shown to Robert. Arianne's card is shown to Maxine. Maxine'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:2 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 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maxine can now know whether Maxine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Arianne","Robert","Maxine"],"index":11444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9828621745,"difficulty":0.0171378255}
-{"premise":"There are three persons. Everyone is visible 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 (~(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":"William can now know that Robin can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Robin","Eleanor"],"index":51725,"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. 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 Rex's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 2) ] 0","hypothesis":"Carole can now know whether Christopher can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Rex","Carole","Lyndsay"],"index":49174,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995782971,"difficulty":0.0004217029}
-{"premise":"There are two persons. Everyone is visible 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 Una'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":"Una can now know that Rodney can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rodney","Una"],"index":27164,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997549653,"difficulty":0.0002450347}
-{"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 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":"Kathleen can now know that Kathleen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Thomas","Lizzie"],"index":37447,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9915493727,"difficulty":0.0084506273}
-{"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. Robert's card is shown to Robert. Bobby's card is shown to Robert. Shirley's card is shown to Bobby. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Judy picked a red card. It is publicly announced that Judy does not know whether Judy 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 whether 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":"Robert can now know whether Judy can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Judy","Robert","Bobby"],"index":53014,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970811009,"difficulty":0.0029188991}
-{"premise":"There are four persons. Everyone is visible 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 Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Casey can now know that Edith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Casey","Diana","Teresa","Edith"],"index":19446,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980080724,"difficulty":0.0019919276}
-{"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 Patricia 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 Charles is thirsty. It is publicly announced that Patricia 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 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (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 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know whether Scott can know whether Christine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Scott","Patricia","Christine"],"index":63780,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985326529,"difficulty":0.0014673471}
-{"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. Kathy's card is shown to Gregory. Gregory's card is shown to Kathy. Julie's card is shown to Avis. Kathy's card is shown to Avis. Avis's card is shown to Avis. 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 (Agentb knows whether 2)","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":"Julie can now know that Gregory can know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julie","Gregory","Kathy","Avis"],"index":61546,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.938996017,"difficulty":0.061003983}
-{"premise":"There are three persons. Everyone is visible 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 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(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) ] [ ! ~(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":["James","Bryan","Regina"],"index":58596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9723296762,"difficulty":0.0276703238}
-{"premise":"There are two persons. Everyone is visible 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":"Cynthia can now know that Philip can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cynthia","Philip"],"index":21364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997404218,"difficulty":0.0002595782}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lavonne 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 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":"Raymond can now know that Svetlana can know that Lavonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Lavonne","Svetlana"],"index":51746,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982136488,"difficulty":0.0017863512}
-{"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 Sandra is thirsty. It is publicly announced that Lynn does not know whether Amy is thirsty. It is publicly announced that Sandra does not know whether Lynn 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 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":"Sandra can now know whether Lynn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Lynn","Sandra"],"index":42104,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9639142156,"difficulty":0.0360857844}
-{"premise":"There are 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)","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":"Cristina can now know whether Beverly can know whether Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janet","Donald","Cristina","Beverly"],"index":39619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997240901,"difficulty":0.0002759099}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Clayton can now know that Clayton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Lisa","Angeline","Clayton"],"index":20885,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9807586074,"difficulty":0.0192413926}
-{"premise":"There are two persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lyndsay can now know that Tony can know that Lyndsay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lyndsay","Tony"],"index":11193,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959679842,"difficulty":0.0040320158}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kylie does not know whether Diane 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) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"James can now know whether Diane is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kylie","John","James","Diane"],"index":9603,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941872358,"difficulty":0.0058127642}
-{"premise":"There are four 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 Richard knows whether Kurt is 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) ] 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Daniel can now know whether Richard can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tina","Daniel","Kurt","Richard"],"index":38937,"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 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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Mary can now know whether Richard can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Mary"],"index":54952,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8904061317,"difficulty":0.1095938683}
-{"premise":"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 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|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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 whether Bertha can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Richard","Paul","Bertha"],"index":62509,"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. It is publicly announced that Robert knows whether Josephine's forehead is muddy.","smcdel_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 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":"Robert can now know that Stanley can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Stanley","Josephine"],"index":43291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997649789,"difficulty":0.0002350211}
-{"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) ] [ ! ~(1) ] Agenta 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":"John can now know that Jolynn can know whether Jolynn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Jolynn","Miriam"],"index":45624,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9953616261,"difficulty":0.0046383739}
-{"premise":"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))) ] 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) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Charles can now know whether Ruby can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charles","Ruby"],"index":20820,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823983312,"difficulty":0.0176016688}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verona's card is shown to Jamie. Jamie's card is shown to Verona. Jamie's card is shown to Allison. Verona's card is shown to Allison. Allison's card is shown to Allison. It is publicly announced that someone picked a red card. It is publicly announced that Allison knows whether Verona 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 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":"Allison can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jamie","Verona","Allison"],"index":11181,"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). Estelle's card is shown to Timothy. Patricia's card is shown to Matthew. Matthew's card is shown to Estelle. Estelle's card is shown to Estelle. Patricia's card is shown to Estelle. Matthew'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:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","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":"Estelle can now know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Timothy","Matthew","Estelle","Patricia"],"index":18463,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8242865801,"difficulty":0.1757134199}
-{"premise":"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 knows whether Patrice's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrice knows whether Patrice's forehead 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":"Patrice can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patrice","Barbara","Mildred"],"index":10347,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983984828,"difficulty":0.0016015172}
-{"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 David 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) ] [ ! ~(Agentd knows whether (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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(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":["Barbara","David","Nancy","George"],"index":19973,"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 Paul does not know whether Cory is 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 (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":"Harley can now know whether Cory can know whether Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cory","Harley","Paul","Ingrid"],"index":5855,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986061454,"difficulty":0.0013938546}
-{"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 Justin. Justin's card is shown to Josefa. Richard'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:4 Agentb:1 Agentc:2 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 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know that Justin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Richard","Josefa","Lisa"],"index":40480,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974271655,"difficulty":0.0025728345}
-{"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 not thirsty. It is publicly announced that Mary knows whether or not everyone is thirsty. It is publicly announced that Douglas does not know whether Peter is thirsty. It is publicly announced that Peter knows whether Peter 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":"Peter can now know whether Mary can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Douglas","Peter"],"index":22499,"s-l":"internal-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 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) ] 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) ] [ ! ~(2) ] 0","hypothesis":"John can now know that Robert can know that Rene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Robert","Rene"],"index":18670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9956840277,"difficulty":0.0043159723}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcus knows whether or not everyone is thirsty. It is publicly announced that Dewitt 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)","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":"Marcus can now know whether Dewitt is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dewitt","Marcus"],"index":65594,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9678891301,"difficulty":0.0321108699}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jane 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 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":"Mary can now know that Allison is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jane","Mary","Allison","Frances"],"index":8099,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962965846,"difficulty":0.0037034154}
-{"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 Paula. Paula's card is shown to Theresa. Theresa's card is shown to Theresa. Theresa's card is shown to John. Theresa's card is shown to April. John's card is shown to April. 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) ] Agentd 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:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"April can now know whether Paula can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Theresa","John","April"],"index":34398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995651841,"difficulty":0.0004348159}
-{"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 Christine is thirsty. It is publicly announced that Daniel does not know whether Christine 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 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":"Daniel can now know whether Christine can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Christine"],"index":52466,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9972283244,"difficulty":1.9972283244}
-{"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 (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":"Ryan can now know whether Maria can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nelson","Ryan","Christopher","Maria"],"index":25975,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999782145,"difficulty":0.000217855}
-{"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 Shari. Shari's card is shown to John. Fred's card is shown to John. William's card is shown to John. Shari's card is shown to Fred. Fred'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:4 Agentb:1,3,4 Agentc: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:4 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fred can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shari","John","Fred","William"],"index":61602,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983862638,"difficulty":0.0016137362}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaclyn knows whether someone's forehead is muddy. It is publicly announced that Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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)) ] [ ! 3 ] 0","hypothesis":"Sara can now know whether Jackie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jaclyn","James","Sara","Jackie"],"index":51702,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995334148,"difficulty":0.0004665852}
-{"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. Melvin's card is shown to Virginia. Melvin's card is shown to Melvin. Oscar's card is shown to Melvin. Christopher's card is shown to Oscar. Oscar's card is shown to Oscar. 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) ] (Agentc knows whether 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":"Christopher can now know whether Oscar picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virginia","Melvin","Christopher","Oscar"],"index":12997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.871288836,"difficulty":0.128711164}
-{"premise":"There are four persons. Everyone is visible 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Jami can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Juanita","Jami","Anthony"],"index":52292,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997724891,"difficulty":0.0002275109}
-{"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 Lee. Lee's card is shown to Ashli. Ashli's card is shown to Ashli. Lee's card is shown to Frederick. Ashli's card is shown to Frederick. Lee's card is shown to Jennifer. Jennifer's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Ashli picked a black card. It is publicly announced that Ashli does not know whether Jennifer 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 that (Agentc knows whether (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":"Lee can now know that Frederick can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lee","Ashli","Frederick","Jennifer"],"index":32963,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6836388111,"difficulty":0.3163611889}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvester 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 (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":"Sylvester can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sylvester","Michelle"],"index":47769,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982942939,"difficulty":0.0017057061}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail'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 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":"Michael can now know whether Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Esther","Gail","Michael","Lee"],"index":49955,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995385408,"difficulty":0.0004614592}
-{"premise":"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 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":"Louis can now know whether Virgil can know whether Virgil's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elaine","Pamela","Virgil","Louis"],"index":45312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9851065874,"difficulty":0.0148934126}
-{"premise":"There are two persons. Everyone is visible 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 everyone'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 Betty'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 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":"Eva can now know that Eva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Betty","Eva"],"index":18541,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8215709329,"difficulty":0.1784290671}
-{"premise":"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 does not know whether Lisa's forehead is muddy. It is publicly announced that Lisa does not know 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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (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 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alvin can now know whether Alvin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lynne","Lisa","Alvin","Andrew"],"index":20480,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9300078154,"difficulty":0.0699921846}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Graciela's forehead is muddy. It is publicly announced that Jordan 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 (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":"Graciela can now know whether Jordan can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jordan","Graciela"],"index":25240,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alexandria's card is shown to Joyce. Joyce's card is shown to Marina. Alexandria's card is shown to Marina. Marina's card is shown to Rosa. Joyce's card is shown to Alexandria. Rosa's card is shown to Alexandria. It is publicly announced that someone picked a red card. It is publicly announced that Alexandria does not know whether Alexandria picked a red card. It is publicly announced that Joyce knows whether or not nobody picked a red card. It is publicly announced that Rosa 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 (Agentd knows that 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":"Rosa can now know that Alexandria can know that Alexandria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Marina","Rosa","Alexandria"],"index":25880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7472211123,"difficulty":0.2527788877}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Jeffrey. Luis's card is shown to Jeffrey. Jeffrey's card is shown to Bruce. Bruce's card is shown to Bruce. Luis's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Bruce 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)) ] (Agenta knows whether 2)","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":"Jeffrey can now know whether Bruce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Bruce","Luis"],"index":21540,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6863513589,"difficulty":1.6863513589}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (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":"Carol can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Christopher","Carol"],"index":23668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982597232,"difficulty":0.0017402768}
-{"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 (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":"Pablo can now know that Monique can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monique","Laura","Marlena","Pablo"],"index":57514,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997525811,"difficulty":0.0002474189}
-{"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. John's card is shown to Barbara. Danielle's card is shown to John. Barbara'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 Barbara picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Barbara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Danielle","Barbara","John"],"index":43017,"s-l":"explicit-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 Theresa does not know whether Theresa's forehead 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 (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":"Lisa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theresa","Miriam","Lisa"],"index":14034,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986126423,"difficulty":0.0013873577}
-{"premise":"There are three persons. Everyone is visible 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 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":"Tracy can now know that Emma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Emma","Dorothy"],"index":61857,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966530204,"difficulty":0.0033469796}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lillie does not know whether Samuel is thirsty. It is publicly announced that William does not know whether Samuel is thirsty.","smcdel_problem":"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) ] Agentd 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 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"William can now know that Lillie can know that Samuel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maxine","Lillie","Samuel","William"],"index":57639,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944518209,"difficulty":0.0055481791}
-{"premise":"There are four persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Sherry can now know that Lyle can know whether Sue's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sherry","Lyle","Helen","Sue"],"index":60152,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997287393,"difficulty":0.0002712607}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb 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:1,2,3,4 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":"Russell 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":["Russell","Douglas","Elizabeth","James"],"index":35917,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jill knows whether Mary's forehead is muddy. It is publicly announced that Peggy'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 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":"Mary can now know whether Jill's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ramon","Peggy","Jill","Mary"],"index":34318,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997338653,"difficulty":0.0002661347}
-{"premise":"There are 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 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":"Brenda can now know that Evelyn can know that Evelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Thomas","Evelyn","Ann"],"index":25078,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985789061,"difficulty":0.0014210939}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bruno does not know whether or not everyone is thirsty. It is publicly announced that Heather knows whether someone is thirsty. It is publicly announced that Michael does not know whether Heather is thirsty. It is publicly announced that Michael 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 (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 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&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Heather can now know that John can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","John","Michael","Bruno"],"index":42254,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980137348,"difficulty":0.0019862652}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guillermo's card is shown to Guillermo. Marie's card is shown to Marie. Guillermo's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(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:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Marie can now know that David can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Guillermo","Marie","David"],"index":39544,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9430311322,"difficulty":0.0569688678}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hattie 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) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Robert 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":["Robert","David","Hattie","Mary"],"index":51189,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983556867,"difficulty":0.0016443133}
-{"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 Jessica. Robert's card is shown to Jessica. Michael's card is shown to Michael. Jessica's card is shown to Joan. Michael's card is shown to Joan. Jessica's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Joan picked a red card. It is publicly announced that Joan does not know whether Joan picked a red card.","smcdel_problem":"VARS 1,2,3,4 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 (~(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":"Robert can now know whether Michael can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Michael","Joan","Robert"],"index":13402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995589852,"difficulty":0.0004410148}
-{"premise":"There are two persons. Everyone is visible 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 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) ] [ ! (~(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) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Jeanette can now know that Hazel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hazel","Jeanette"],"index":54049,"s-l":"forehead_mirror-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 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 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":"John can now know whether Buffy can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arthur","John","Buffy","Gail"],"index":14316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963327646,"difficulty":0.0036672354}
-{"premise":"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. It is publicly announced that Judith's forehead is not 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Stacey can now know that Diane can know whether Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judith","Stacey","Rose","Diane"],"index":63979,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.778788507,"difficulty":0.221211493}
-{"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 Horace. Horace's card is shown to Timothy. 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 Timothy picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 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) ] [ ! 2 ] 0","hypothesis":"Horace can now know whether Timothy can know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Horace","Timothy"],"index":12646,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9951964021,"difficulty":0.0048035979}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracie knows whether Joanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 2) ] 0","hypothesis":"Cortney can now know that Tracie can know whether Joanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracie","Joanne","Cortney","Jeffrey"],"index":10311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997496009,"difficulty":0.0002503991}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy is thirsty. It is publicly announced that David is not thirsty. It is publicly announced that Shelly does not know whether Charlotte is thirsty. It is publicly announced that Peggy does not know whether Shelly is 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) ] 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) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Charlotte can now know that Peggy can know that Peggy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peggy","Shelly","Charlotte","David"],"index":57103,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9643762112,"difficulty":0.0356237888}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond 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 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":"Joan can now know that Raymond can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ann","Joan","Raymond"],"index":15517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983691573,"difficulty":0.0016308427}
-{"premise":"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 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":"Jerome can now know whether Scott can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Jerome","Kimberly"],"index":7815,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
-{"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 Ginger. Kathleen's card is shown to Ginger. Kathleen's card is shown to Kathleen. 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 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:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vincent can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vincent","Ginger","Ruby","Kathleen"],"index":65720,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949087501,"difficulty":0.0050912499}
-{"premise":"There are four persons. Everyone is visible 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 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":"Sara can now know that Gerald can know whether Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sara","Jeffrey","Gerald","Tamara"],"index":16598,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994982481,"difficulty":0.0005017519}
-{"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 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 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":"Simone can now know that Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","David","Simone"],"index":25594,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9458001256,"difficulty":0.0541998744}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josie knows whether someone's forehead is muddy. It is publicly announced that Toby'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 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":"Toby can now know that Josie can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Josie","Toby"],"index":11042,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
-{"premise":"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 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":"Shantelle can now know that Lucy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shantelle","Evelyn","Lucy","Vickie"],"index":28951,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982250333,"difficulty":0.0017749667}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Noelle knows whether or not everyone's forehead is muddy. It is publicly announced that Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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|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":"Lance can now know that Lana can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lana","Lance","Noelle","Ralph"],"index":47989,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997875094,"difficulty":0.0002124906}
-{"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 James is thirsty. It is publicly announced that Steven 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) ] [ ! ~(Agenta 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 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pauline can now know that Pauline is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","James","Pauline","Dorothy"],"index":31693,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9786927104,"difficulty":0.0213072896}
-{"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 Ann. George's card is shown to Ann. George's card is shown to Paula. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether or not everyone picked a red card. It is publicly announced that George does not know whether Paula picked a red card. It is publicly announced that George 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)) ] (Agentc knows that 1)","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":"George can now know that Ann picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ann","Paula","George"],"index":23245,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5521969199,"difficulty":0.4478030801}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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":"Susan can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Audrey","Wilma","Susan","Sheila"],"index":55884,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999761045,"difficulty":0.000238955}
-{"premise":"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 Florence's forehead is muddy. It is publicly announced that Lakesha 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 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":"Lakesha can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florence","Fred","Lakesha","Curtis"],"index":59241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977891445,"difficulty":0.0022108555}
-{"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 Mitchell. Mitchell's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Mitchell 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)) ] Agenta knows whether (Agentb 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":"Mitchell can now know whether Richard can know that Mitchell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mitchell","Richard","Pamela"],"index":49453,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9609717727,"difficulty":1.9609717727}
-{"premise":"There are four persons. Everyone is visible 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 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":"Richard 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":["Lori","Justin","Robert","Richard"],"index":39493,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995927215,"difficulty":0.0004072785}
-{"premise":"There are three persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 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":"Clinton can now know that Michael can know that Clinton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clinton","Terrence","Michael"],"index":33893,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942289591,"difficulty":0.0057710409}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arleen's card is shown to Mary. Louis's card is shown to Arleen. Arleen's card is shown to Arleen. Kenneth's card is shown to Arleen. Kenneth's card is shown to Kenneth. 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 Kenneth picked a red card. It is publicly announced that Louis 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 that (Agentb knows that (~(1|2|3|4)))","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":"Arleen can now know that Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louis","Mary","Arleen","Kenneth"],"index":58825,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978681803,"difficulty":0.0021318197}
-{"premise":"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 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) ] [ ! (Agentc knows whether 3) ] 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jason can now know whether Raymond can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Jason","Carol"],"index":19918,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995597005,"difficulty":0.0004402995}
-{"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 Shirley is thirsty. It is publicly announced that Shirley 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 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) ] [ ! 2 ] 0","hypothesis":"Cynthia can now know whether Cynthia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Linda","Shirley","Cynthia"],"index":56201,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976008534,"difficulty":0.0023991466}
-{"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 Todd is thirsty. It is publicly announced that Daniel 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(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 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Daniel can now know that Layne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lydia","Daniel","Todd","Layne"],"index":45912,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967136383,"difficulty":0.0032863617}
-{"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 Joseph. Joseph's card is shown to Eva. Joseph's card is shown to Araceli. 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) ] 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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eva can now know that Joseph can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Eva","Araceli"],"index":37712,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984397292,"difficulty":0.0015602708}
-{"premise":"There are four persons. Everyone is visible 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 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":"James can now know that Israel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Ralph","Israel","Patrica"],"index":37349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984303117,"difficulty":0.0015696883}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmie is not thirsty. It is publicly announced that Julissa is not thirsty. It is publicly announced that Jimmie does not know whether Leonard is 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) ] Agentc knows that (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) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Gladys can now know that Jimmie can know whether Leonard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leonard","Jimmie","Gladys","Julissa"],"index":21143,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8320851326,"difficulty":0.1679148674}
-{"premise":"There are four persons. Everyone is visible 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 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":"Matthew can now know that Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Matthew","Patrick","Kenneth"],"index":32834,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981556535,"difficulty":0.0018443465}
-{"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 Rebecca is thirsty. It is publicly announced that James does not know whether Lillian is thirsty. It is publicly announced that Rebecca 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) ] [ ! ~(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":"Margaret can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillian","Margaret","James","Rebecca"],"index":23923,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984641075,"difficulty":0.0015358925}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgia does not know whether Sean is thirsty.","smcdel_problem":"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 (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 2) ] 0","hypothesis":"Mildred can now know whether Georgia can know whether Georgia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Georgia","Sean","Martha","Mildred"],"index":56741,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990926981,"difficulty":0.0009073019}
-{"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)) ] 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Walter can now know whether James can know that Caprice is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caprice","Walter","James"],"index":22473,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.993070662,"difficulty":0.006929338}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brianna's card is shown to Brianna. Marian's card is shown to Jonah. Jonah's card is shown to Marian. Marian's card is shown to Marian. Brianna's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Joshua knows whether Brianna 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 that (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":"Joshua can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brianna","Jonah","Marian","Joshua"],"index":44080,"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 Shannon knows whether or not everyone'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) ] [ ! (Agentc 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:1,2,3,4 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":"Shannon can now know that Arthur can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronnie","Arthur","Shannon","Nancy"],"index":18164,"s-l":"forehead_mirror-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 not everyone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy. It is publicly announced that Keith 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) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (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) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Christopher can now know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Keith","Christopher","Ashley"],"index":65033,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8679227829,"difficulty":1.8679227829}
-{"premise":"There are three persons. Everyone is visible 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 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 (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) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jerry can now know whether Cindy can know that Cindy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cindy","Jerry","Jennifer"],"index":13545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996449947,"difficulty":0.0003550053}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene knows whether Carlton'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 (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 2) ] 0","hypothesis":"Rene can now know whether Carlton can know that Rene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rene","Carlton"],"index":14774,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765352607,"difficulty":0.0234647393}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Alejandro 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 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":"Valerie can now know that Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Juanita","Valerie","Alejandro"],"index":40245,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.647742331,"difficulty":1.647742331}
-{"premise":"There are four persons. Everyone is visible 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)) ] 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":"James can now know that Elizabeth can know that Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Michael","Jeffrey","Elizabeth"],"index":8045,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984105825,"difficulty":0.0015894175}
-{"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 Margaret. 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 LAW Top OBS Agenta:1 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:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Margaret can now know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Margaret"],"index":20713,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9640715122,"difficulty":1.9640715122}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Michael can now know whether Terese can know that Terese's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Terese","Thomas"],"index":33034,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996323586,"difficulty":0.0003676414}
-{"premise":"There are four persons. Everyone is visible 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 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":"John can now know that William can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Michael","John","Stephanie"],"index":60590,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9949989319,"difficulty":0.0050010681}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grady's card is shown to Grady. Frank's card is shown to Robert. Eloise'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 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","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":"Robert can now know whether Grady picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eloise","Grady","Robert","Frank"],"index":4026,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7152653933,"difficulty":1.7152653933}
-{"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 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 everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jose","Brian"],"index":66437,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985817671,"difficulty":0.0014182329}
-{"premise":"There are 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 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":"Gilberto can now know that Robert can know that Gilberto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carmela","Robert","Gilberto"],"index":34690,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983947873,"difficulty":0.0016052127}
-{"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 David is thirsty. It is publicly announced that Phyllis 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Lydia can now know that David can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phyllis","Esperanza","David","Lydia"],"index":15685,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965968728,"difficulty":0.0034031272}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ora 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ora can now know that Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theresa","Ava","Ora","Ann"],"index":36602,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978146553,"difficulty":0.0021853447}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara 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)","n_announcements":1,"pbcheck":"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":"Clara can now know whether Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clara","Cole","Donna"],"index":46040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990485311,"difficulty":0.0009514689}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla knows whether Henry'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":"Carla can now know that Henry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Henry","Carla"],"index":45286,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983133078,"difficulty":0.0016866922}
-{"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. 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 Dale picked a red card. It is publicly announced that Dale 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 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":"Michael can now know that Dale can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Michael"],"index":55267,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5243933797,"difficulty":1.5243933797}
-{"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 Jill is thirsty. It is publicly announced that Jill 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Greg can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Jill","Bobby","Greg"],"index":18315,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9814994931,"difficulty":0.0185005069}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorthea knows whether Dorthea's forehead is muddy. It is publicly announced that Molly 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 2) ] [ ! (Agentd 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Martha can now know that Carrie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Dorthea","Martha","Molly"],"index":31833,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997353673,"difficulty":0.002646327}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sanjuanita 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) ] (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 2) ] 0","hypothesis":"Sanjuanita can now know whether Frances is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sanjuanita","Mary","Frances"],"index":25331,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966325164,"difficulty":0.0033674836}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marsha knows whether someone's forehead is muddy. It is publicly announced that Marsha knows whether or not everyone'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 1,2,3,4 LAW Top OBS 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 (Agentc 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 (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lela can now know that Marsha can know that Marsha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Lela","Marsha","Tia"],"index":65895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8847057223,"difficulty":0.1152942777}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristie's card is shown to Katherine. Anna's card is shown to Anna. Dwayne's card is shown to Anna. Kristie's card is shown to Dwayne. Anna's card is shown to Kristie. 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) ] (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:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Katherine can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Katherine","Anna","Dwayne","Kristie"],"index":42218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928863645,"difficulty":0.0071136355}
-{"premise":"There are four 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 Valene 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 (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Elaine can now know that Kevin can know that Elaine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elaine","Kevin","Jeremy","Valene"],"index":51678,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9010599852,"difficulty":0.0989400148}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randy does not know whether Joanna is thirsty. It is publicly announced that Randy knows whether Randy 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) ] (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 3) ] 0","hypothesis":"Randy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joanna","Peter","Randy"],"index":24622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
-{"premise":"There are four persons. Everyone is visible 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. 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 (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":"Alfred can now know that Boyd can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Tom","Alfred","Boyd"],"index":33710,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997115731,"difficulty":0.0002884269}
-{"premise":"There are three persons. Everyone is visible 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 not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Barry'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":"Barry can now know that Peggy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Peggy","Barry","James"],"index":37945,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986035228,"difficulty":0.0013964772}
-{"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 (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":"Joanne can now know whether Ramon can know that Ramon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ervin","Joanne","Nathan","Ramon"],"index":5786,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5542958379,"difficulty":0.4457041621}
-{"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 Emil knows whether Christina is 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) ] 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Emil can now know that Christina can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emil","Christina","John","Daniel"],"index":14439,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997056365,"difficulty":0.002943635}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darlene's card is shown to Darlene. Thomas's card is shown to Thomas. Thomas's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Darlene 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 ] 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:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Andre can now know whether Thomas can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","Thomas","Andre","Michael"],"index":15079,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.994189024,"difficulty":0.005810976}
-{"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 Tanner. Tanner's card is shown to Herman. Shirley's card is shown to Brenda. 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) ] (Agentc knows whether 2)","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":"Herman can now know whether Tanner picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Tanner","Herman","Brenda"],"index":51526,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6720391512,"difficulty":0.3279608488}
-{"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 Dorothy is thirsty. It is publicly announced that Patricia 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Marjorie can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Patricia","Marjorie"],"index":10805,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7424535155,"difficulty":0.2575464845}
-{"premise":"There are three persons. Everyone is visible 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 Joe's forehead is muddy.","smcdel_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 (~(1|2|3)))","n_announcements":1,"pbcheck":"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":"Joe can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alton","Scott","Joe"],"index":24158,"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. Each person draws a card, face unrevealed (red or black). Sophie's card is shown to Joan. Douglas's card is shown to Joan. Joan's card is shown to Stacie. Stacie's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Joan does not know whether Sophie 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) ] (Agentb knows whether (1&2&3&4))","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":"Joan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sophie","Joan","Stacie","Douglas"],"index":47618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9843450189,"difficulty":0.0156549811}
-{"premise":"There are two persons. Everyone is visible 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 (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":"Lillian can now know that Debbie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Debbie","Lillian"],"index":24327,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999783814,"difficulty":0.000216186}
-{"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 Archie. Archie's card is shown to Sharon. 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. It is publicly announced that Sharon does not know whether Sharon 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":"Sharon can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Archie","Sharon"],"index":10651,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
-{"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 Trent. Evelyn's card is shown to Evelyn. Nancy's card is shown to Nancy. It is publicly announced that someone 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:3 Agentb:3 Agentc:4 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:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Trent 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","Trent","Evelyn","Nancy"],"index":62982,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999538064,"difficulty":0.000461936}
-{"premise":"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 Dwight's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwight's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Thelma can now know whether Thelma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thelma","Terry","Gary","Dwight"],"index":51500,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8810533881,"difficulty":0.1189466119}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mercedes does not know whether 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) ] [ ! ~(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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Velma can now know that Mercedes can know that Velma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Velma","Mercedes","Raymond","Lawrence"],"index":12768,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969850183,"difficulty":0.0030149817}
-{"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 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":"David can now know that Anna can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Ben","David"],"index":56528,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960105419,"difficulty":0.0039894581}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. Derek's card is shown to Randall. Randall's card is shown to Derek. Frederick's card is shown to Derek. Randall'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:1,2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","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":"Derek can now know whether Derek picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randall","Derek","Frederick"],"index":54589,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7189929485,"difficulty":1.7189929485}
-{"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 or 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 Scott knows whether George is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 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)) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Scott can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Scott","George"],"index":31626,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99548316,"difficulty":0.00451684}
-{"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 Angela is thirsty. It is publicly announced that Angela 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 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Diane can now know that Angela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pamela","Anthony","Angela","Diane"],"index":11273,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997271359,"difficulty":0.002728641}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Hortencia can now know whether Wayne can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","Christopher","Hortencia","Josh"],"index":52635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997053742,"difficulty":0.0002946258}
-{"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 Roberto. Tiffany's card is shown to Tiffany. It is publicly announced that someone picked a red card. It is publicly announced that Roberto does not know whether or not everyone picked a red card. It is publicly announced that Roberto does not know whether or not everyone picked a red card. It is publicly announced that Roberto knows whether someone picked a red card. It is publicly announced that Tiffany 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":"Roberto can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roberto","Tiffany"],"index":15305,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997133613,"difficulty":0.0002866387}
-{"premise":"There are four persons. Everyone is visible 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'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)) ] Agentb knows whether (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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Orlando can now know whether Olga can know that Olga's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francisco","Orlando","Olga","Josephine"],"index":36652,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996826649,"difficulty":0.0003173351}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (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":"Brandon can now know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephanie","Brandon"],"index":62390,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9658574462,"difficulty":0.0341425538}
-{"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 Cheryl. Sonja's card is shown to Sonja. Ruthie's card is shown to Ruthie. Sonja'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:2 Agentb:2 Agentc:3 Agentd:2 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:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruthie can now know that Jean can know that Jean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Sonja","Ruthie","Jean"],"index":650,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979168773,"difficulty":0.0020831227}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicita's card is shown to Felicita. 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 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Felicita can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Felicita","David"],"index":12927,"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 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 (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 Margaret can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judith","Ben","Margaret","Vivian"],"index":400,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997810721,"difficulty":0.0002189279}
-{"premise":"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 Kirk 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 (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":"Karl can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Billy","Kirk","Karl"],"index":6117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9783475399,"difficulty":0.0216524601}
-{"premise":"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 Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Thomas'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) ] Agentc 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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Scott can now know that Anthony can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Thomas","Scott"],"index":18977,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973406196,"difficulty":0.0026593804}
-{"premise":"There are three persons. Everyone is visible 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 (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&2&3)) ] 0","hypothesis":"Marlene can now know whether Gene can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Gene","Marlene"],"index":51332,"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. Each person draws a card, face unrevealed (red or black). John's card is shown to Evelyn. Helen's card is shown to Evelyn. Evelyn's card is shown to John. John's card is shown to Matthew. Helen'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:2,3 Agentb:1 Agentc:2,3 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:2,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Evelyn can know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Evelyn","John","Helen","Matthew"],"index":36523,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.62172997,"difficulty":1.62172997}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jon's card is shown to Monique. Carla's card is shown to Monique. Jon's card is shown to Carla. 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 (~(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":"Jon can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Monique","Jon","Carla"],"index":12729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999722898,"difficulty":0.000277102}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. 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 James knows whether Lindsay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"James can now know that Rita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","Lindsay","James","Ricky"],"index":557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979720712,"difficulty":0.0020279288}
-{"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. John's card is shown to Brian. Brian's card is shown to John. 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:1,3 Agentb:1 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:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Karen can now know that Brian can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Karen","John"],"index":16356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925691485,"difficulty":0.0074308515}
-{"premise":"There are four persons. Everyone is visible 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 muddy. It is publicly announced that James knows whether Ronald's forehead is muddy. It is publicly announced that Margaret 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) ] Agentb knows whether (Agentd 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 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Margaret can now know whether Ronald can know whether Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Margaret","James","Ronald"],"index":8482,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996879101,"difficulty":0.0003120899}
-{"premise":"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 knows whether Victoria's forehead 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":"Albert can now know that Victoria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Victoria","Albert"],"index":34179,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983286262,"difficulty":0.0016713738}
-{"premise":"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.","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 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":"Paul can now know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Douglas","Michael"],"index":59243,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978144169,"difficulty":0.0021855831}
-{"premise":"There are 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":"Dallas can now know that Joyce can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dallas","Nora","Joyce","Geraldine"],"index":22174,"s-l":"forehead_mirror-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 is thirsty. It is publicly announced that Marian does not know whether Lena is thirsty. It is publicly announced that Marian does not know whether or not everyone is thirsty. It is publicly announced that Dana 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) ] 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Dana can now know whether Lena can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lena","Marian","Dana"],"index":42469,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960049987,"difficulty":0.0039950013}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karmen knows whether or not nobody's forehead is muddy. It is publicly announced that Karmen 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 (~(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":"Gary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Gary","Julia","Karmen"],"index":64085,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980908036,"difficulty":0.0019091964}
-{"premise":"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 knows whether Melissa's forehead is muddy. It is publicly announced that Gerald knows whether Melissa's forehead is muddy. It is publicly announced that Melissa 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) ] [ ! (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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Melissa can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Melissa","Gerald","Arthur"],"index":59433,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997127652,"difficulty":0.0002872348}
-{"premise":"There are three persons. Everyone is visible 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 knows whether George's forehead is muddy. It is publicly announced that Nathan 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 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":"Frances can now know that Nathan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Nathan","Frances"],"index":47922,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983953834,"difficulty":0.0016046166}
-{"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 Kent is thirsty. It is publicly announced that Kent does not know whether Verna is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Verna can now know whether Jessica can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Verna","Kent","Jessica"],"index":55659,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994356036,"difficulty":0.0005643964}
-{"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 Mavis. 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 or not everyone 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&2&3)) ] (Agentb knows whether 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&2&3)) ] 0","hypothesis":"Christopher can now know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mavis","Christopher","Margaret"],"index":40531,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6061878204,"difficulty":1.6061878204}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone'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 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":"Bernice can now know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bernice","Elizabeth","Andrea"],"index":50897,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995678067,"difficulty":0.0004321933}
-{"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 Myrtle. Rose's card is shown to Benjamin. Benjamin's card is shown to Rose. 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 that (Agenta knows that (~(1|2|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":"Benjamin can now know that Myrtle can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Myrtle","Benjamin","Rose"],"index":65066,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985886216,"difficulty":0.0014113784}
-{"premise":"There are three persons. Everyone is visible 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 Aurelia 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|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":"Mary can now know that James can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aurelia","James","Mary"],"index":52480,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9953060746,"difficulty":0.0046939254}
-{"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. Louis's card is shown to Evelyn. Matthew's card is shown to Matthew. Matthew's card is shown to Louis. 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 (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":"Matthew can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Matthew","Louis"],"index":59513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985057116,"difficulty":0.0014942884}
-{"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 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":"Dorothy can now know whether Johnny can know that Johnny's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Mary","Dorothy","Johnny"],"index":66786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9219531417,"difficulty":0.0780468583}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Sandra'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":"Sandra can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sandra","Nora"],"index":26948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9813350439,"difficulty":0.0186649561}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike 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 3)","n_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":"Angela can now know that Mike can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mike","Angela","John"],"index":57863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6503105164,"difficulty":0.3496894836}
-{"premise":"There are four persons. Everyone is visible 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 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":"Cindy can now know that Sharon can know whether Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Lisa","Mark","Cindy"],"index":14313,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996398687,"difficulty":0.0003601313}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allen knows whether Allen's forehead is muddy.","smcdel_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 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) ] 0","hypothesis":"Allen can now know whether Steven can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Allen","Steven","William"],"index":8371,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997538924,"difficulty":0.0002461076}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeana's card is shown to Jeana. Patricia's card is shown to Jeana. Maxine's card is shown to Jeana. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeana can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeana","Patricia","Maxine"],"index":5181,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998334229,"difficulty":0.001665771}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agentc knows whether 3) ] (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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jesse can now know whether Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jesse","Christine","Russell","Kathryn"],"index":26117,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997106194,"difficulty":0.0002893806}
-{"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 Martha. Martha's card is shown to Martha. Martha'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 Mark does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta 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:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mark can now know whether Martha can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Martha","Michael"],"index":36158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999524951,"difficulty":0.000475049}
-{"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 Arlene 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|2|3)) ] [ ! ~(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|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Linda can now know whether Helen can know whether Arlene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Linda","Arlene"],"index":10379,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988786578,"difficulty":0.0011213422}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"William can now know whether Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Vicki","Marilyn","Mattie"],"index":65615,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999743402,"difficulty":0.000256598}
-{"premise":"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 knows whether Pauline'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 (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":"Linda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pauline","Linda"],"index":36274,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998457551,"difficulty":0.001542449}
-{"premise":"There are two 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. It is publicly announced that someone is thirsty. It is publicly announced that Omar knows whether Jennifer 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) ] 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) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jennifer can now know whether Omar can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Omar"],"index":37971,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
-{"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 Daryl 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 (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":"Daryl can now know that Thomas can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ryan","Thomas","Daryl"],"index":30793,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998421073,"difficulty":0.001578927}
-{"premise":"There are two persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Jason 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 (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":"Jerry can now know that Jason can know that Jerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jason","Jerry"],"index":61421,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974516034,"difficulty":0.0025483966}
-{"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 or not everyone is thirsty. It is publicly announced that Julia 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jeanette can now know that Julia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julia","Betty","Jeanette","Claude"],"index":39001,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9514376521,"difficulty":0.0485623479}
-{"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 Cynthia. Carroll's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia does not know whether Cynthia picked a red card. It is publicly announced that Carroll knows whether Norma 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 2) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Cynthia can now know that Carroll can know whether Carroll picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carroll","Cynthia","William","Norma"],"index":39497,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9840754867,"difficulty":1.9840754867}
-{"premise":"There are four persons. Everyone is visible 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 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":"Kathleen can now know that Jonathon can know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Raymond","Kathleen","Jonathon"],"index":64343,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984517097,"difficulty":0.0015482903}
-{"premise":"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. It is publicly announced that Richard knows whether 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: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 ] 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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Alan can now know whether Robert can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alan","Robert","Richard"],"index":27599,"s-l":"forehead-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). Nia's card is shown to Michael. Nia's card is shown to Mary. Nia's card is shown to Nia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 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:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Mary","Nia"],"index":64126,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983287454,"difficulty":0.0016712546}
-{"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 Alonzo. Alonzo'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 Alonzo does not know whether Harry 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:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2&3))","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":"Alonzo can now know whether Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alonzo","Mary","Harry"],"index":42160,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9955940843,"difficulty":0.0044059157}
-{"premise":"There are three persons. Everyone is visible 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 Andrew's forehead is muddy. It is publicly announced that Harry 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 whether (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 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Harry can now know whether Andrew can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Andrew","Nicholas"],"index":20004,"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. 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. It is publicly announced that Tyler does not know whether Tyler'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&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":"Gary can now know that Tyler can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tyler","Gary"],"index":34359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983987212,"difficulty":0.0016012788}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dianne does not know whether Ashley 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) ] [ ! ~(Agenta knows whether 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Ashley can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dianne","Susan","Ashley"],"index":22630,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969797134,"difficulty":0.0030202866}
-{"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 Joanne is thirsty. It is publicly announced that Joanne 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 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 (~(1|2|3|4))) ] 0","hypothesis":"Roberta can now know that Joanne can know that Eleanor is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberta","Raymond","Eleanor","Joanne"],"index":64628,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967209697,"difficulty":0.0032790303}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurine's card is shown to Dale. Todd's card is shown to Dale. Todd'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:2,4 Agentb:4 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:2,4 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dale can now know whether Maurine can know that Dale picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dale","Maurine","Glenn","Todd"],"index":17136,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6449739933,"difficulty":1.6449739933}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theodore does not know whether Mary is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty. It is publicly announced that Theodore is thirsty. It is publicly announced that Mary does not know whether Karla is 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) ] (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) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Karla can now know whether Theodore is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karla","Allen","Theodore","Mary"],"index":21527,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7473989725,"difficulty":0.2526010275}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Larry'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) ] (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)) ] [ ! ~(3) ] 0","hypothesis":"Stacy can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Stacy","Larry","Anthony"],"index":39986,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999610126,"difficulty":0.000389874}
-{"premise":"There are four persons. Everyone is visible 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 Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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) ] 0","hypothesis":"Ashley can now know whether Heidi can know whether Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Robin","Anna","Heidi"],"index":38307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997082353,"difficulty":0.0002917647}
-{"premise":"There are two persons. Everyone is visible 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 (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":"Mara can now know whether Melvin can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melvin","Mara"],"index":36961,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996782541,"difficulty":0.0003217459}
-{"premise":"There are three persons. Everyone is visible 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 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)","n_announcements":1,"pbcheck":"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":"Anthony can now know that Linda can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","Linda","Anthony"],"index":55725,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9467709064,"difficulty":0.0532290936}
-{"premise":"There are three persons. Everyone is visible 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 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":"Ina can now know whether Alisha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alisha","Bernadette","Ina"],"index":14493,"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. It is publicly announced that someone is thirsty. It is publicly announced that Christine knows whether or not nobody is thirsty. It is publicly announced that Edward does not know whether or not everyone is thirsty. It is publicly announced that Jackie knows 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 (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Edward can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christine","Edward","Jackie"],"index":36537,"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 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 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":"Juanita can now know that Charles can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Brian","Juanita"],"index":39332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965856075,"difficulty":0.0034143925}
-{"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 Gregory 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)) ] Agentd knows whether (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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Gregory can know that Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Eva","Joseph","Timothy"],"index":57599,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9897056818,"difficulty":0.0102943182}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricardo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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 that Rhonda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricardo","Rhonda","Alberta","Stephanie"],"index":248,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.96161443,"difficulty":0.03838557}
-{"premise":"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 knows whether Katherine's forehead is muddy. It is publicly announced that Jaime's forehead 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 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":"Katherine can now know that Jaime can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Jaime","Katherine"],"index":63868,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6772735715,"difficulty":0.3227264285}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adriana's card is shown to Lillian. Lillian'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. It is publicly announced that Adriana 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)) ] (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|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Lillian can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adriana","Lillian","Mary"],"index":981,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983657002,"difficulty":0.0016342998}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucia knows whether Joy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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 2) ] 0","hypothesis":"Nancy can now know whether Lucia can know that Greta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucia","Joy","Greta","Nancy"],"index":1027,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976477027,"difficulty":0.0023522973}
-{"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 Clark. Clark's card is shown to James. Gertrude's card is shown to James. Gertrude's card is shown to Gertrude. 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 (Agentb knows whether (1&2&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":"Clark can now know that James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clark","James","Gertrude"],"index":66863,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9847988486,"difficulty":0.0152011514}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rowena's card is shown to Rowena. Ashley's card is shown to David. Ashley's card is shown to Kurt. Rowena's card is shown to Ashley. It is publicly announced that someone picked a red card. It is publicly announced that Kurt picked a red card. It is publicly announced that Kurt does not know whether David 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) ] 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:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rowena can now know that David can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rowena","David","Kurt","Ashley"],"index":4305,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985468984,"difficulty":0.0014531016}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Greg is not thirsty. It is publicly announced that Greg does not know whether Raymond is thirsty. It is publicly announced that Ernest knows whether Ernest is 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) ] 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) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Greg can now know whether Ernest can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Greg","Raymond","Ernest","Mariah"],"index":60584,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6247435808,"difficulty":0.3752564192}
-{"premise":"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 does not know whether David'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 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":"Hugo can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Asa","David","Hugo"],"index":26949,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962189794,"difficulty":0.0037810206}
-{"premise":"There are four persons. Everyone is visible 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 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":"Cynthia can now know that Grace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lee","Cynthia","Grace","John"],"index":540,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970936775,"difficulty":0.0029063225}
-{"premise":"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|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":"Leo can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","Robert","Leo"],"index":21865,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981587529,"difficulty":0.0018412471}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Una 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 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":"Anglea can now know whether Stephen can know whether Peggie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Peggie","Anglea","Una"],"index":25440,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992150068,"difficulty":0.0007849932}
-{"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 Paulina. Bobby's card is shown to Laura. Brian's card is shown to Laura. It is publicly announced that someone picked a red card. It is publicly announced that Bobby knows whether or not everyone picked a red card. It is publicly announced that Paulina knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Bobby can now know that Bobby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bobby","Paulina","Laura","Brian"],"index":53947,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9243687987,"difficulty":1.9243687987}
-{"premise":"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. It is publicly announced that Joshua's forehead is muddy. It is publicly announced that Jerry 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 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)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jerry can now know that Joshua can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Jerry","Joshua"],"index":51299,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981151819,"difficulty":0.0018848181}
-{"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) ] [ ! ~(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":"Genevieve can now know that Matthew can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Genevieve","Matthew","Rosita","William"],"index":54183,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997124076,"difficulty":0.0002875924}
-{"premise":"There are two persons. Everyone is visible 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 Latasha knows whether Latasha'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&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":"Latasha can now know whether Mary can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Latasha","Mary"],"index":33493,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996038079,"difficulty":0.0003961921}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christina's card is shown to Christina. Kelly's card is shown to Christina. Christina's card is shown to Greg. Greg's card is shown to Greg. Kelly's card is shown to Greg. Christina'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:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Greg can now know that Kelly can know whether Kelly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christina","Greg","Kelly"],"index":7602,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9669226408,"difficulty":1.9669226408}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas is not thirsty. It is publicly announced that Jack knows whether Douglas is thirsty. It is publicly announced that Douglas does not know whether Amber is 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|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":"Jack can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jack","Jill","Amber","Douglas"],"index":36701,"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 is thirsty. It is publicly announced that Jane does not know whether Andrew is thirsty. It is publicly announced that Jane 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)) ] (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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Jane can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jane","Louis","Nickolas","Andrew"],"index":18221,"s-l":"internal-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 Patty does not know whether or not everyone's forehead is muddy. It is publicly announced that Walton knows whether Patty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] 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)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Edward can now know that Walton can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walton","Edward","Griselda","Patty"],"index":6679,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997152686,"difficulty":0.0002847314}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_problem":"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 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":"Debbie can now know that Veronica can know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Veronica","Debbie"],"index":47650,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962361455,"difficulty":0.0037638545}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver 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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Johnny can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Johnny","Oliver","Roberto"],"index":40548,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999682188,"difficulty":0.000317812}
-{"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 Paula. Amber's card is shown to Chris. Paula's card is shown to Elizabeth. Amber's card is shown to Elizabeth. Amber's card is shown to Amber. It is publicly announced that someone picked a red card. It is publicly announced that Paula knows whether Chris picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Chris can now know whether Amber can know whether Paula picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Chris","Elizabeth","Amber"],"index":3941,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980194569,"difficulty":0.0019805431}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 (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) ] [ ! 4 ] 0","hypothesis":"Philip can now know that Joann can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joann","Jim","Veronica","Philip"],"index":11586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5927280784,"difficulty":0.4072719216}
-{"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 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 (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":"Timothy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Timothy","Dante"],"index":24843,"s-l":"internal-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 Charlene'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":"Mary can now know whether Charlene can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Charlene"],"index":20638,"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. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne does not know 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) ] [ ! ~(Agentd knows whether 2) ] 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) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Yvonne can now know that Jesse can know that Edith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Edith","Jesse","Yvonne"],"index":37231,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978917241,"difficulty":0.0021082759}
-{"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 Mark. Osvaldo's card is shown to Osvaldo. Mark's card is shown to Darrell. Osvaldo's card is shown to Edith. 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 whether (Agentc knows that 2)","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":"Mark can now know whether Darrell can know that Osvaldo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Osvaldo","Darrell","Edith"],"index":39910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.871088922,"difficulty":0.128911078}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Charles. Andrea's card is shown to Charles. Andrea's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Andrea picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb: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:2,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Clarence can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Clarence","Andrea"],"index":26914,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
-{"premise":"There are two persons. Everyone is visible 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 Marlene 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 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":"Dionna can now know that Marlene can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marlene","Dionna"],"index":23499,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997825027,"difficulty":0.0002174973}
-{"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 or not everyone is thirsty. It is publicly announced that Clarence does not know whether Roger is thirsty. It is publicly announced that Roger 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 (1&2&3&4)) ] [ ! ~(Agenta knows whether 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: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":"Clarence can now know that William can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clarence","Roger","Bonita","William"],"index":31497,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988325238,"difficulty":0.0011674762}
-{"premise":"There are two persons. Everyone is visible 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.","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":"Beverly can now know that Patricia can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Beverly","Patricia"],"index":20507,"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. Each person draws a card, face unrevealed (red or black). Kyung's card is shown to Kyung. Kyung'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 Willie picked a red card. It is publicly announced that Kyung 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 that 1)","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":"Kyung can now know that Willie can know that Kyung picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kyung","Willie"],"index":46105,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6786722541,"difficulty":0.3213277459}
-{"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 George is thirsty. It is publicly announced that Cynthia does not know whether George is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Jimmie 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jimmie can now know that Cynthia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Jimmie","Virginia","Cynthia"],"index":20474,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956296682,"difficulty":0.0043703318}
-{"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 Roy. James's card is shown to Roy. Roy's card is shown to Sarah. Sarah's card is shown to Sarah. 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:1,3 Agentb:1,2 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:1,3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sarah can now know that James can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roy","Sarah","James"],"index":19011,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964093566,"difficulty":0.0035906434}
-{"premise":"There are four 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 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":"Betty can now know that James can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Betty","Jon","James"],"index":58077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983845949,"difficulty":0.0016154051}
-{"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 Andrea. Andrea's card is shown to James. James's card is shown to Brett. Brett's card is shown to Brett. 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 (Agentc 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":"Andrea can now know whether Brett can know whether Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrea","James","Brett"],"index":1836,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9978269935,"difficulty":1.9978269935}
-{"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 Sam. Sam's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. Sam's card is shown to Sonya. Jeffrey'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 Sharon does not know whether Sonya picked a red card. It is publicly announced that Sam knows whether Sonya 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 that (Agentb 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":"Sam can now know that Jeffrey can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sam","Jeffrey","Sonya","Sharon"],"index":41894,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
-{"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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Louise can now know whether Larry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Mary","Rosemary","Louise"],"index":43755,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9616885185,"difficulty":0.0383114815}
-{"premise":"There are three persons. Everyone is visible 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 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) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michael can now know whether Debra can know whether Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Debra","Lora"],"index":17100,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995241165,"difficulty":0.0004758835}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Denis's card is shown to Donald. Denis's card is shown to Edmund. 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 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":"Denis can now know that Donald can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Denis","Edmund"],"index":6822,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9901245236,"difficulty":0.0098754764}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earlene'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 (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) ] [ ! ~(3) ] 0","hypothesis":"Joseph can now know whether Jacqueline can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gail","Jacqueline","Earlene","Joseph"],"index":48945,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6178340316,"difficulty":1.6178340316}
-{"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 or not everyone is thirsty.","smcdel_problem":"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 (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":"Emily can now know that Wendy can know that Gary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Betty","Wendy","Emily"],"index":55943,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9202338457,"difficulty":0.0797661543}
-{"premise":"There are two 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 Briana knows whether Marie 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":"Marie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marie","Briana"],"index":52703,"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. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Grace knows whether Alice's forehead is muddy.","smcdel_problem":"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|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":"Alice can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alice","Grace","Kim"],"index":51412,"s-l":"forehead_mirror-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 Jamie does not know whether Lois is thirsty. It is publicly announced that Kenneth does not know whether Nichol 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) ] Agentd 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Nichol can now know that Jamie can know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Lois","Jamie","Nichol"],"index":37330,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953357577,"difficulty":0.0046642423}
-{"premise":"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'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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ethel can now know that Paul can know whether Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ethel","Paul"],"index":28723,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6181416512,"difficulty":0.3818583488}
-{"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 George. Arthur's card is shown to Jesus. George's card is shown to Arthur. 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:2 Agentb:3 Agentc: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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jesus can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Jesus","Arthur"],"index":22199,"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). Annie's card is shown to Annie. 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 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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Annie can now know that David can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annie","David","Patricia"],"index":9140,"s-l":"explicit-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's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy. It is publicly announced that Shaniqua knows whether Martha's forehead is muddy. It is publicly announced that Shaniqua does not know whether Shaniqua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Martha can now know whether Shaniqua can know whether Christy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Christy","Shaniqua","Martha"],"index":13695,"s-l":"forehead-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.","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 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":"Ilene can now know that Dale can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dale","Odell","Ilene","Mary"],"index":47132,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983112812,"difficulty":0.0016887188}
-{"premise":"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 Jorge knows whether Jorge'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 whether (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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jorge can now know whether Gail can know that Jorge's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jorge","Gail"],"index":49663,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6921615005,"difficulty":1.6921615005}
-{"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. Chas's card is shown to Chas. It is publicly announced that someone picked a red card. It is publicly announced that Helen does not know whether John 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) ] (Agentb knows that (~(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":"Helen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Helen","Chas"],"index":41620,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984667897,"difficulty":0.0015332103}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Deborah. Juanita's card is shown to Linda. Juanita's card is shown to Marcos. Linda's card is shown to Marcos. Marcos's card is shown to Marcos. 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:2 Agentb:2 Agentc:2,3,4 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:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Juanita can now know that Juanita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Juanita","Linda","Marcos"],"index":59348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8463759422,"difficulty":0.1536240578}
-{"premise":"There are three 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 Carmen 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 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":"Carmen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Sara","Carmen"],"index":37572,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950866103,"difficulty":0.0049133897}
-{"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 Wayne. Douglas's card is shown to Wayne. Wilber's card is shown to Wilber. Douglas's card is shown to Wilber. Douglas's card is shown to Jamie. Wilber's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether Wilber 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 whether (Agentb 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":"Douglas can now know whether Wilber can know that Douglas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wayne","Wilber","Jamie","Douglas"],"index":21728,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.873093307,"difficulty":1.873093307}
-{"premise":"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 does not know whether Willie's forehead is muddy. It is publicly announced that Hilda'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) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Joseph can now know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Joseph","Jack","Hilda"],"index":63810,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9779637456,"difficulty":0.0220362544}
-{"premise":"There are two persons. Everyone is visible 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&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":"Mary can now know whether Craig can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Craig","Mary"],"index":36255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996121526,"difficulty":0.0003878474}
-{"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. Kathleen's card is shown to Jamie. Margarita's card is shown to Jamie. Jamie's card is shown to Barbara. Kathleen's card is shown to Barbara. Margarita's card is shown to Kathleen. Jamie's card is shown to Margarita. Kathleen's card is shown to Margarita. 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 that (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":"Barbara can now know that Jamie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jamie","Barbara","Kathleen","Margarita"],"index":11809,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
-{"premise":"There are four persons. Everyone is visible 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 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 3) ] 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 3) ] 0","hypothesis":"Sandra can now know that Jean can know that Dale's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Dale","Sandra","Leah"],"index":22032,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985752106,"difficulty":0.0014247894}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathleen does not know whether Cathleen's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Cathleen can now know whether Rozanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dale","Rozanne","Cathleen","Christine"],"index":56011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992190599,"difficulty":0.0007809401}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phillip 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 (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":"Robert can now know whether Doris can know that Doris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phillip","Laura","Robert","Doris"],"index":12870,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6229080558,"difficulty":1.6229080558}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caroline 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 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 (1|2|3|4)) ] 0","hypothesis":"Linda can now know whether Caroline can know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Linda","Don","Caroline"],"index":59395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963267446,"difficulty":0.0036732554}
-{"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 or not everyone is 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&2&3&4))","n_announcements":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":"Alan can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacy","Edward","Troy","Alan"],"index":32218,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6704860926,"difficulty":1.6704860926}
-{"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 Emil. Jared's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Jared does not know whether or not everyone picked a red card. It is publicly announced that Emil 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 ] Agenta knows that (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)) ] [ ! 1 ] 0","hypothesis":"Emil can now know that Jared can know that Jared picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emil","Jared"],"index":14989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.976744473,"difficulty":0.023255527}
-{"premise":"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 everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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 2) ] 0","hypothesis":"Shelley can now know whether Shelley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bruce","Robert","Shelley","Lillie"],"index":42178,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8636279106,"difficulty":0.1363720894}
-{"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 (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":"William can now know that Donald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Crystal","William","Donald"],"index":189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9934853911,"difficulty":0.0065146089}
-{"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 Billy. William's card is shown to Billy. Billy'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 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 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":"William can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Billy","William"],"index":42682,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9955174327,"difficulty":0.0044825673}
-{"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. Naomi's card is shown to Naomi. Boyd's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Boyd 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)) ] (Agenta knows that 1)","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":"Boyd can now know that Boyd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Boyd","Kevin","Naomi","Harold"],"index":25045,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8338783979,"difficulty":1.8338783979}
-{"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. Earl's card is shown to Michael. Robert's card is shown to Michael. Earl's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Francis does not know whether Francis 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) ] [ ! ~(Agenta 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:2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Francis can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Michael","Earl","Robert"],"index":57932,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997105002,"difficulty":0.0002894998}
-{"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. David's card is shown to Doris. Nathaniel's card is shown to Nancy. David's card is shown to David. David's card is shown to Nathaniel. 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:3 Agentd: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:1,3 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathaniel can now know whether Doris can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Nancy","David","Nathaniel"],"index":65390,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8897590041,"difficulty":0.1102409959}
-{"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 Leroy is thirsty. It is publicly announced that Deborah 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)) ] 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jerri can now know whether Deborah can know that Marie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerri","Marie","Deborah","Leroy"],"index":34496,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9929795861,"difficulty":0.0070204139}
-{"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 Bonnie. Jack's card is shown to Bonnie. Mark's card is shown to Jack. Mark's card is shown to Roger. Jack'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:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jack can now know that Bonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonnie","Jack","Roger","Mark"],"index":67584,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981909394,"difficulty":0.0018090606}
-{"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 Robert. Alfonso's card is shown to Robert. Robert's card is shown to Richard. Richard's card is shown to Richard. Alfonso's card is shown to Richard. Robert's card is shown to Alfonso. It is publicly announced that someone picked a red card. It is publicly announced that Richard 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))) ] Agentc 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":"Alfonso can now know that Richard can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Richard","Alfonso"],"index":46452,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967903495,"difficulty":0.0032096505}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marvin's forehead is muddy. It is publicly announced that Ursula does not know whether Ursula's forehead is muddy. It is publicly announced that Ursula knows whether Abraham's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Marvin can now know that Aaron can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Abraham","Aaron","Ursula"],"index":46397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9723165035,"difficulty":0.0276834965}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eugenia's card is shown to Eugenia. Eugenia's card is shown to Ramona. Eugenia's card is shown to Darrin. It is publicly announced that someone picked a red card. It is publicly announced that Darrin does not know whether Ramona 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) ] (Agentc 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Darrin can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eugenia","Ramona","Darrin"],"index":8057,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997256398,"difficulty":0.0002743602}
-{"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 Donald. Joshua's card is shown to Donald. Barbara's card is shown to Joshua. Donald's card is shown to Sal. Sal's card is shown to Sal. 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:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(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 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Donald can now know that Joshua can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Donald","Joshua","Sal"],"index":41753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985327721,"difficulty":0.0014672279}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Craig. James's card is shown to Craig. 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 Craig 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)))","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":"James can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Craig","James"],"index":64766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999720633,"difficulty":0.000279367}
-{"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 Sarah. Sarah's card is shown to Teresa. David's card is shown to Teresa. Sarah'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:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","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":"David can now know that Teresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Teresa","David"],"index":33569,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983680844,"difficulty":0.0016319156}
-{"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 Raquel. Raquel's card is shown to Kimberly. Erin's card is shown to Kimberly. Raquel's card is shown to Erin. Kimberly's card is shown to Erin. It is publicly announced that someone picked a red card. It is publicly announced that Raquel knows whether or not nobody picked a red card. It is publicly announced that Erin does not know whether Erin picked a red card. It is publicly announced that Erin 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)) ] Agenta knows that (Agentc knows that (1|2|3|4))","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":"Raquel can now know that Erin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raquel","Kimberly","Erin","Sarah"],"index":6493,"s-l":"explicit-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 Martha knows whether Cheryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Jonathan can now know whether Robert can know whether Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Martha","Cheryl","Jonathan"],"index":54228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994834661,"difficulty":0.0005165339}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lela knows whether or not nobody's forehead is muddy. It is publicly announced that Latoya'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 (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) ] 0","hypothesis":"Lela can now know that Latoya can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Latoya","Lela"],"index":16308,"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. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Arnold. Joaquin's card is shown to Arnold. Joaquin's card is shown to Joaquin. 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 (Agentb 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":"Arnold can now know whether Joaquin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arnold","Joaquin"],"index":30116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997084737,"difficulty":0.0002915263}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lida's card is shown to Lida. Lida's card is shown to Louis. Kurt's card is shown to Louis. Kurt's card is shown to Kurt. Kurt'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:1,3 Agentc:3 Agentd: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 Agentb:1,3 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kurt can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lida","Louis","Kurt","Patricia"],"index":25531,"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 Randy does not know whether Steven is thirsty. It is publicly announced that Steven is not thirsty. It is publicly announced that Randy 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 (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) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Randy can now know that Patrick can know whether Norma is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Randy","Patrick","Norma"],"index":38984,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8483225703,"difficulty":0.1516774297}
-{"premise":"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":"Freda can now know whether Liz can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Freda","Liz","Kelsey","Sheila"],"index":63795,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9837964177,"difficulty":0.0162035823}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andy's card is shown to Randy. Kenneth's card is shown to Randy. Andy's card is shown to Andy. Jamie's card is shown to Andy. Randy's card is shown to Kenneth. Kenneth's card is shown to Kenneth. Randy's card is shown to Jamie. Kenneth's card is shown to Jamie. It is publicly announced that someone picked a red card. It is publicly announced that Andy does not know whether Kenneth 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) ] Agentb knows whether (Agenta 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":"Andy can now know whether Randy can know that Randy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Andy","Kenneth","Jamie"],"index":22553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8993630409,"difficulty":0.1006369591}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Augusta 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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Christine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Augusta","Christine","Shirley"],"index":17436,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982600808,"difficulty":0.0017399192}
-{"premise":"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 Gary's forehead is muddy. It is publicly announced that Gary knows whether Evelyn'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) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 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 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Evelyn can now know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Charles","Gary"],"index":15545,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9277757406,"difficulty":0.0722242594}
-{"premise":"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's forehead is not muddy. It is publicly announced that Jean does not know whether Jean'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) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(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) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Michelle can now know whether Edward can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Edward","Jean"],"index":347,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9099458456,"difficulty":0.0900541544}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louie 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 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":"Louie can now know whether Bonnie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonnie","James","Louie","Harold"],"index":13413,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940051436,"difficulty":0.0059948564}
-{"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 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 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|2|3))) ] 0","hypothesis":"William can now know whether David can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leslie","David","William"],"index":59145,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9447603226,"difficulty":0.0552396774}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Warren's card is shown to Warren. Donald's card is shown to Warren. Warren's card is shown to Heriberto. Warren'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:1,3 Agentb:1 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 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Heriberto can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Warren","Heriberto","Donald"],"index":48621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
-{"premise":"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 Florence'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) ] 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know whether Kevin can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Florence","Robert"],"index":62484,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997007847,"difficulty":0.0002992153}
-{"premise":"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 Alice knows whether or not nobody's forehead is muddy. It is publicly announced that Alice does not know whether Alice's forehead is muddy. It is publicly announced that Henry knows whether Victoria's forehead 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) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Alice can now know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victoria","Alice","Henry"],"index":33378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.97606498,"difficulty":0.02393502}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugenie knows whether Eugenie's forehead is muddy. It is publicly announced that Clara knows whether Eugenie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Eugenie can now know that Clara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clara","Eugenie","Melissa","Robin"],"index":67468,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984636307,"difficulty":0.0015363693}
-{"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 Anna. Anna's card is shown to Stephan. Stephan's card is shown to Stephan. Bertha's card is shown to Stephan. Emma's card is shown to Stephan. Stephan's card is shown to Bertha. Emma's card is shown to Emma. 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 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:4 Agentb:1,2,3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bertha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anna","Stephan","Bertha","Emma"],"index":19743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Kim'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 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":"Kim can now know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Kim","Alice"],"index":34882,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9930284619,"difficulty":0.0069715381}
-{"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 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 that (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":"Johnson can now know that Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Johnson"],"index":30571,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990361929,"difficulty":0.0009638071}
-{"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. Ellen's card is shown to Maria. Maria's card is shown to Chris. Ellen's card is shown to Chris. Chris's card is shown to Chris. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Rafael 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:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 2 ] Agentc knows whether (Agentb knows that 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) ] [ ! ~(Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Ellen can now know whether Maria can know that Chris picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rafael","Maria","Ellen","Chris"],"index":26532,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9482775331,"difficulty":0.0517224669}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Wendy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Jordon","Josefina","Terrell"],"index":63938,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981296659,"difficulty":0.0018703341}
-{"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 Erin is thirsty. It is publicly announced that Martha 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 3) ] [ ! ~(Agentd knows whether 3) ] Agentb 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Catherine can now know that Martha can know that Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margarete","Catherine","Erin","Martha"],"index":17830,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.505274713,"difficulty":1.505274713}
-{"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 Christoper. Wayne's card is shown to Wayne. Christoper's card is shown to Diane. Wayne's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Diane 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 (Agentc knows whether 2)","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":"Wayne can now know that Diane can know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christoper","Wayne","Diane","Melissa"],"index":18426,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9643449187,"difficulty":1.9643449187}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! 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":"Rebecca can now know whether James can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eula","James","Rebecca"],"index":1417,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994853735,"difficulty":0.0005146265}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Al knows whether Al's forehead is muddy.","smcdel_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 (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) ] 0","hypothesis":"Joseph can now know that Al can know whether Freeman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Al","Freeman","Joseph"],"index":42354,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997385144,"difficulty":0.0002614856}
-{"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 knows whether Matthew is thirsty. It is publicly announced that Matthew does not know whether Erin 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)","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":"Willie can now know that Erin can know that Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Erin","Willie"],"index":4936,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9557627439,"difficulty":0.0442372561}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lessie's card is shown to Lessie. Ruth's card is shown to Lessie. Helen's card is shown to Nevada. Ruth's card is shown to Nevada. Lessie's card is shown to Helen. Ruth's card is shown to Helen. Lessie's card is shown to Ruth. Nevada'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:1,4 Agentb:3,4 Agentc:1,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 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":"Ruth can now know whether Lessie can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lessie","Nevada","Helen","Ruth"],"index":63019,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8457663059,"difficulty":1.8457663059}
-{"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 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":"Ruth can now know whether Alethia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Alethia","Ruth","Teresa"],"index":54445,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996300936,"difficulty":0.0003699064}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather 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)) ] Agentc 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Donna can now know whether Reuben can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heather","Michael","Donna","Reuben"],"index":23460,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9881738424,"difficulty":0.0118261576}
-{"premise":"There are four persons. Everyone is visible 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 William's forehead is muddy. It is publicly announced that Sheila 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 2) ] [ ! (Agenta knows whether 2) ] 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) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Betty can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheila","William","Deedra","Betty"],"index":49454,"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. It is publicly announced that someone is thirsty. It is publicly announced that Darryl does not know whether Mary is thirsty. It is publicly announced that Kelly does not know whether Darryl 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) ] (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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mary can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Darryl","Kelly"],"index":24320,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
-{"premise":"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 Wanda's forehead is muddy. It is publicly announced that Wanda does not know whether Wanda's forehead is muddy. It is publicly announced that Wanda 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)) ] 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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Wanda can now know that Dennis can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Wanda"],"index":48540,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joy does not know whether Joy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Benjamin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joy","Benjamin","Jenny","Clora"],"index":8633,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999740541,"difficulty":0.000259459}
-{"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 Kathleen. Lisa's card is shown to Henry. Henry's card is shown to Lisa. 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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 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:4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Henry can now know whether Henry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Henry","Andrew","Lisa"],"index":15419,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9954679012,"difficulty":1.9954679012}
-{"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 Joseph. Alisha's card is shown to Joseph. Joseph's card is shown to Anthony. Lewis's card is shown to Anthony. Alisha's card is shown to Anthony. Joseph's card is shown to Lewis. Anthony's card is shown to Alisha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 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:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Alisha can know whether Lewis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Anthony","Lewis","Alisha"],"index":28618,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6553108692,"difficulty":1.6553108692}
-{"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 Matthew. Jonathan's card is shown to Matthew. Matthew'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 Matthew 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 that 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":"Robert can now know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Robert","Jonathan"],"index":2255,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9882931113,"difficulty":0.0117068887}
-{"premise":"There are 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 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":"Doris can now know whether Chad can know whether Rafael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chad","Alfred","Rafael","Doris"],"index":36122,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997244477,"difficulty":0.0002755523}
-{"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 Ronny is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Ronny 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)) ] Agentb knows that (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) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Angelo can now know that Ronny can know whether Peggy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronny","Angelo","Peggy"],"index":29726,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6203919649,"difficulty":0.3796080351}
-{"premise":"There are three persons. Everyone is visible 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 Jennifer's forehead is muddy. It is publicly announced that Tamara 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 2) ] [ ! (Agentc knows whether 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Tamara 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":["David","Jennifer","Tamara"],"index":35962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983383417,"difficulty":0.0016616583}
-{"premise":"There are two persons. Everyone is visible 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 or not nobody'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:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(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:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"George can now know that Julio can know that Julio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["George","Julio"],"index":9211,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974800944,"difficulty":0.0025199056}
-{"premise":"There are four persons. Everyone is visible 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 Cecile's forehead is muddy. It is publicly announced that Cecile's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Cecile 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":["Calvin","Dwight","Cecile","Robert"],"index":54426,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8923752904,"difficulty":0.1076247096}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mickie's card is shown to Anne. Mickie's card is shown to Mickie. Donna's card is shown to Mickie. Anne'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 (Agentb 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":"Anne can now know that Mickie can know that Anne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anne","Mickie","Donna"],"index":32360,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976186156,"difficulty":0.0023813844}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beulah knows whether Beulah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Charles can now know that Paul can know that Beulah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Tom","Charles","Beulah"],"index":26266,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998059094,"difficulty":0.001940906}
-{"premise":"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 Joseph does not know 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) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 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) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Russell can now know that Leola can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Leola","Russell"],"index":701,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982652068,"difficulty":0.0017347932}
-{"premise":"There are four 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 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 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":"Beulah can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jami","John","Irene","Beulah"],"index":13853,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6409822702,"difficulty":0.3590177298}
-{"premise":"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 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)","n_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":"Cynthia can now know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cynthia","Judy","Gregory"],"index":32130,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993240118,"difficulty":0.006759882}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rodney does not know whether Terry 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 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":"Rodney can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rodney","Terry"],"index":9660,"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 Anna's forehead is not 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) ] [ ! ~(2) ] [ ! ~(4) ] 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) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Shelly can now know whether Ester can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ester","Anna","Shelly","Ethel"],"index":5152,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997105002,"difficulty":0.0002894998}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gaynelle's card is shown to Betty. Kristen's card is shown to Kristen. It is publicly announced that someone picked a red card. It is publicly announced that Betty picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb: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:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Betty can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Gaynelle","Kristen"],"index":15100,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984679818,"difficulty":0.0015320182}
-{"premise":"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 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (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 (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Jackie can now know whether Jackie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jackie","Kenneth","Sandra"],"index":44409,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725126028,"difficulty":0.0274873972}
-{"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. Cruz's card is shown to Craig. Edwin's card is shown to Craig. Cruz's card is shown to Cruz. Edwin's card is shown to Cruz. Cruz's card is shown to Wesley. Craig's card is shown to Edwin. Cruz'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:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Craig can now know whether Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Craig","Cruz","Wesley","Edwin"],"index":25875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5345227122,"difficulty":0.4654772878}
-{"premise":"There are four persons. Everyone is visible 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 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 1) ] 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) ] 0","hypothesis":"Cynthia can now know that Clarence can know that Clarence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Loretta","Clarence","Mary"],"index":18858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984450936,"difficulty":0.0015549064}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendell 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 (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":"Wendell can now know that Catherine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teresa","Catherine","Wendell"],"index":56069,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983372688,"difficulty":0.0016627312}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Azzie knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Dino knows whether Azzie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] (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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Dino can now know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marie","Azzie","Ola","Dino"],"index":22410,"s-l":"forehead-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 Katie 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 (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":"William can now know whether Gina can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katie","Gina","Wayne","William"],"index":7986,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997871518,"difficulty":0.0002128482}
-{"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 Brian knows whether Brian 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":"Brian can now know that Candida can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Candida","Brian"],"index":18620,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9895021319,"difficulty":0.0104978681}
-{"premise":"There are 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 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":"Harold can now know whether Marianne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Theodore","Harold","Marianne"],"index":45137,"s-l":"forehead_mirror-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 Clarence 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) ] [ ! (Agentd knows whether 1) ] 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) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Mary can now know whether Christy can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Daniel","Christy","Clarence"],"index":4159,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996571541,"difficulty":0.0003428459}
-{"premise":"There are three persons. Everyone is visible 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 Derek's forehead is muddy.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Bob can now know that Bob's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bob","Derek","Cecelia"],"index":63596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982396364,"difficulty":0.0017603636}
-{"premise":"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's forehead is not muddy. It is publicly announced that Annie does not know whether Annie's forehead is muddy. It is publicly announced that Annie 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)) ] 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) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know that Annie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Annie","Anthony"],"index":21462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969763756,"difficulty":0.0030236244}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laverne knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Nancy can now know that Stephen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Laverne","Hilma","Stephen"],"index":28296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984288812,"difficulty":0.0015711188}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ezekiel's card is shown to Lisa. Lisa's card is shown to Jonelle. Jonelle's card is shown to Jonelle. Ezekiel's card is shown to Jonelle. Jonelle's card is shown to Ezekiel. 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) ] (Agentb knows whether 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":"Jonelle can now know whether Ezekiel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Jonelle","Ezekiel"],"index":27940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7471250296,"difficulty":0.2528749704}
-{"premise":"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 knows whether someone'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) ] [ ! (Agentd knows whether (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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Stephen can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andrew","Stephen","Patricia","Scott"],"index":43136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
-{"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. 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:1 Agentb: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 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Scott","Dominique","Andrew"],"index":30618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9607226253,"difficulty":0.0392773747}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Aldo's card is shown to Kathleen. Gabriel's card is shown to Kathleen. Gabriel's card is shown to Richard. Aldo's card is shown to Aldo. Richard's card is shown to Gabriel. Gabriel's card is shown to Gabriel. It is publicly announced that someone picked a red card. It is publicly announced that Aldo knows whether someone picked a red card. It is publicly announced that Kathleen picked a red card. It is publicly announced that Richard does not know whether Aldo 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 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: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":"Richard can now know that Gabriel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Richard","Aldo","Gabriel"],"index":19742,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997852445,"difficulty":0.0002147555}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miriam's card is shown to Miriam. Marla's card is shown to Miriam. Jose's card is shown to Jose. Jose's card is shown to Marla. Marla's card is shown to Marla. Jose's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Miriam does not know whether Harry picked a red card. It is publicly announced that Marla 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 that 4)","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":"Miriam can now know that Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Miriam","Jose","Marla","Harry"],"index":45688,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9463752508,"difficulty":0.0536247492}
-{"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 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 4)","n_announcements":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 Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Thomas","Elizabeth","Joseph"],"index":52064,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977434874,"difficulty":0.0022565126}
-{"premise":"There are two persons. Everyone is visible 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 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":"Vernon can now know that Tyrone can know that Tyrone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Vernon","Tyrone"],"index":20311,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982337952,"difficulty":0.0017662048}
-{"premise":"There are four persons. Everyone is visible 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 Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Kimberly can now know that Jesus can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Mark","Jesus","Kimberly"],"index":1298,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985931516,"difficulty":0.0014068484}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Truman does not know whether Jo is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Jo 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) ] (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 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"James can now know whether Jo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Truman","Jo"],"index":26105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9836204052,"difficulty":0.0163795948}
-{"premise":"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 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 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":"Vanessa can now know that Samuel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vanessa","Ted","Samuel","Frances"],"index":25920,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946693778,"difficulty":0.0053306222}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Jerrod can now know whether Mary can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Jerrod","Patricia","Raymond"],"index":948,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996004701,"difficulty":0.0003995299}
-{"premise":"There are three persons. Everyone is visible 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 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 3)","n_announcements":1,"pbcheck":"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":"Natalie can now know whether Natalie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edna","Pamela","Natalie"],"index":31854,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992877841,"difficulty":0.0007122159}
-{"premise":"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 does not know whether Norbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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 3) ] 0","hypothesis":"Clifton can now know that Claudia can know whether Claudia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Claudia","Clifton","Norbert","Deborah"],"index":56219,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9861078262,"difficulty":0.0138921738}
-{"premise":"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 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":"Kevin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Crystal","Kevin","Rodolfo"],"index":21055,"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 Willie does not know whether Mark is thirsty. It is publicly announced that Willie 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)) ] (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) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mark can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Willie"],"index":65996,"s-l":"internal-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 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Rose can now know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Silvia","Rose","Vanessa"],"index":32060,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969177246,"difficulty":0.0030822754}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Latoya does not know whether Dustin is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Latoya does not know whether Angela is thirsty. It is publicly announced that Dawn does not know whether Dustin is thirsty.","smcdel_problem":"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 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 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Latoya can now know that Dawn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Latoya","Dawn","Angela","Dustin"],"index":51510,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954505563,"difficulty":0.0045494437}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelly's card is shown to Theresa. Shelly's card is shown to Shelly. Alan's card is shown to Shelly. It is publicly announced that someone picked a red card. It is publicly announced that Theresa 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)) ] (Agenta knows that (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":"Theresa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Theresa","Shelly","Lucille","Alan"],"index":49396,"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 not everyone is thirsty. It is publicly announced that Meghan knows whether Elizabeth 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 (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":"Meghan can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Meghan"],"index":45725,"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 Margaret 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) ] (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)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Clyde can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margaret","Charles","Clyde","Martin"],"index":57868,"s-l":"internal-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 Brian does not know whether Joy 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 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":"Joy can now know that Katherine can know that Joy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Joy","Katherine"],"index":1535,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967388511,"difficulty":0.0032611489}
-{"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 or not everyone is thirsty. It is publicly announced that Ralph 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)) ] (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&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Matthew can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marguerite","Ralph","Matthew"],"index":47195,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997194409,"difficulty":0.0002805591}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Marcia can now know whether Theresa can know whether Roy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Theresa","Marcia","Roy"],"index":54422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997289777,"difficulty":0.0002710223}
-{"premise":"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 knows whether or not everyone's forehead is muddy. It is publicly announced that Troy'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 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":"Susan can now know that Kevin can know that Troy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Troy","Kevin"],"index":24128,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8434805274,"difficulty":0.1565194726}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlene's card is shown to Charlene. Ethel's card is shown to Charlene. Carol'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 Agentb: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 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charlene can now know whether Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charlene","Ethel","Michael","Carol"],"index":24517,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9005775452,"difficulty":1.9005775452}
-{"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 Margret is thirsty. It is publicly announced that Margret 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Thomas can now know whether Lora can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margret","Lora","Jason","Thomas"],"index":50763,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998251617,"difficulty":0.001748383}
-{"premise":"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 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 whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Joseph can now know whether Ella's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Ella"],"index":3051,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995445609,"difficulty":0.0004554391}
-{"premise":"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 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 (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)) ] [ ! (1|2|3) ] 0","hypothesis":"Scott can now know whether Danielle can know that Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Danielle","Larry"],"index":17936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.955683887,"difficulty":0.044316113}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alberto 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 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":"Charlotte can now know whether Alberto can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlotte","Alberto","Dennis"],"index":7774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997574687,"difficulty":0.0002425313}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dustin does not know whether Katherine is thirsty. It is publicly announced that Marissa 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)) ] (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 3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Marissa can now know that Katherine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dustin","Marissa","Katherine"],"index":6975,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980059266,"difficulty":0.0019940734}
-{"premise":"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 Marilyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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) ] 0","hypothesis":"Marilyn can now know whether Nicole can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","Nicole","Kristin","Thomas"],"index":3111,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997622371,"difficulty":0.0002377629}
-{"premise":"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. It is publicly announced that Timothy 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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Angela can now know that Timothy can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Paula","Timothy","Angela"],"index":5362,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9024373293,"difficulty":0.0975626707}
-{"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 (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":"Bernice can now know that Joseph can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernice","Linwood","Joseph"],"index":45839,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964003563,"difficulty":0.0035996437}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymon 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 (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":"Catrina can now know that Robin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Catrina","Robin","Raymon"],"index":5962,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9692339897,"difficulty":0.0307660103}
-{"premise":"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.","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 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":"Sage can now know whether Sage's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michelle","James","Sage"],"index":66524,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9669114947,"difficulty":1.9669114947}
-{"premise":"There are three persons. Everyone is visible 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":"Sandra can now know that Frank can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Sandra","Aaron"],"index":7545,"s-l":"forehead_mirror-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 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 (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":"Erin can now know that Kenneth can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Ronald","Erin"],"index":10015,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983502626,"difficulty":0.0016497374}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Melissa can now know whether Nancy can know whether Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Nancy","Melissa","Maria"],"index":25261,"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top 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 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":"Shannon can now know that Brianna can know that Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Brianna","Shannon","Floyd"],"index":42680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998342514,"difficulty":0.001657486}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Casey knows whether Addie'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:1,2,3,4 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 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":"Glen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Glen","Brian","Addie","Casey"],"index":32584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985753298,"difficulty":0.0014246702}
-{"premise":"There are three 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.","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))","n_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":"Gail can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Christina","Gail"],"index":27667,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826034904,"difficulty":0.0173965096}
-{"premise":"There are two 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 or not everyone's forehead is muddy. It is publicly announced that Louise 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 (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 (1&2)) ] 0","hypothesis":"Louise can now know whether Leonard can know whether Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leonard","Louise"],"index":57273,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972524047,"difficulty":0.0027475953}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Shannon. Paul's card is shown to Shannon. Rickie's card is shown to Shannon. Shannon's card is shown to Paul. Rickie's card is shown to Paul. Rickie's card is shown to Rickie. 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 3)","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":"Rickie can now know that Rickie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shannon","Paul","Rickie"],"index":43333,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913860559,"difficulty":0.0086139441}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 3) ] 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"James can now know whether Wilbur can know whether Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Charles","Brenda","Wilbur"],"index":44214,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997356534,"difficulty":0.0002643466}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Tracie 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 (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":"Tracie can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Katrina","James","Tracie"],"index":59613,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9732354283,"difficulty":0.0267645717}
-{"premise":"There are four 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. It is publicly announced that Erika 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 (1|2|3|4)) ] [ ! ~(Agentb 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"William can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Erika","Bryan","William"],"index":28077,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999706924,"difficulty":0.000293076}
-{"premise":"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's forehead is not muddy. It is publicly announced that Henry 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) ] [ ! ~(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":"Henry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Henry","Joyce","Frank"],"index":67275,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983225465,"difficulty":0.0016774535}
-{"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 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) ] (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 1) ] 0","hypothesis":"Donald can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Kevin","Eugene","Joyce"],"index":43208,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985712767,"difficulty":0.0014287233}
-{"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 Tammie is thirsty. It is publicly announced that Tammie 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))) ] 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tammie can now know that Edward can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Jacqueline","Melissa","Tammie"],"index":24667,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985340834,"difficulty":0.0014659166}
-{"premise":"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 (~(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":"Angela can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Angela","Larae"],"index":65658,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982402325,"difficulty":0.0017597675}
-{"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 Paul. Wanda's card is shown to Paul. Jonathan's card is shown to Paul. Paul's card is shown to Wanda. Wanda's card is shown to Wanda. Wanda's card is shown to Jonathan. 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) ] (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 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wanda can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Debra","Wanda","Jonathan"],"index":67238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983587861,"difficulty":0.0016412139}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elena does not know whether or not everyone is thirsty. It is publicly announced that Elena does not know whether William is thirsty. It is publicly announced that William knows whether Elena 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 whether (Agenta 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 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Elena can now know whether William can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Elena"],"index":5175,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976571798,"difficulty":0.0023428202}
-{"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 Roosevelt. Brenda's card is shown to Mark. Roosevelt's card is shown to Brenda. Mark's card is shown to Brenda. 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. It is publicly announced that Roosevelt 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 whether 2)","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":"Roosevelt can now know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roosevelt","Mark","Brenda"],"index":9131,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6980827451,"difficulty":0.3019172549}
-{"premise":"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 Dorothy'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) ] Agentb 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) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Dorothy can now know whether Domingo can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Dorothy","Domingo"],"index":28585,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9706793427,"difficulty":0.0293206573}
-{"premise":"There are four persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Donna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Suzanne","Peter","Donna","Rebecca"],"index":59455,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984508753,"difficulty":0.0015491247}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber does not know whether Maryann is thirsty. It is publicly announced that Amber does not know whether Betty is thirsty. It is publicly announced that 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] Agentc knows that (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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] 0","hypothesis":"Amber can now know that Manuel can know that Manuel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Manuel","Maryann","Amber","Betty"],"index":42942,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9479011893,"difficulty":0.0520988107}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandy's card is shown to Brandy. William's card is shown to Brandy. William's card is shown to William. Thomas's card is shown to William. Brandy's card is shown to Thomas. William's card is shown to Thomas. 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:1,2 Agentb:2,3 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:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brandy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brandy","William","Thomas"],"index":34435,"s-l":"explicit-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 Winnie knows whether someone's forehead is muddy. It is publicly announced that Winnie knows whether Ferdinand'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 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)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Ferdinand can know that Ferdinand's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Philip","Ferdinand","Winnie"],"index":32406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960600734,"difficulty":0.0039399266}
-{"premise":"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 Marian 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)) ] Agentb 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Marian can now know whether Mary can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Marian","Mary"],"index":18449,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9738143086,"difficulty":0.0261856914}
-{"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 Anita. Donna's card is shown to Joy. Anita's card is shown to Donna. Joy'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: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 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Anita can now know whether Donna can know whether Joy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anita","Joy","Donna"],"index":44021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987693429,"difficulty":0.0012306571}
-{"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 Marjorie. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether someone picked a red card. It is publicly announced that Anthony does not know whether Marjorie 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 that (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":"Marjorie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anthony","Marjorie"],"index":15974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985561967,"difficulty":0.0014438033}
-{"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&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":"Lai can now know whether Nellie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lai","Patricia","Bryan","Nellie"],"index":35267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.987416625,"difficulty":0.012583375}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Garrett can now know whether Arturo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Garrett","Shawn","Melinda","Arturo"],"index":12941,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999520421,"difficulty":0.000479579}
-{"premise":"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 (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Eric can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pedro","Eric"],"index":9341,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985327721,"difficulty":0.0014672279}
-{"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 Corey. Corey's card is shown to Mercedes. John's card is shown to Mercedes. Emil's card is shown to Mercedes. Corey's card is shown to Emil. 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 John does not know whether Mercedes picked a red card. It is publicly announced that Corey 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 whether (1&2&3&4))","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":"John can now know that Mercedes can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Corey","Mercedes","John","Emil"],"index":42735,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8215059638,"difficulty":0.1784940362}
-{"premise":"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 (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":"Michael can now know whether Daniel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Stephen","Michael","Estell"],"index":40884,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996075034,"difficulty":0.0003924966}
-{"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 Mary. William's card is shown to William. Wanda'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:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Mary can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","William","Wanda"],"index":60912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953839183,"difficulty":0.0046160817}
-{"premise":"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 Laura knows whether Amber's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] (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) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Alisha can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bradley","Amber","Alisha","Laura"],"index":30516,"s-l":"forehead-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 Margaret'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 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":"Tracy can now know whether Margaret can know whether Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","Margaret","Laura","Henry"],"index":57815,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997172952,"difficulty":0.0002827048}
-{"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 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) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Thomas can now know that Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diana","Carl","Thomas","Patricia"],"index":49063,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6088799238,"difficulty":0.3911200762}
-{"premise":"There are two persons. Everyone is visible 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 Edward knows whether Phyllis'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 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) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Phyllis can now know whether Edward can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edward","Phyllis"],"index":60059,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996432066,"difficulty":0.0003567934}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Eliseo can now know that Kimberly can know whether Eliseo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eliseo","Donald","Kimberly","Michael"],"index":20387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995336533,"difficulty":0.0004663467}
-{"premise":"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 Carol knows whether or not nobody's forehead is muddy. It is publicly announced that Carol knows whether Marguerite'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 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":"Marguerite can now know that Carol can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marguerite","Carol"],"index":65945,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9917336702,"difficulty":0.0082663298}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monique knows whether Rebecca's forehead is muddy. It is publicly announced that Rebecca knows whether Monique'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 (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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Monique can now know that Rebecca can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rebecca","Monique"],"index":55967,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984995127,"difficulty":0.0015004873}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Carl 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 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":"Austin can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daisy","Austin","Carl"],"index":59820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997202754,"difficulty":0.0002797246}
-{"premise":"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 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 3)","n_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":"Rita can now know whether Rita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristy","Christopher","Rita"],"index":35959,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958075285,"difficulty":0.0041924715}
-{"premise":"There are three persons. Everyone is visible 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 Lillie's forehead is muddy.","smcdel_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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Ellen can now know that Johnny can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Johnny","Ellen","Lillie"],"index":449,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984947443,"difficulty":0.0015052557}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvatore's card is shown to Bess. Jimmy's card is shown to Jimmy. Matthew's card is shown to Jimmy. Salvatore's card is shown to Jimmy. Jimmy's card is shown to Matthew. Matthew's card is shown to Salvatore. It is publicly announced that someone picked a red card. It is publicly announced that Salvatore 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)","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":"Jimmy can now know that Bess picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bess","Jimmy","Matthew","Salvatore"],"index":40224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8476005793,"difficulty":0.1523994207}
-{"premise":"There are three 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 Terri's forehead is muddy. It is publicly announced that Shirley knows whether Terri's forehead is muddy. It is publicly announced that Scott 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Shirley can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Scott","Terri","Shirley"],"index":26530,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998672843,"difficulty":0.001327157}
-{"premise":"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 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) ] [ ! (Agentc 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) ] [ ! (Agentc 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":["Laura","Ann","Darrell","Barry"],"index":32015,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979870319,"difficulty":0.0020129681}
-{"premise":"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 Kendall's forehead 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 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) ] [ ! 2 ] 0","hypothesis":"Tommy can now know whether Kendall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carla","Kendall","Tommy"],"index":4855,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995959401,"difficulty":0.0004040599}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tarsha 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 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":"Dorothy can now know that Donna can know that Marie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tarsha","Marie","Dorothy","Donna"],"index":19513,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9080273509,"difficulty":0.0919726491}
-{"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 Sally. Sally's card is shown to Sharon. Sharon's card is shown to Sharon. Sally's card is shown to Kendall. Sharon's card is shown to Kendall. 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) ] (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:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wayne can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sally","Sharon","Wayne","Kendall"],"index":55501,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984028935,"difficulty":0.0015971065}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Shannon can now know whether Natalie can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Shannon","Robert","Natalie"],"index":52442,"s-l":"forehead_mirror-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 Pauline 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 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":"Byron can now know whether Michael can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Byron","Michael","Pauline"],"index":22173,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5393611789,"difficulty":0.4606388211}
-{"premise":"There are three 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.","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":"Karla can now know that Bonnie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Gabriel","Karla"],"index":10469,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9702560902,"difficulty":0.0297439098}
-{"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 Jarvis. Jarvis's card is shown to Paul. Paul's card is shown to Steven. Mark's card is shown to Steven. Steven's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Jarvis 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) ] (Agentd 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":"Mark can now know that Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jarvis","Paul","Steven","Mark"],"index":42814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967767596,"difficulty":0.0032232404}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marisa's forehead is muddy. It is publicly announced that Marisa's forehead is muddy. It is publicly announced that Clarence's forehead is muddy.","smcdel_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 (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":"Clarence can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tillie","Clarence","Marisa"],"index":65995,"s-l":"forehead_mirror-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 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) ] [ ! 3 ] 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) ] [ ! 3 ] 0","hypothesis":"Beverley can now know that Gary can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Beverley","Wanda","Lisa"],"index":45028,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9871525168,"difficulty":0.0128474832}
-{"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 Lindsay. Mary's card is shown to Marie. Marie's card is shown to Cody. Cody's card is shown to Cody. Lindsay's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Lindsay does not know whether Mary picked a red card. It is publicly announced that Marie 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) ] (Agentd knows that 2)","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":"Mary can now know that Marie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lindsay","Marie","Cody","Mary"],"index":11254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.954249382,"difficulty":0.045750618}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erik 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":"Erik can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Matthew","Jay","Erik"],"index":23103,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997423291,"difficulty":0.0002576709}
-{"premise":"There are two persons. Everyone is visible 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":"Raymond can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Raymond","Randy"],"index":36820,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986281395,"difficulty":0.0013718605}
-{"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 Mary. Patrick's card is shown to Patrick. Daniel's card is shown to Patrick. Maurice's card is shown to Daniel. Patrick's card is shown to Maurice. 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) ] (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:4 Agentd:2 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":["Mary","Patrick","Daniel","Maurice"],"index":26466,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997703433,"difficulty":0.0002296567}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony 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 4)","n_announcements":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":"Kristy can now know that Anthony can know whether Kristy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rebecca","Anthony","Wilmer","Kristy"],"index":32041,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971690774,"difficulty":0.0028309226}
-{"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. Iris's card is shown to James. Iris's card is shown to Rita. Darlene's card is shown to Iris. Iris's card is shown to Iris. 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:1,4 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:2,4 Agentb:4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darlene can now know that Rita can know that Darlene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darlene","James","Rita","Iris"],"index":18665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99775213,"difficulty":0.00224787}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Candace 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 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":"Candace can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Robert","Katherine","Candace"],"index":41710,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973291159,"difficulty":0.0026708841}
-{"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 Laura is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Robert is thirsty. It is publicly announced that Dana knows 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 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (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 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Laura can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vivian","Robert","Dana","Laura"],"index":26694,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984614849,"difficulty":0.0015385151}
-{"premise":"There are three persons. Everyone is visible 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 nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Jay","Josephine"],"index":44492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984556437,"difficulty":0.0015443563}
-{"premise":"There are 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 (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":"James can now know whether Jeanette can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Christopher","Jeanette"],"index":20591,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997516274,"difficulty":0.0002483726}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catalina knows whether Catalina 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 (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":"Terri can now know that Catalina can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Terri","Elizabeth","Catalina"],"index":23803,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9563533068,"difficulty":0.0436466932}
-{"premise":"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 not muddy. It is publicly announced that James does not know whether James'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: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 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Doris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","James","Ola"],"index":55162,"s-l":"forehead-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 Eva knows 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) ] [ ! (Agentb 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 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patricia","Eva"],"index":8829,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947974682,"difficulty":0.0052025318}
-{"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 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&2&3) ] 0","hypothesis":"Joan can now know whether Rhonda can know that Rhonda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joan","Rhonda","Mario"],"index":46981,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9765732288,"difficulty":0.0234267712}
-{"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. Earl's card is shown to Dorothy. Dorothy's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Earl 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 that 1)","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":"Earl can now know that Dorothy can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Earl"],"index":66928,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8667244315,"difficulty":0.1332755685}
-{"premise":"There are two 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 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (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":"Ethel can now know that Clara can know that Ethel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ethel","Clara"],"index":1935,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5484620929,"difficulty":0.4515379071}
-{"premise":"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) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lenora can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elsie","Michael","Lenora"],"index":3029,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
-{"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 Leo. William's card is shown to Leo. Frank's card is shown to William. Frank's card is shown to Frank. Frank's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Frank 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:1,2 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(1) ] (Agentb knows that 4)","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":"William can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leo","William","Frank","Robert"],"index":53695,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8630063534,"difficulty":0.1369936466}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to Phyllis. James's card is shown to Phyllis. Phyllis's card is shown to Kevin. Kevin's card is shown to Kevin. James's card is shown to James. Phyllis's card is shown to Bertha. Kevin's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Phyllis does not know whether Bertha picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 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:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"James can now know whether Phyllis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Phyllis","Kevin","James","Bertha"],"index":19357,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candace's card is shown to Candace. Jessie's card is shown to Candace. Candace's card is shown to Jessie. 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) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessie can now know whether Candace can know that Carol picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Candace","Jessie","Carol"],"index":45434,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9397929907,"difficulty":1.9397929907}
-{"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 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":"Joseph can now know whether Frank is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Lynette","Joseph","Frank"],"index":7533,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977206588,"difficulty":0.0022793412}
-{"premise":"There are four persons. Everyone is visible to others. 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:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (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) ] [ ! ~(3) ] 0","hypothesis":"James can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","James","Ethel","David"],"index":12072,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956291914,"difficulty":0.0043708086}
-{"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 Maria. Wilhelmina's card is shown to Wilhelmina. Maria's card is shown to Christina. Howard'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:4 Agentb:2 Agentc:1 Agentd: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 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christina can now know whether Howard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Wilhelmina","Christina","Howard"],"index":21691,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8275219202,"difficulty":1.8275219202}
-{"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 Ted. Ted's card is shown to Ted. Henry's card is shown to Ted. Ted's card is shown to Henry. 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":"John can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Ted","Henry"],"index":27417,"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). Michael's card is shown to Gertrude. Jesus's card is shown to Michael. Michael's card is shown to Michael. Jesus's card is shown to Cindy. Gertrude's card is shown to Cindy. It is publicly announced that someone picked a red card. It is publicly announced that Gertrude knows whether or not everyone picked a red card. It is publicly announced that Jesus 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) ] (Agentc 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":"Michael can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jesus","Gertrude","Michael","Cindy"],"index":29332,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
-{"premise":"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'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 (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":"Stella can now know whether Gary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stella","Gary","Emma"],"index":47101,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ursula'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 (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) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know whether Darlene can know whether Darlene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darlene","Michael","Ursula"],"index":51529,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.743899405,"difficulty":0.256100595}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Riley 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|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":"Riley can now know whether Luz can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Riley","Arthur","Luz"],"index":18092,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999704659,"difficulty":0.000295341}
-{"premise":"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 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":"Stephanie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Lenore","Terry","Stephanie"],"index":57477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978314042,"difficulty":0.0021685958}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Lynn'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":"Mark can now know that Jayson can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Jayson","Mark"],"index":45397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976517558,"difficulty":0.0023482442}
-{"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 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 that Clifford is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Jason","Clifford"],"index":65842,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971388578,"difficulty":0.0028611422}
-{"premise":"There are four persons. Everyone is visible 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 (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) ] [ ! 3 ] 0","hypothesis":"John can now know whether Kristen can know whether Justin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Constance","John","Kristen"],"index":23289,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997029901,"difficulty":0.0002970099}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darcy'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":"Darcy can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Darcy","Marcus"],"index":3574,"s-l":"forehead-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's forehead is muddy. It is publicly announced that Jose 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 (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&2&3&4)) ] 0","hypothesis":"Jerry can now know whether Jose can know that Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Jerry","Jonathan","Ralph"],"index":50903,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9943957329,"difficulty":0.0056042671}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Maria can now know that Daniel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Maria","Kevin"],"index":31038,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997636676,"difficulty":0.0002363324}
-{"premise":"There are three 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 Beverly does not know whether or not everyone is thirsty. It is publicly announced that Beverly does not know whether or not everyone 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) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc 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) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Brian can now know that Brian is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Beverly","Barry"],"index":64501,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8979053497,"difficulty":1.8979053497}
-{"premise":"There are three persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 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 Penny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Penny","Cindy","Belinda"],"index":19312,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998382926,"difficulty":0.001617074}
-{"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 John. Jennifer's card is shown to John. Jennifer's card is shown to Benjamin. John's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that John picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card. It is publicly announced that Jennifer does not know whether Benjamin 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 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":"Benjamin can now know that John can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Benjamin","Jennifer"],"index":11520,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6917074323,"difficulty":1.6917074323}
-{"premise":"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 Carla 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)) ] (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 3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Charles can now know that Carla's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carla","Irma","Charles"],"index":63318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.803881526,"difficulty":0.196118474}
-{"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 Sanjuanita is thirsty. It is publicly announced that Dorothy is thirsty. It is publicly announced that Sanjuanita 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|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":"Dorothy can now know that Nancy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Dorothy","Sanjuanita"],"index":9754,"s-l":"internal-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 Jerrell knows whether Jerrell's forehead is muddy. It is publicly announced that Lottie knows whether Jerrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Jerrell can now know that Lottie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lottie","Jerrell","Stasia","Ruth"],"index":41127,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998331368,"difficulty":0.001668632}
-{"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) ] [ ! ~(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) ] [ ! ~(1) ] 0","hypothesis":"Alana can now know whether Raymond can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Deidra","Johnnie","Alana"],"index":39240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5420043468,"difficulty":0.4579956532}
-{"premise":"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. 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 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":"Nicholas can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricky","Kathleen","Nicholas","Robert"],"index":15254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924082756,"difficulty":0.0075917244}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Regina does not know whether Robert is thirsty. It is publicly announced that Robert does not know whether Regina is thirsty.","smcdel_problem":"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) ] Agentc 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 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Robert can now know that Regina can know that Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Regina","Robert","Mark"],"index":16201,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953169823,"difficulty":0.0046830177}
-{"premise":"There are four persons. Everyone is visible 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 not muddy. It is publicly announced that Josephine 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 (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":"Josephine 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":["Josephine","Lillian","Harold","Jennifer"],"index":28729,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978458881,"difficulty":0.0021541119}
-{"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 Fernando. Anthony's card is shown to James. Wanda's card is shown to James. Fernando's card is shown to Anthony. James's card is shown to Anthony. James'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 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 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:2 Agentb:3,4 Agentc:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anthony can now know that Fernando can know that Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Fernando","James","Anthony","Wanda"],"index":42963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978567958,"difficulty":0.0021432042}
-{"premise":"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 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) ] [ ! ~(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":"Edgar can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Edgar"],"index":45148,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9934421778,"difficulty":0.0065578222}
-{"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 (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":"Kelly can now know whether Melisa can know that Melisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melisa","Dorothy","Andrea","Kelly"],"index":56751,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9479440451,"difficulty":0.0520559549}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether Samuel is thirsty. It is publicly announced that Linda knows whether Samuel 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 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 2) ] 0","hypothesis":"Linda can now know whether Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Linda","Samuel"],"index":58999,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990555644,"difficulty":0.0009444356}
-{"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 Allen. Debra's card is shown to Allen. Allen's card is shown to Denise. Denise's card is shown to Denise. Allen's card is shown to Debra. Denise's card is shown to Debra. It is publicly announced that someone picked a red card. It is publicly announced that Allen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Allen can now know that Trudy can know that Trudy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Allen","Denise","Trudy","Debra"],"index":56895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9264578819,"difficulty":0.0735421181}
-{"premise":"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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Clifford can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clifford","Effie","Edward","Priscilla"],"index":41709,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9923138022,"difficulty":0.0076861978}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marshall knows whether Marshall 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 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":"Marshall can now know that Donald can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Maritza","Marshall"],"index":32200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997677207,"difficulty":0.0002322793}
-{"premise":"There are two persons. Everyone is visible 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's forehead is not 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) ] [ ! ~(1) ] [ ! (Agentb knows whether 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) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know that Jo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jo","David"],"index":44239,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9923827052,"difficulty":0.0076172948}
-{"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 Robert 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 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":"Robert can now know that Kevin can know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Kevin"],"index":28962,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971374273,"difficulty":0.0028625727}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Natalie's card is shown to Jeffery. Natalie's card is shown to Staci. Staci's card is shown to Natalie. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery does not know whether or not everyone picked a red card. It is publicly announced that Staci 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 (Agentc knows that 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":"Staci can now know that Natalie can know that Jeffery picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffery","Staci","Natalie"],"index":10256,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5144587159,"difficulty":1.5144587159}
-{"premise":"There are three persons. Everyone is visible to others. 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. 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 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":"Jean can now know whether Betty can know whether Anabel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jean","Anabel","Betty"],"index":47959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994359612,"difficulty":0.0005640388}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 whether Heather can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Aubrey","Heather","Jeffrey"],"index":64173,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
-{"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 Robbie is thirsty.","smcdel_problem":"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":"Darrell can now know whether Robbie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Glen","Carl","Robbie","Darrell"],"index":44916,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7892221212,"difficulty":0.2107778788}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! (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":"Katherine can now know that Katherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Katherine","Anthony","Michelle","Victor"],"index":57918,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977282882,"difficulty":0.0022717118}
-{"premise":"There are three persons. Everyone is visible to others. 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 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":"James can now know that Patrick can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","James","Patrick"],"index":11300,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979841709,"difficulty":0.0020158291}
-{"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 or not everyone is thirsty.","smcdel_problem":"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":"Wesley can now know that Richard can know that Wesley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wesley","Richard","Joel","Jamie"],"index":18862,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9351829886,"difficulty":0.0648170114}
-{"premise":"There are four persons. Everyone is visible 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 Arthur knows whether Iris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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) ] Agenta knows that (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) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Iris can now know that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Iris","Mary","Arthur","Elizabeth"],"index":11988,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997522235,"difficulty":0.0002477765}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agenta 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:1,2,3,4 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":"Brian can now know that Arturo can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Brian","Arturo","Donna"],"index":23742,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983155727,"difficulty":0.0016844273}
-{"premise":"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) ] [ ! (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: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":"Nick can now know whether Randall can know that Brittney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brittney","Gerald","Randall","Nick"],"index":8352,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979447722,"difficulty":0.0020552278}
-{"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.","smcdel_problem":"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 (~(1|2|3|4)))","n_announcements":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":"Charles can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Joshua","Stephen","David"],"index":17640,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998259604,"difficulty":0.001740396}
-{"premise":"There are two 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 or not 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Deborah can now know that John can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Deborah","John"],"index":47500,"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 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Stephanie can now know that Kenneth can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Roger","Stephanie","Helen"],"index":65198,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955897331,"difficulty":0.0044102669}
-{"premise":"There are two 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 or not everyone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy. It is publicly announced that Marshall knows whether Christopher'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) ] 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 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Marshall can now know that Christopher can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marshall","Christopher"],"index":65283,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9887652397,"difficulty":0.0112347603}
-{"premise":"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. 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 (~(1|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 (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Benjamin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Benjamin","Charles"],"index":18616,"s-l":"forehead-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 Roy's forehead is muddy.","smcdel_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 (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":"Roy can now know whether Charles can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Adelina","Roy"],"index":29842,"s-l":"forehead_mirror-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 not everyone's forehead is muddy. It is publicly announced that Gilda'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) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Jessica can now know that Marion's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Gilda","Jessica","Travis"],"index":18464,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9872881174,"difficulty":0.0127118826}
-{"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 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 (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)) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Carol can now know whether Wanda can know that Carol is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Wanda","George","Aaron"],"index":26115,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.98041749,"difficulty":0.01958251}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vickie is not thirsty. It is publicly announced that Margaret knows whether or not everyone is thirsty. It is publicly announced that Vickie 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 (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) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Margaret can now know whether Kim can know whether Andrew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Andrew","Vickie","Kim"],"index":32861,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989638329,"difficulty":0.0010361671}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elias knows whether Kellee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Glen can now know whether Elias can know whether Elias's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andy","Elias","Glen","Kellee"],"index":12743,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.914983511,"difficulty":0.085016489}
-{"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 Barry. Rebecca's card is shown to Bryce. Bryce'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:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 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":"Bryce can now know whether Rebecca picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barry","Bryce","Rebecca"],"index":19420,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.625764966,"difficulty":1.625764966}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Joan knows whether Paula's forehead is muddy. It is publicly announced that Paula 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 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)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know whether Joan can know that Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Joan","Sharon","Paula"],"index":985,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8758512139,"difficulty":1.8758512139}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathryn does not know whether Paul is thirsty. It is publicly announced that Kathryn does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agentb knows that (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 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Cherry can now know that Paul can know that Cherry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","Cherry","Kathryn"],"index":62156,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8847382069,"difficulty":0.1152617931}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randal does not know whether David is thirsty. It is publicly announced that David does not know whether Robert is thirsty. It is publicly announced that Randal does not know whether David is thirsty. It is publicly announced that Randal does not know 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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Randal can now know that David can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","David","Robert","Randal"],"index":27135,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9890483022,"difficulty":0.0109516978}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia does not know whether Julia'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) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Julia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denny","Julia","John"],"index":44485,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976021647,"difficulty":0.0023978353}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"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 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":"Desmond can now know that James can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Desmond","David"],"index":24646,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985369444,"difficulty":0.0014630556}
-{"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 Timothy 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) ] (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 3) ] [ ! (1&2&3&4) ] 0","hypothesis":"Walter can now know whether Walter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Walter","Rebecca","Timothy","Pamela"],"index":20921,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984544516,"difficulty":0.0015455484}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stephan's card is shown to Stephan. Owen's card is shown to Stephan. Alan's card is shown to Owen. Owen'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:1,2 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:1,2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephan","Owen","Alan"],"index":22702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983758926,"difficulty":0.0016241074}
-{"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 Quentin is thirsty. It is publicly announced that Michelle 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 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) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Michelle can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Quentin","Michelle"],"index":58561,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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|2|3|4))) ] [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Patricia can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Lynne","Charla","Patricia"],"index":20266,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993306398,"difficulty":0.0006693602}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan 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 (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":"Toni can now know that Fred can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Toni","Juan","Fred","Allie"],"index":44546,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9034125209,"difficulty":1.9034125209}
-{"premise":"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. It is publicly announced that Monica does not know whether Monica's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Laura 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Monica can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","James","Monica"],"index":24277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986568689,"difficulty":0.0013431311}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karla's card is shown to Mathew. Patricia's card is shown to Patricia. Mathew's card is shown to Karla. Patricia's card is shown to Karla. 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 (Agenta knows whether (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":"Patricia can now know whether Mathew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mathew","Patricia","Karla"],"index":56881,"s-l":"explicit-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 is thirsty.","smcdel_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 (~(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":"Peggy can now know that Nancy can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Paul","Nancy","Peggy"],"index":48884,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983264804,"difficulty":0.0016735196}
-{"premise":"There are three 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 Kent does not know whether Jackeline 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) ] (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)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Jackeline can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jackeline","Kathy","Kent"],"index":153,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970255494,"difficulty":0.0029744506}
-{"premise":"There are four persons. Everyone is visible 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 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) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Carolyn can now know that Bruce can know whether Johnny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bruce","Carolyn","Matthew","Johnny"],"index":59357,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999736011,"difficulty":0.000263989}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emma's card is shown to William. Carla's card is shown to Emma. William's card is shown to Carla. Emma's card is shown to Carla. 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) ] Agenta knows that (Agentc knows that 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":"William can now know that Carla can know that Carla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Emma","Carla"],"index":719,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9955170751,"difficulty":0.0044829249}
-{"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 Brenda. Christine's card is shown to Christine. 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 Christine 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 (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 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":"Brenda can now know whether Christine can know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brenda","Christine"],"index":16717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954511523,"difficulty":0.0045488477}
-{"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. Betty's card is shown to Stephen. Stephen's card is shown to Betty. Jena's card is shown to Betty. Betty's card is shown to Jena. Stephen's card is shown to Harriet. It is publicly announced that someone picked a red card. It is publicly announced that Betty knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Betty picked a black card. It is publicly announced that Stephen does not know whether Harriet 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) ] Agentc knows that (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":"Jena can now know that Harriet can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Betty","Jena","Harriet"],"index":55013,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"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":"Kenneth can now know that Calvin can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Norman","Calvin","Kenneth"],"index":17921,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997807145,"difficulty":0.0002192855}
-{"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 Terri is thirsty.","smcdel_problem":"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 (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 2) ] 0","hypothesis":"Tina can now know that Ralph can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ralph","Terri","John","Tina"],"index":49211,"s-l":"internal-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 John knows whether someone's forehead is muddy. It is publicly announced that Nellie 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 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":"John can now know that Nellie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Kari","Lawrence","Nellie"],"index":52245,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.565197587,"difficulty":0.434802413}
-{"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 (~(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":"Oscar can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Oscar","Celeste","Staci"],"index":2282,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981825352,"difficulty":0.0018174648}
-{"premise":"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 (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&2&3)) ] 0","hypothesis":"Brittany can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Brittany","Dwight"],"index":22065,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5221931934,"difficulty":0.4778068066}
-{"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 Pat. Elizabeth's card is shown to Jeff. Jeff's card is shown to Jeff. Jeff's card is shown to Ralph. 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 whether (Agentc knows whether 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":"Pat can now know whether Jeff can know whether Ralph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pat","Elizabeth","Jeff","Ralph"],"index":43840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982410669,"difficulty":0.0017589331}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Caleb does not know whether Jerry is thirsty. It is publicly announced that Jerry does not know whether Caleb is thirsty. It is publicly announced that Jan does not know whether or not everyone is thirsty. It is publicly announced that Jan 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 that 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":"Jerry can now know that Caleb is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerry","Jan","Caleb"],"index":32171,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6783592105,"difficulty":0.3216407895}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Natalie knows whether someone is thirsty. It is publicly announced that Shelby knows whether or not nobody is thirsty. It is publicly announced that Shelby 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)) ] [ ! (Agenta knows whether (~(1|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 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shelby can now know that Natalie can know whether Natalie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shelby","Natalie"],"index":59523,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982509017,"difficulty":0.0017490983}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vergie's card is shown to Vergie. Vickie's card is shown to Samantha. Vergie's card is shown to Samantha. 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 whether (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vergie can now know whether Vickie can know whether Vickie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vickie","Vergie","Samantha"],"index":19322,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943585992,"difficulty":0.0056414008}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samantha 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 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":"Samantha can now know whether Morgan can know that Samantha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Morgan","Samantha"],"index":7514,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9907519817,"difficulty":0.0092480183}
-{"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 James does not know whether Michael is thirsty. It is publicly announced that Charles does not know whether James is thirsty. It is publicly announced that Charles does not know whether Bobbie is thirsty.","smcdel_problem":"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 (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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"James can now know whether Bobbie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bobbie","James","Michael","Charles"],"index":43481,"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 Andrew does not know whether Andrew'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 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 (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":"James can now know whether Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","James","Andrew"],"index":59066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8855918646,"difficulty":0.1144081354}
-{"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. Julio's card is shown to Tammy. Aileen's card is shown to Tammy. Tammy's card is shown to Julio. Julio's card is shown to Julio. Tammy's card is shown to Aileen. 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) ] Agentc 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 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Aileen can now know that Tammy can know that Aileen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tammy","Julio","Aileen"],"index":13051,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967233539,"difficulty":0.0032766461}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beatrice knows whether Barbara's forehead is muddy. It is publicly announced that Richard'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 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":"Richard can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Beatrice","Richard","Barbara"],"index":33996,"s-l":"forehead_mirror-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 Edmund does not know whether Edmund's forehead is muddy. It is publicly announced that Oscar's forehead 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 (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":"Oscar can now know that Edmund can know whether Edmund's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edmund","Jorge","Oscar"],"index":51722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7963290215,"difficulty":0.2036709785}
-{"premise":"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 or not nobody'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) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 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) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Gary can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Gary"],"index":56964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8518058062,"difficulty":0.1481941938}
-{"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 Wallace is thirsty. It is publicly announced that Wallace knows whether Wallace 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) ] (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 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Micheal can now know that Gary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Micheal","Gary","Wallace"],"index":32064,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966186285,"difficulty":0.0033813715}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy knows whether Billy'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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Billy can now know that Kelli's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kelli","Billy"],"index":27926,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980660081,"difficulty":0.0019339919}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather 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 (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":"Heather can now know that Roger can know that Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Rene","Heather","Natalie"],"index":49692,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984232187,"difficulty":0.0015767813}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Grace. Grace'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 Inez 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Grace can now know that Grace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Grace","Inez"],"index":15669,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9675891399,"difficulty":1.9675891399}
-{"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 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":"Evangelina can now know that Eugene can know whether Eugene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evangelina","Eugene","Gene"],"index":64846,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938759208,"difficulty":0.0061240792}
-{"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 Leo. Keith's card is shown to Keith. John's card is shown to Keith. John's card is shown to John. Leo's card is shown to Daisy. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:1 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:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Leo can now know that Keith can know that Leo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leo","Keith","John","Daisy"],"index":49688,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5483937263,"difficulty":1.5483937263}
-{"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 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) ] [ ! ~(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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Craig can now know whether Annie can know that Adam is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Craig","Annie","Nancy","Adam"],"index":15226,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9930832386,"difficulty":0.0069167614}
-{"premise":"There are four persons. Everyone is visible 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 George's forehead is muddy. It is publicly announced that Scott'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) ] Agentc 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 3) ] [ ! ~(1) ] 0","hypothesis":"George can now know that Scott can know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Joseph","George","Teresa"],"index":6205,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9800706506,"difficulty":0.0199293494}
-{"premise":"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 Eva does not know whether Eva's forehead 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) ] (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)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Eva can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Ann","Eva"],"index":6301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941447377,"difficulty":0.0058552623}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanie's forehead is muddy. 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","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":"Jeanie can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["George","Jeanie"],"index":44048,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8806032538,"difficulty":0.1193967462}
-{"premise":"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 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:2 Agentb:1 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Richard can now know whether Angel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angel","Richard"],"index":64919,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996153116,"difficulty":0.0003846884}
-{"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 Michael. Kiera'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 Kiera 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 (1&2&3))","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":"Kiera can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kiera","Michael","Gerald"],"index":3299,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968978167,"difficulty":0.0031021833}
-{"premise":"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 knows whether Chrissy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Esther can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rocio","Esther","Chrissy","Norman"],"index":31192,"s-l":"forehead-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 is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Genevieve does not know whether Helene is 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 (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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Genevieve can now know that John can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Genevieve","Helene","John"],"index":31319,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967352748,"difficulty":0.0032647252}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcos's card is shown to Marcos. John's card is shown to Marcos. Ashley's card is shown to Ashley. Marcos's card is shown to John. Ashley'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 Marcos knows whether Marcos picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2,3 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:1,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"John can now know that Marcos can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marcos","Ashley","John"],"index":44467,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940108657,"difficulty":0.0059891343}
-{"premise":"There are two persons. Everyone is visible 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 Jennifer'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 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":"Hannah can now know that Jennifer can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jennifer","Hannah"],"index":22110,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962909222,"difficulty":0.0037090778}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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":"Robin can now know whether Benjamin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Robert","Benjamin","Shelia"],"index":22685,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9846994281,"difficulty":0.0153005719}
-{"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. Mary's card is shown to Louise. Francisco's card is shown to Francisco. Louise'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:1,3 Agentb:2 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:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Francisco can now know whether Louise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louise","Francisco","Mary"],"index":40568,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6271041632,"difficulty":0.3728958368}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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|2|3|4)) ] 0","hypothesis":"Jean can now know whether Cristina can know that Cristina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Jean","Larry","Cristina"],"index":8819,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999561727,"difficulty":0.000438273}
-{"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 Chung is thirsty. It is publicly announced that Michael 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 that (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) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Shawn can now know that Michael can know whether Chung is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shawn","Kristin","Michael","Chung"],"index":49683,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6037815213,"difficulty":0.3962184787}
-{"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. Jesse's card is shown to Linda. Jerrod's card is shown to Jerrod. 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. It is publicly announced that Jerrod 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 ] (Agentb knows whether 1)","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":"Jesse can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Jesse","Linda","Jerrod"],"index":20162,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7091971636,"difficulty":1.7091971636}
-{"premise":"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) ] [ ! ~(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:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Duane can now know whether Carolyn can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Harold","Duane"],"index":43014,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999577105,"difficulty":0.000422895}
-{"premise":"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 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":"Katherine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Beth","Katherine","William"],"index":4915,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983983636,"difficulty":0.0016016364}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Jackqueline can now know that Lawrence can know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jackqueline","Lawrence","Peggy","Rose"],"index":62193,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983479977,"difficulty":0.0016520023}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rachal's card is shown to Matt. Margaret's card is shown to Matt. Debra's card is shown to Matt. Matt's card is shown to Margaret. Margaret's card is shown to Margaret. Margaret'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:2,3,4 Agentb:1,3 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:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matt can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Matt","Rachal","Margaret","Debra"],"index":50655,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983869791,"difficulty":0.0016130209}
-{"premise":"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.","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":"Heidi can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Heidi","Michael"],"index":29382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977738261,"difficulty":0.0022261739}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Bianca. Bianca'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 Bianca does not know whether Bianca picked a red card. It is publicly announced that Bianca does not know whether Bianca 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 whether (~(1|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":"Bianca can now know whether Nancy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bianca","Nancy"],"index":38198,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997035861,"difficulty":0.0002964139}
-{"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 Ashley. Ashley's card is shown to Leonard. Ashley's card is shown to Leah. Leonard's card is shown to Leah. 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":"Ashley can now know whether Leah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ashley","Leonard","Leah"],"index":62569,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9953014851,"difficulty":0.0046985149}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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":"Levi can now know whether Marian can know whether Levi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Levi","Marian","Maria"],"index":60931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991337657,"difficulty":0.0008662343}
-{"premise":"There are four persons. Everyone is visible 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 Joshua's forehead is muddy. It is publicly announced that 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) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 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) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Richard can now know that Vicky can know whether Elizabeth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Elizabeth","Vicky","Richard"],"index":37913,"s-l":"forehead_mirror-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 is thirsty. It is publicly announced that Russell 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) ] [ ! ~(Agentb knows whether 4) ] Agenta knows whether (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 4) ] 0","hypothesis":"Dean can now know whether Thomas can know whether Gladys is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dean","Russell","Thomas","Gladys"],"index":35454,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990039468,"difficulty":0.0009960532}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Francisco. Mary's card is shown to Francisco. Francisco's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Earnest 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 (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|2|3)) ] 0","hypothesis":"Francisco can now know whether Earnest can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Earnest","Francisco","Mary"],"index":18593,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999022603,"difficulty":0.000977397}
-{"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 Helen knows whether Kimberly 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 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":"Kimberly can now know whether Helen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kimberly","Helen"],"index":60229,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9809882641,"difficulty":0.0190117359}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gladys's card is shown to Gladys. James's card is shown to Gladys. Nicholas's card is shown to Gladys. James's card is shown to James. Nicholas's card is shown to James. Gladys's card is shown to Nicholas. Darryl's card is shown to Darryl. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Darryl 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 3)","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":"Darryl can now know whether Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","James","Nicholas","Darryl"],"index":19905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8706453443,"difficulty":0.1293546557}
-{"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 Daniel is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Renee 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) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd 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) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Daniel can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Robert","Kevin","Renee"],"index":30874,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keri 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 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Fred 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":["Keri","Richard","Fred"],"index":7468,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995341301,"difficulty":0.0004658699}
-{"premise":"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 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 (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":"Debbie can now know that Jeffrey can know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debbie","Tonya","Jeffrey","Wilma"],"index":58814,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99813205,"difficulty":0.00186795}
-{"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 Angela is thirsty. It is publicly announced that Velvet 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 3) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Elizabeth","Angela","Velvet"],"index":20087,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986755252,"difficulty":0.0013244748}
-{"premise":"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 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|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":"Brandon can now know that Chad can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Brandon","Chad"],"index":41451,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977217317,"difficulty":0.0022782683}
-{"premise":"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'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 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":"Dorothea can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Susan","Dorothea","Michael","Lawrence"],"index":13730,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
-{"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 Cynthia. Charles's card is shown to Mary. Mary's card is shown to Mary. Mary'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:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 1)","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":"Cynthia can now know that Mary can know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Charles","Mary","Sharon"],"index":40945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9123696685,"difficulty":0.0876303315}
-{"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 Toni. Toni's card is shown to Toni. Jerry's card is shown to Toni. Toni'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 Agentb:1,2,3 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:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Toni can now know that Dennis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Toni","Jerry"],"index":5859,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984467626,"difficulty":0.0015532374}
-{"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 Diane is thirsty. It is publicly announced that Brett does not know whether Diane is thirsty. It is publicly announced that Vanessa does not know whether Nicolas 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 (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 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Diane can now know that Nicolas can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Diane","Nicolas","Brett","Vanessa"],"index":36112,"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 Denise 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Rebecca can now know whether Denise can know whether Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marta","Rebecca","Denise","Lisa"],"index":41609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9931771755,"difficulty":0.0068228245}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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":"Monica can now know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Monica","Elizabeth"],"index":13639,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977430105,"difficulty":0.0022569895}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eleanor's card is shown to Eleanor. Eleanor'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 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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Elizabeth can now know that Eleanor can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eleanor","Elizabeth"],"index":66564,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7233832479,"difficulty":1.7233832479}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Agnes does not know whether Agnes's forehead is muddy. It is publicly announced that Rene 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 whether (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) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Rene can now know whether Agnes can know that Rene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rene","Agnes"],"index":29917,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.885641098,"difficulty":1.885641098}
-{"premise":"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 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 2) ] Agentc 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 2) ] 0","hypothesis":"Nickolas can now know that Evelyn can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Evelyn","Andrew","Nickolas","Susan"],"index":45316,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981769323,"difficulty":0.0018230677}
-{"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. Raymond's card is shown to John. John's card is shown to Albert. Lee's card is shown to Lee. Albert's card is shown to Raymond. Lee's card is shown to Raymond. Raymond'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:1,4 Agentb:1 Agentc:3 Agentd: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:1,4 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Albert","Lee","Raymond"],"index":12517,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6863503456,"difficulty":1.6863503456}
-{"premise":"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 Gloria knows whether or not nobody's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Gloria 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":"Gloria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Gloria"],"index":15331,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975575209,"difficulty":0.0024424791}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vicki's card is shown to Dirk. Dirk's card is shown to Vicki. It is publicly announced that someone picked a red card. It is publicly announced that Dirk does not know whether Dirk 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":"Dirk can now know that Vicki can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dirk","Vicki"],"index":37835,"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'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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gail can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gail","Carol","Charles"],"index":43427,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997343421,"difficulty":0.0002656579}
-{"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 Earl. 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 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:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Earl","David","Rebecca"],"index":28267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997658134,"difficulty":0.0002341866}
-{"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 Kenneth 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)","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":"Kenneth can now know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kenneth","Michael"],"index":38375,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9908183217,"difficulty":0.0091816783}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jenifer does not know whether Suzanne is thirsty. It is publicly announced that Jennifer does not know whether Jenifer is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Robert can now know that Jenifer can know whether Jenifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jenifer","Robert","Suzanne","Jennifer"],"index":47916,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990460277,"difficulty":0.0009539723}
-{"premise":"There are four persons. Everyone is visible 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) ] 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Steven can now know that Jack can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Steven","Jack","Janet"],"index":42321,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997439981,"difficulty":0.0002560019}
-{"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 Sidney. Sidney's card is shown to Mark. Mark's card is shown to Mark. Henrietta's card is shown to Mark. Mark's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Sidney 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 (Agentc knows that (1&2&3&4))","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":"Sidney can now know that Mark can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sidney","Rebecca","Mark","Henrietta"],"index":31713,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979979396,"difficulty":0.0020020604}
-{"premise":"There are three 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.","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 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":"Michael can now know whether Abraham can know whether Doris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Abraham","Doris"],"index":20620,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989286065,"difficulty":0.0010713935}
-{"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 Jonathan is thirsty. It is publicly announced that Jonathan 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 2) ] [ ! ~(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 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rosa can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","Jonathan","Rosa","Shirley"],"index":1359,"s-l":"internal-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). Stephen's card is shown to Stephen. Joni's card is shown to Stephen. Stephen's card is shown to Joni. It is publicly announced that someone picked a red card. It is publicly announced that Will does not know whether Will 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) ] (Agenta knows whether 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":"Stephen can now know whether Joni picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Will","Joni"],"index":10734,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9226631522,"difficulty":1.9226631522}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Titus'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":"Titus can now know that Mark can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Titus"],"index":34555,"s-l":"forehead_mirror-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. It is publicly announced that James 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 James knows whether 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) ] [ ! (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 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)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Paul can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Paul","Suzanne"],"index":36921,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7577688694,"difficulty":0.2422311306}
-{"premise":"There are four persons. Everyone is visible 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 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 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) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Aaron can now know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Timothy","Aaron","Marvin"],"index":30710,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980024695,"difficulty":0.0019975305}
-{"premise":"There are three persons. Everyone is visible 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 ] 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 ] 0","hypothesis":"Penny can now know that Mary can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Patrick","Penny"],"index":62877,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996054769,"difficulty":0.0003945231}
-{"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 Sherry. Lloyd's card is shown to Theodore. Theodore's card is shown to Lloyd. 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 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":"Lloyd can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Theodore","Lloyd"],"index":36577,"s-l":"explicit-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 Kenneth 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) ] [ ! ~(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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kenneth can now know that Charlie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Kathleen","Virginia","Charlie"],"index":7425,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982891679,"difficulty":0.0017108321}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (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":"Ryan can now know that Rose can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frances","Rose","Ryan"],"index":3755,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999753058,"difficulty":0.000246942}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Dionne 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":"Dionne can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dionne","Debra"],"index":2359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981709719,"difficulty":0.0018290281}
-{"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 Clara. John's card is shown to John. Catherine's card is shown to John. Catherine's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Wayne 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) ] [ ! 4 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Clara can now know whether Clara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clara","John","Catherine","Wayne"],"index":53797,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7110053897,"difficulty":0.2889946103}
-{"premise":"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) ] (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 3) ] 0","hypothesis":"Thomas can now know that Alene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alene","Christopher","Thomas"],"index":29808,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971831441,"difficulty":0.0028168559}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"William can now know that Charles can know whether Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tammy","William","Ron","Charles"],"index":49227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995630383,"difficulty":0.0004369617}
-{"premise":"There are 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 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":"Sharon can now know whether Gladys can know whether Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Gladys","Randall","Sharon"],"index":17006,"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's forehead is muddy. It is publicly announced that Jeremy does not know whether Jeremy's forehead is muddy. It is publicly announced that Catalina knows whether Catalina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Pedro can now know that Jeremy can know that Jeremy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pedro","Carrie","Catalina","Jeremy"],"index":43562,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936705828,"difficulty":0.0063294172}
-{"premise":"There are two persons. Everyone is visible 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 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":"Lissette can now know whether Sara can know that Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lissette","Sara"],"index":34629,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999553144,"difficulty":0.000446856}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlene knows whether 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) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Debra can now know whether Charlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debra","Charlene","Paula"],"index":18853,"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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry 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 (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":"Katherine can now know whether Kerry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Eugene","Kerry","Katherine"],"index":45868,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997112155,"difficulty":0.0002887845}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leon is 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 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":"Sara can now know that Mary can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adan","Mary","Leon","Sara"],"index":46648,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9613934755,"difficulty":0.0386065245}
-{"premise":"There are three persons. Everyone is visible 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 Sol's forehead is muddy.","smcdel_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":"Sylvia can now know that Sol can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sol","Sylvia","Tracy"],"index":49797,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983472824,"difficulty":0.0016527176}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonia knows whether Ellie's forehead is muddy.","smcdel_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 (~(1|2|3)))","n_announcements":1,"pbcheck":"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":"Ellie can now know that Tonia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cheryl","Ellie","Tonia"],"index":19642,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998185575,"difficulty":0.001814425}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Consuela 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) ] [ ! ~(Agentc knows whether 1) ] Agentb 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) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Ronnie can now know whether Dorothy can know whether Vikki is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Ronnie","Consuela","Vikki"],"index":60225,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998914957,"difficulty":0.001085043}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frederick does not know whether William is thirsty. It is publicly announced that Frederick does not know whether or not everyone is thirsty. It is publicly announced that Frederick does not know 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 (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb 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 (1&2)) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"William can now know whether Frederick can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frederick","William"],"index":55823,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9904829264,"difficulty":0.0095170736}
-{"premise":"There are three persons. Everyone is visible 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 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|2|3)))","n_announcements":1,"pbcheck":"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":"Christopher can now know that Adam can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adam","Christopher","Wayne"],"index":34901,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997511506,"difficulty":0.0002488494}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teresa's card is shown to Teresa. Teresa's card is shown to Kim. Teresa's card is shown to April. Kim's card is shown to April. 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.","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 (1|2|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":"April can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Teresa","Kim","April"],"index":14686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janis's card is shown to Ronald. Bryan's card is shown to Bryan. Janis's card is shown to Janis. 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|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":"Ronald can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Bryan","Janis"],"index":41235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997612834,"difficulty":0.0002387166}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcus's card is shown to Marcus. Gia's card is shown to Marcus. Elin's card is shown to Marcus. Marcus's card is shown to Gia. Gia's card is shown to Gia. Albert's card is shown to Gia. Elin's card is shown to Gia. Marcus's card is shown to Albert. Elin's card is shown to Albert. Marcus's card is shown to Elin. It is publicly announced that someone picked a red card. It is publicly announced that Elin does not know whether Gia picked a red card. It is publicly announced that Elin does not know whether Albert picked a red card. It is publicly announced that Marcus does not know whether Albert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Albert can now know whether Gia can know whether Albert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcus","Gia","Albert","Elin"],"index":28703,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966737032,"difficulty":0.0033262968}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgia does not know whether Allan is thirsty. It is publicly announced that Georgia 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 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 3) ] [ ! ~(1) ] 0","hypothesis":"Allan can now know that Jeff can know whether Allan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Georgia","Jeff","Allan"],"index":43286,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5341739058,"difficulty":0.4658260942}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paige's card is shown to Paige. Adrianne's card is shown to Paige. Adrianne's card is shown to Darius. 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:1,2 Agentb:2 Agentc: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 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darius can now know whether Paige can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paige","Adrianne","Darius","Gregory"],"index":57548,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Debbie's card is shown to Debbie. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Debbie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Francis can now know whether Debbie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Francis","Evelyn"],"index":43875,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9819552302,"difficulty":0.0180447698}
-{"premise":"There are two 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 or not everyone's forehead is muddy. It is publicly announced that Enrique 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 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":"Enrique can now know that Celeste can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Celeste","Enrique"],"index":54442,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
-{"premise":"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 Andre does not know whether Andre'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&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 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) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"John can now know whether Marie can know whether Andre's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andre","Marie","John"],"index":62007,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994262457,"difficulty":0.0005737543}
-{"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 Bernadine. Kandi's card is shown to Bernadine. Kandi's card is shown to Joanne. Bernadine's card is shown to Kandi. Agnes's card is shown to Kandi. It is publicly announced that someone picked a red card. It is publicly announced that Joanne picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Kandi can now know that Agnes picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernadine","Joanne","Kandi","Agnes"],"index":59450,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9712923169,"difficulty":0.0287076831}
-{"premise":"There are three persons. Everyone is visible 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 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 (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) ] [ ! 2 ] [ ! (1&2&3) ] 0","hypothesis":"Raymond can now know that Nadia can know whether Nadia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Raymond","Nadia"],"index":60779,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995904565,"difficulty":0.0004095435}
-{"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 Brent. Brent's card is shown to Lauren. Herbert's card is shown to Lauren. Sarah's card is shown to Herbert. Lauren'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:2 Agentb:1,4 Agentc:2,3 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:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sarah can now know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brent","Sarah","Lauren","Herbert"],"index":59647,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9694645405,"difficulty":1.9694645405}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marci 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 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":"Samantha can now know that Clyde's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Marci","Clyde","Samantha"],"index":15280,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977983236,"difficulty":0.0022016764}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Helen can now know whether Clifford's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Clifford","Dale","Helen","Kelly"],"index":11773,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997399449,"difficulty":0.0002600551}
-{"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 (~(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":"Jeannette can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeannette","Robin","Willie"],"index":31106,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983789921,"difficulty":0.0016210079}
-{"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 Edwin. Edwin's card is shown to Donald. Donald's card is shown to Donald. Mary's card is shown to Donald. Donald's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether Donald 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) ] [ ! (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:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Edwin can now know that Mary can know that Edwin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edwin","Donald","Mary"],"index":38121,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9951785803,"difficulty":0.0048214197}
-{"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. Charlotte's card is shown to Denise. Denise's card is shown to Angela. Charlotte's card is shown to Angela. Angela's card is shown to Charlotte. 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 3)","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":"Charlotte can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denise","Angela","Charlotte"],"index":28719,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9911319613,"difficulty":0.0088680387}
-{"premise":"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. 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) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows whether (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|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Heather can now know whether Debbie can know whether Debbie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Debbie","Mabel","Heather"],"index":39325,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7343569398,"difficulty":1.7343569398}
-{"premise":"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 does not know whether Guadalupe's forehead is muddy. It is publicly announced that Winfred 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)) ] (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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Felipa can now know that Winfred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guadalupe","Winfred","Felipa","John"],"index":3353,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.696323812,"difficulty":0.303676188}
-{"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 James. James's card is shown to James. Wilbert's card is shown to James. Thomas's card is shown to Wilbert. 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 whether (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":"Thomas can now know that James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","James","Wilbert"],"index":14761,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9831526875,"difficulty":0.0168473125}
-{"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 Delbert 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 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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Andrea can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Delbert","Sarah","Andrea","James"],"index":22324,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985439777,"difficulty":0.0014560223}
-{"premise":"There are three persons. Everyone is visible 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 Araceli'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: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 (~(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":"Christopher can now know whether Blanca can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Araceli","Christopher","Blanca"],"index":41595,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999715507,"difficulty":0.000284493}
-{"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. Marie's card is shown to Jennifer. Ellen's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb 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":"Jennifer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ellen","Jennifer","Marie"],"index":64074,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997853637,"difficulty":0.0002146363}
-{"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 Frederick. Mary's card is shown to Mary. 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 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta 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":"Frederick can now know that Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frederick","Mary","James"],"index":19036,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982261062,"difficulty":0.0017738938}
-{"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 or not everyone is thirsty. It is publicly announced that Christine does not know whether Maria 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 that (Agentb 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) ] [ ! (1|2) ] 0","hypothesis":"Maria can now know that Christine can know whether Christine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","Christine"],"index":30876,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990509152,"difficulty":0.0009490848}
-{"premise":"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. 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) ] [ ! ~(Agentd knows whether (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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Donna can now know whether Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Phillip","Donna","Albert"],"index":29165,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7454238534,"difficulty":1.7454238534}
-{"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. Sara's card is shown to Ronald. Sara's card is shown to Sara. It is publicly announced that someone picked a red card. It is publicly announced that Sara 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|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":"Mark can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Ronald","Sara"],"index":10144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997057319,"difficulty":0.0002942681}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cortez's card is shown to Angla. Maurice's card is shown to Angla. Maurice's card is shown to Cortez. Angla's card is shown to Benjamin. Maurice's card is shown to Maurice. 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 3)","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":"Benjamin can now know that Benjamin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angla","Cortez","Benjamin","Maurice"],"index":32257,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979712367,"difficulty":0.0020287633}
-{"premise":"There are two persons. Everyone is visible 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'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 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":"Ella can now know that Bryan can know that Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ella","Bryan"],"index":44893,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9736708999,"difficulty":0.0263291001}
-{"premise":"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 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(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&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cesar can now know that Scott can know that Scott's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Scott","Cesar"],"index":36248,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9433261752,"difficulty":1.9433261752}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoinette 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 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":"Antoinette can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Antoinette","Jesse"],"index":57766,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997435212,"difficulty":0.0002564788}
-{"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 Lisa is thirsty. It is publicly announced that Tina 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)) ] (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 3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Lisa can now know whether Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jose","Tina","Lisa"],"index":51930,"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's forehead is muddy. It is publicly announced that Martha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Steve can now know that Melissa can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steve","Dana","Melissa","Martha"],"index":37491,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6404103637,"difficulty":1.6404103637}
-{"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 Alvin 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 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) ] [ ! (1&2&3) ] 0","hypothesis":"Alvin can now know whether John can know whether Alvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Alvin","John"],"index":11010,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986602068,"difficulty":0.0013397932}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Annie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ada","Jorge","Annie"],"index":56858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951804876,"difficulty":0.0048195124}
-{"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 Pricilla. Dean's card is shown to Dean. Julie's card is shown to Dean. Pricilla's card is shown to Melissa. Melissa's card is shown to Melissa. Julie's card is shown to Melissa. Pricilla'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 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 that (Agentc knows whether 1)","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":"Pricilla can now know that Melissa can know whether Pricilla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pricilla","Dean","Melissa","Julie"],"index":62809,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6191657186,"difficulty":1.6191657186}
-{"premise":"There are 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 (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":"Allan can now know that Willie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Allan","Willie","Gaston"],"index":59545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999766171,"difficulty":0.000233829}
-{"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. Jasper's card is shown to Susan. James's card is shown to Susan. Susan's card is shown to Jasper. Jasper's card is shown to Jasper. It is publicly announced that someone picked a red card. It is publicly announced that Jasper knows whether James 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 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 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jasper can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susan","Jasper","James"],"index":49931,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.839732945,"difficulty":1.839732945}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Helen does not know whether Helen'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 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":"Helen can now know whether Jane can know whether Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Jane"],"index":61750,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.77697891,"difficulty":0.22302109}
-{"premise":"There are four persons. Everyone is visible 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 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":"Adrian can now know whether John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bok","Adrian","Rick","John"],"index":50456,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995834231,"difficulty":0.0004165769}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrtle's card is shown to Michael. Michael's card is shown to Roger. Roger's card is shown to Roger. Michael's card is shown to Myrtle. Roger's card is shown to Myrtle. It is publicly announced that someone picked a red card. It is publicly announced that Roger knows whether Roger picked a red card. It is publicly announced that Michael does not know whether Roger 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) ] (Agentb 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":"Roger can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Roger","Myrtle"],"index":36720,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9852804542,"difficulty":0.0147195458}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lisa's card is shown to Lisa. Winston's card is shown to Lisa. Lisa's card is shown to Winston. 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 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":"Lisa can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lisa","Winston"],"index":50650,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985798597,"difficulty":0.0014201403}
-{"premise":"There are three persons. Everyone is visible 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 knows whether Alonzo's forehead is muddy.","smcdel_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 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":"Jessie can now know that Johnnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Johnnie","Alonzo"],"index":40058,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998365581,"difficulty":0.001634419}
-{"premise":"There are four persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows 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":"Lydia can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ethel","Lydia","Amber","Therese"],"index":15031,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997852445,"difficulty":0.0002147555}
-{"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 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 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)) ] [ ! (~(1&2)) ] 0","hypothesis":"Christin can now know that Thomas can know that Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christin","Thomas"],"index":47220,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9854302406,"difficulty":0.0145697594}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agentc knows whether 3) ] (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":"Betty can now know whether Ramon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cornelius","Ramon","Michael","Betty"],"index":32454,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997300506,"difficulty":0.0002699494}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Monique can now know that Genia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eva","Joanne","Monique","Genia"],"index":5446,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984200001,"difficulty":0.0015799999}
-{"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 Geraldine. Geraldine's card is shown to Roy. Dennis's card is shown to Roy. Geraldine's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Roy 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)) ] Agentb knows that (Agenta 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Roy can now know that Geraldine can know whether Dennis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geraldine","Roy","Dennis"],"index":35196,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7493456006,"difficulty":0.2506543994}
-{"premise":"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. It is publicly announced that Gerald 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 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Linda can now know that Donna can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Donna","Joyce","Linda"],"index":53954,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997259974,"difficulty":0.0002740026}
-{"premise":"There are three persons. Everyone is visible 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 not muddy. It is publicly announced that Keri 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 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":"Keri can now know that Keri's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victoria","Keri","Donald"],"index":38094,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947841763,"difficulty":0.0052158237}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Billy can now know that William can know whether Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Christine","Billy"],"index":29696,"s-l":"forehead_mirror-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). Gearldine's card is shown to Patricia. Gearldine's card is shown to John. Gearldine's card is shown to Gladys. John'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 Patricia 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 Agentc: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 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Gearldine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Gearldine","John","Gladys"],"index":65905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980304837,"difficulty":0.0019695163}
-{"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. Victoria's card is shown to Richard. Beth's card is shown to Victoria. Richard's card is shown to Beth. It is publicly announced that someone picked a red card. It is publicly announced that Edgar knows whether or not nobody picked a red card. It is publicly announced that Richard 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))) ] 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: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":"Edgar can now know that Richard can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edgar","Richard","Victoria","Beth"],"index":33429,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9064071774,"difficulty":0.0935928226}
-{"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 Laurette. Steve's card is shown to Laurette. Nicole's card is shown to Shannon. Shannon's card is shown to Shannon. Steve's card is shown to Shannon. Laurette's card is shown to Steve. Nicole's card is shown to Steve. Steve's card is shown to Steve. It is publicly announced that someone picked a red card. It is publicly announced that Shannon 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 ] Agentb knows whether (Agentc knows whether 2)","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":"Nicole can now know whether Shannon can know whether Nicole picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laurette","Nicole","Shannon","Steve"],"index":48905,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982130527,"difficulty":0.0017869473}
-{"premise":"There are three persons. Everyone is visible 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 Jeffrey's forehead is muddy.","smcdel_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 (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 3) ] 0","hypothesis":"Jeffrey can now know whether Laura can know whether Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Junior","Jeffrey"],"index":55119,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997095466,"difficulty":0.0002904534}
-{"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 Jack. Donna's card is shown to Donna. Donna'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 LAW Top OBS Agenta:3 Agentb:2 Agentc: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:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"William can now know whether Donna can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Donna","William"],"index":54791,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996826649,"difficulty":0.0003173351}
-{"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 Donald. Bernice's card is shown to Donald. Tracy's card is shown to Michael. Michael's card is shown to Bernice. Donald's card is shown to Tracy. 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:2,3 Agentb:4 Agentc:2 Agentd:1 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:2,3 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Michael","Bernice","Tracy"],"index":48248,"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 is thirsty. It is publicly announced that Matthew does not know whether Lois is thirsty. It is publicly announced that Lea does not know whether Matthew is thirsty. It is publicly announced that Matthew 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&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":"Lois can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lea","Matthew","Lois","Keith"],"index":56718,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5923597217,"difficulty":1.5923597217}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Valerie does not know whether Bernadette is thirsty. It is publicly announced that Matthew does not know whether Bernadette is thirsty. It is publicly announced that Matthew does not know whether Bernadette is thirsty.","smcdel_problem":"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) ] (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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Benjamin can now know that Benjamin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Valerie","Benjamin","Bernadette","Matthew"],"index":4614,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9919954538,"difficulty":0.0080045462}
-{"premise":"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":"Allen can now know that Sharon can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Sharon","Allen","Nathan"],"index":44458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943321943,"difficulty":0.0056678057}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Geneva 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 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) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Henry can now know that Randy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geneva","Henry","Randy"],"index":23922,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997856021,"difficulty":0.0002143979}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory knows whether Gregory 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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Gregory can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dannie","Gregory"],"index":65138,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9834165573,"difficulty":0.0165834427}
-{"premise":"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":"Alison can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elmer","Alison","Jason","James"],"index":22460,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997448325,"difficulty":0.0002551675}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wayne's card is shown to Wayne. Wayne's card is shown to Johnny. It is publicly announced that someone picked a red card. It is publicly announced that Johnny does not know whether Johnny picked a red card. It is publicly announced that Johnny 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 (~(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":"Johnny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Wayne","Johnny"],"index":61855,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984627962,"difficulty":0.0015372038}
-{"premise":"There are three persons. Everyone is visible 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 Roberta 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":"Herman can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cynthia","Herman","Roberta"],"index":36302,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981966615,"difficulty":0.0018033385}
-{"premise":"There are four 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.","smcdel_problem":"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 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":"Jennifer can now know that June is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","June","Minnie","Maude"],"index":42629,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981513619,"difficulty":0.0018486381}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyler 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 (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) ] 0","hypothesis":"Robert can now know that Joyce can know that Tyler is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tyler","Robert","Joyce"],"index":5480,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9907835722,"difficulty":0.0092164278}
-{"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 Michael 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Denis can know that Denis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Denis","David"],"index":5,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9034239054,"difficulty":0.0965760946}
-{"premise":"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 (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":"William can now know whether Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Mary","James","William"],"index":34523,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818307757,"difficulty":0.0181692243}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Ann'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) ] Agenta 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|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Ann can now know that Jimmy can know whether Dane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ann","Jimmy","Dane"],"index":28707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996061921,"difficulty":0.0003938079}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Mary knows 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (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: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":"Eric can now know that Lenora can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Eric","Lenora","Clarence"],"index":49840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9482505918,"difficulty":0.0517494082}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jordan knows whether Larry'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 Jordan knows whether Dana's forehead is muddy. It is publicly announced that Jordan 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (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) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Larry can now know whether Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jordan","Dana","David","Larry"],"index":60247,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6385079622,"difficulty":1.6385079622}
-{"premise":"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 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)","n_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":"Denise can now know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bryan","Denise","Jose"],"index":63470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978924394,"difficulty":0.0021075606}
-{"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 Warren is thirsty. It is publicly announced that Christina 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 ] 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 ] 0","hypothesis":"Warren can now know that Steven can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Warren","Christina","Steven"],"index":58490,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984253645,"difficulty":0.0015746355}
-{"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 Mark 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 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) ] 0","hypothesis":"Mark can now know whether Brandon can know whether Peggy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Peggy","Brandon"],"index":45392,"s-l":"internal-1","deberta_pred":1,"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). Herbert's card is shown to Herbert. Herbert's card is shown to Mike. Mike's card is shown to Gladys. 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:1 Agentb:1 Agentc: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:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mike can now know that Gladys picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Herbert","Mike","Gladys"],"index":45891,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996258378,"difficulty":0.003741622}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marguerite's card is shown to Marguerite. Rebecca's card is shown to Rebecca. Kathryn's card is shown to Rebecca. Marguerite's card is shown to Kathryn. 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 that 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":"Marguerite can now know that Rebecca can know that Rebecca picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marguerite","Rebecca","Kathryn"],"index":56054,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977512956,"difficulty":0.0022487044}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Albert 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 (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":"Joshua can now know that Hattie can know that Joshua is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Albert","Hattie"],"index":741,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8652514219,"difficulty":0.1347485781}
-{"premise":"There are two persons. Everyone is visible 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) ] 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&2) ] 0","hypothesis":"Tim can now know that Martin can know that Martin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tim","Martin"],"index":52946,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9950910807,"difficulty":0.0049089193}
-{"premise":"There are three persons. Everyone is visible 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 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) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Stanley can now know that Wanda can know that Thelma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","Stanley","Wanda"],"index":64257,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980796576,"difficulty":0.0019203424}
-{"premise":"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 Maria knows whether someone's forehead is muddy. It is publicly announced that Tom knows whether Kenneth'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) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (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) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Tom can now know that Maria can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Tom","Michael","Maria"],"index":31139,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9266370535,"difficulty":0.0733629465}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Domonique does not know whether Wendell is thirsty. It is publicly announced that Domonique 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 whether 3) ] Agenta 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 3) ] 0","hypothesis":"Wendell can now know that Domonique can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wendell","Domonique","Richard"],"index":43351,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941225648,"difficulty":0.0058774352}
-{"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 Mark. Carlos's card is shown to Gloria. Gloria's card is shown to Carlos. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Mark picked a red card. It is publicly announced that Gloria 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 (Agentc 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":"Mark can now know that Carlos can know whether Carlos picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Gloria","Carlos"],"index":22648,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9875850677,"difficulty":1.9875850677}
-{"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 Roy. 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:3 Agentb: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:3 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether Roy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roy","David","Anthony"],"index":12837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.610471487,"difficulty":0.389528513}
-{"premise":"There are two persons. Everyone is visible 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 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":"Tracy can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Tracy"],"index":64234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997577071,"difficulty":0.0002422929}
-{"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 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 that (Agentb knows that 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":"Betty can now know that Velda can know that Velda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","Velda"],"index":28524,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998083353,"difficulty":0.001916647}
-{"premise":"There are two persons. Everyone is visible 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 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 (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":"Mark can now know that Vanessa can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vanessa","Mark"],"index":40217,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997549653,"difficulty":0.0002450347}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danielle knows whether someone is thirsty. It is publicly announced that David knows whether David 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 (~(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":"David can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Danielle"],"index":62975,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998334825,"difficulty":0.001665175}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Blaine does not know whether Travis is thirsty. It is publicly announced that 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 3) ] [ ! 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) ] [ ! ~(Agenta knows whether 3) ] [ ! 2 ] 0","hypothesis":"Judy can now know that Laura can know that Travis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Blaine","Judy","Travis","Laura"],"index":20184,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9771220088,"difficulty":0.0228779912}
-{"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. Mary's card is shown to Helen. Mary's card is shown to Mary. Anton's card is shown to Anton. 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) ] Agentb knows that (Agentc knows that (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":"Mary can now know that Anton can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Mary","Anton"],"index":43466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983422756,"difficulty":0.0016577244}
-{"premise":"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) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd 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) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know whether Donald can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Debbie","Susan","John"],"index":26874,"s-l":"forehead-1","deberta_pred":1,"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). James's card is shown to Victor. Julie's card is shown to Victor. Julie's card is shown to James. Victor's card is shown to Julie. Susan's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that James picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Julie can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","James","Julie","Susan"],"index":59864,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9739698172,"difficulty":0.0260301828}
-{"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 (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":"Sabrina can now know whether Shawn can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adrienne","Shawn","Sabrina"],"index":63594,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997835755,"difficulty":0.0002164245}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roger does not know whether Jesus is thirsty. It is publicly announced that Jesus does not know whether Brent is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Roger can now know whether Jesus can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Roger","Brent","Jesus"],"index":66334,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9914335012,"difficulty":0.0085664988}
-{"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) ] [ ! 4 ] Agentc 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) ] [ ! 4 ] 0","hypothesis":"Jacklyn can now know that Jennifer can know whether Bobby is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jan","Bobby","Jacklyn","Jennifer"],"index":48768,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8662884235,"difficulty":0.1337115765}
-{"premise":"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 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 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Debra can now know whether Wilbur can know whether Wilbur's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wilbur","Debra","Lonnie"],"index":33924,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5651780963,"difficulty":1.5651780963}
-{"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 Anthony. Anthony's card is shown to Leroy. Luis's card is shown to Leroy. Leroy's card is shown to Loretta. Anthony's card is shown to Luis. Loretta's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Luis does not know whether Luis picked a red card. It is publicly announced that Anthony knows whether or not nobody picked a red card. It is publicly announced that Loretta 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) ] Agentd knows whether (Agentb knows that 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":"Luis can now know whether Leroy can know that Leroy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Leroy","Loretta","Luis"],"index":66354,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7277582884,"difficulty":1.7277582884}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margret's card is shown to Margret. Prudence's card is shown to Margret. Margret's card is shown to Prudence. It is publicly announced that someone picked a red card. It is publicly announced that Prudence 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 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) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Prudence can now know that Margret can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Margret","Prudence"],"index":38625,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926604033,"difficulty":0.0073395967}
-{"premise":"There are three persons. Everyone is visible 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 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 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) ] [ ! 2 ] 0","hypothesis":"Diane can now know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Fred","Cheryl"],"index":31991,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997467399,"difficulty":0.0002532601}
-{"premise":"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 knows whether Nick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] 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) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Nick can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tina","Nick","Robert","Esther"],"index":23728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9555981159,"difficulty":0.0444018841}
-{"premise":"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'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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Dona can now know whether Clara can know that Clara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dona","Charles","Virginia","Clara"],"index":21401,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8228590488,"difficulty":0.1771409512}
-{"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 or not everyone is thirsty. It is publicly announced that Jeremy 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 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) ] [ ! (~(1&2)) ] 0","hypothesis":"Jeremy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Jeremy"],"index":31492,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997745156,"difficulty":0.0002254844}
-{"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 Vernon. Vernon's card is shown to Seymour. Seymour's card is shown to Seymour. Stephen's card is shown to Seymour. 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 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vernon can now know whether Seymour picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vernon","Seymour","Stephen"],"index":25667,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7751299143,"difficulty":0.2248700857}
-{"premise":"There are three 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 LAW Top OBS Agenta:1 Agentb:2 Agentc: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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Diane can now know that Cynthia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cynthia","Diane","German"],"index":14198,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998419404,"difficulty":0.001580596}
-{"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 or not everyone is thirsty. It is publicly announced that Louis 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)) ] [ ! ~(Agentb knows whether 3) ] (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)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Pamela can now know that Rachel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rachel","Louis","Paul","Pamela"],"index":47853,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9764690995,"difficulty":0.0235309005}
-{"premise":"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'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 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 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Clarence can now know whether Sadie can know that Sadie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Sadie","Clarence"],"index":60877,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9938150644,"difficulty":0.0061849356}
-{"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 Jerry is thirsty. It is publicly announced that Jerry does not know whether or not everyone is thirsty. It is publicly announced that Nancy is thirsty. It is publicly announced that Jerry does not know whether Benny is 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) ] (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) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Shawn can now know whether Benny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benny","Shawn","Nancy","Jerry"],"index":21048,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5243513584,"difficulty":1.5243513584}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Helen can know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Robert","Amy","Helen"],"index":28575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994570613,"difficulty":0.0005429387}
-{"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 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 (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) ] [ ! 3 ] 0","hypothesis":"Robert can now know whether Judith can know that Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Carmen","Judith","Robert"],"index":19167,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9873641133,"difficulty":0.0126358867}
-{"premise":"There are three persons. Everyone is visible 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 Kyle's forehead is muddy. It is publicly announced that Rose's forehead is not muddy. It is publicly announced that Max 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) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (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 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Rose can now know that Rose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Kyle","Max"],"index":60388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.967220664,"difficulty":0.032779336}
-{"premise":"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 Paul'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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Fred can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evan","Paul","Fred"],"index":24178,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984323382,"difficulty":0.0015676618}
-{"premise":"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 (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":"Roberto can now know that Jeri can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberto","Jeri","Ruben","Deloris"],"index":40203,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945105314,"difficulty":0.0054894686}
-{"premise":"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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Otis can now know whether Jamie can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Otis","Lee","Jamie","Michael"],"index":12823,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995123148,"difficulty":0.0004876852}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank knows whether Frank is thirsty. It is publicly announced that Alvin 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) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Robert can now know whether Frank can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Robert","Alvin"],"index":5658,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9867734909,"difficulty":0.0132265091}
-{"premise":"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 knows whether Miguel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Letha can now know that Francis can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","Janis","Miguel","Letha"],"index":37871,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9879202843,"difficulty":0.0120797157}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether Michael'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 Michael's forehead is muddy. It is publicly announced that Michael knows whether Julia'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 whether (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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether Julia can know that Julia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julia","Michael"],"index":43239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8139616251,"difficulty":0.1860383749}
-{"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 Naomi is thirsty. It is publicly announced that Naomi 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))","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":"Naomi can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jose","Naomi","Jaclyn"],"index":57839,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997892976,"difficulty":0.0002107024}
-{"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. Herbert's card is shown to Kevin. Kevin's card is shown to Kevin. Barry's card is shown to Kevin. Kevin's card is shown to Barry. Barry's card is shown to Barry. 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:2,3 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:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Herbert","Kevin","Barry"],"index":40525,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
-{"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 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 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&2&3)) ] [ ! 2 ] 0","hypothesis":"Margaret can now know that William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Margaret","Verna"],"index":49350,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9879766107,"difficulty":0.0120233893}
-{"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 (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":"Mary can now know that Floyd can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Floyd","Karen","Mary"],"index":58942,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921675324,"difficulty":0.0078324676}
-{"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 or not everyone is 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 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":"Ulysses can now know that Faye can know whether Faye is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ulysses","Faye","Ruby","Donald"],"index":1107,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984217882,"difficulty":0.0015782118}
-{"premise":"There are 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":"Jason can now know whether Darlena can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlena","Travis","Nancy","Jason"],"index":34564,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997138381,"difficulty":0.0002861619}
-{"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.","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 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":"Sandra can now know whether Edward can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandra","Melissa","Edward"],"index":50794,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5462311506,"difficulty":1.5462311506}
-{"premise":"There are three persons. Everyone is visible 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 Jim 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 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":"Christie can now know whether Jim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jerome","Christie","Jim"],"index":49052,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997099042,"difficulty":0.0002900958}
-{"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 Jayne. Jayne's card is shown to Owen. It is publicly announced that someone picked a red card. It is publicly announced that Owen picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb: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:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Dana can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jayne","Dana","Owen"],"index":46167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
-{"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 Marilyn. Marilyn's card is shown to Susan. It is publicly announced that someone picked a red card. It is publicly announced that Calvin picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 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 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Marilyn can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Calvin","Marilyn","Susan"],"index":51490,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8302906156,"difficulty":0.1697093844}
-{"premise":"There are four persons. Everyone is visible 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 Gertrude knows whether Gertrude's forehead is muddy. It is publicly announced that Sarah knows whether Gertrude's forehead is muddy. It is publicly announced that Gertrude 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) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta 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":"Gertrude can now know that Sarah can know that Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Judy","Gertrude","Jason"],"index":2149,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973044395,"difficulty":0.0026955605}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Jacob can now know whether Jeremiah can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jacob","Jeremiah","Dorothy","Michael"],"index":35295,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996626377,"difficulty":0.0003373623}
-{"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 Christin. Christin's card is shown to Eugene. Eugene's card is shown to Emily. 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) ] Agentb knows that (Agentc knows whether 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":"Eugene can now know that Emily can know whether Christin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christin","Eugene","Emily"],"index":20336,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6539701819,"difficulty":0.3460298181}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Craig's card is shown to Daryl. Craig's card is shown to Craig. 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. It is publicly announced that 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:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Craig can now know whether Daryl can know that Daryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daryl","Craig"],"index":26854,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9796143174,"difficulty":0.0203856826}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brandy's card is shown to Brandy. Brandy's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Brandy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Brandy can now know that David can know whether Brandy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandy","David","Dennis"],"index":35170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973395467,"difficulty":0.0026604533}
-{"premise":"There are two persons. Everyone is visible 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.","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":"Adam can now know that Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Adam","Howard"],"index":4164,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9771654606,"difficulty":0.0228345394}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Melinda is thirsty. It is publicly announced that Marquita does not know whether Martha 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 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Martha can now know whether Martha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Melinda","Martha","Marquita"],"index":44446,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989144802,"difficulty":0.0010855198}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chris knows whether or not nobody is thirsty. It is publicly announced that Stanley 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 (~(1|2|3|4))) ] [ ! ~(Agentb knows whether 3) ] 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))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Thomas can now know that Chris can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Stanley","Brenda","Chris"],"index":860,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984177351,"difficulty":0.0015822649}
-{"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 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 1) ] Agentb knows whether (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":"Arthur can now know whether Karen can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Arthur","Michael","Daniel"],"index":22240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9922415018,"difficulty":0.0077584982}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"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":"Irma can now know that Ruth can know that Irma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruth","Irma","Steven"],"index":45161,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9204005599,"difficulty":0.0795994401}
-{"premise":"There are three persons. Everyone is visible 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 3)","n_announcements":1,"pbcheck":"VARS 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":"Edward can now know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ruth","Edward","Teresa"],"index":38864,"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. 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 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":"Jason can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Suzanne","Jason","Johnnie","Sara"],"index":59958,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997673631,"difficulty":0.0002326369}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie knows whether Gary's forehead is muddy. It is publicly announced that Annie 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 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) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Michael can now know whether Annie can know whether Annie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Annie","Michael"],"index":35055,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995902181,"difficulty":0.0004097819}
-{"premise":"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 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":"Michael can now know that Catherine can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Michael"],"index":45942,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9605673552,"difficulty":0.0394326448}
-{"premise":"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 Ellen's forehead is muddy. 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (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) ] [ ! (Agenta knows whether 2) ] [ ! (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":["John","Ellen"],"index":45630,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947012663,"difficulty":0.0052987337}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emory does not know whether or not everyone's forehead is muddy. It is publicly announced that Helga knows whether or not everyone's forehead is muddy. It is publicly announced that Emory does not know whether Emory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Emory can now know that William can know that Emory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Helga","Sheila","Emory"],"index":34673,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8304300308,"difficulty":1.8304300308}
-{"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 Joyce. Rebecca's card is shown to Joyce. Joyce's card is shown to Rebecca. Rebecca's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca 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) ] [ ! 3 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Joyce can now know whether Rodney can know that Rodney picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Joyce","Rebecca","Janet"],"index":18227,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8821001053,"difficulty":1.8821001053}
-{"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. Holly's card is shown to Holly. Sherri's card is shown to Sherri. Sherri's card is shown to Beverley. 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. It is publicly announced that Sherri does not know whether Holly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc 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 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Richard can now know whether Sherri can know whether Holly picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Holly","Sherri","Beverley"],"index":39089,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978237152,"difficulty":0.0021762848}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that John 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 (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"John can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shawn","Stephen","Patricia","John"],"index":15674,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967051148,"difficulty":0.0032948852}
-{"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 Lawrence 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(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 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Robert","Lawrence","Thomas"],"index":39931,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.630264163,"difficulty":0.369735837}
-{"premise":"There are 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)","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 Clarice can know that Johnny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Johnny","Albert","John","Clarice"],"index":65473,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986290932,"difficulty":0.0013709068}
-{"premise":"There are two persons. Everyone is visible 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 Keith 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 that (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":"Keith can now know that Laurel can know whether Laurel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Keith","Laurel"],"index":32117,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996886253,"difficulty":0.0003113747}
-{"premise":"There are four persons. Everyone is visible 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 nobody's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (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 (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Clinton can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clinton","Thomas","Ruby","Angela"],"index":31064,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985111356,"difficulty":0.0014888644}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bill's card is shown to Lynn. Lynn's card is shown to Margaret. Bill's card is shown to Margaret. Margaret's card is shown to Bill. It is publicly announced that someone picked a red card. It is publicly announced that Lynn 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 whether (Agentc knows that 2)","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":"Lynn can now know whether Bill can know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Margaret","Bill"],"index":33205,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9651818871,"difficulty":1.9651818871}
-{"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 Daniel. Daniel's card is shown to Beth. Heather's card is shown to Leslie. 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 (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":"Daniel can now know whether Heather can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Beth","Heather","Leslie"],"index":13850,"s-l":"explicit-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 John does not know whether John'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) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know whether Leroy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Leroy"],"index":61710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997107387,"difficulty":0.0002892613}
-{"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. Charles's card is shown to Edward. Oscar's card is shown to Diane. Oscar's card is shown to Charles. Diane'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:2,4 Agentb:1 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Diane can now know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oscar","Edward","Diane","Charles"],"index":11807,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5007836223,"difficulty":1.5007836223}
-{"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 Ronda. Ronda's card is shown to Sandra. Mark's card is shown to Sandra. Sandra's card is shown to Sandra. 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:3 Agentb: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:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Ronda can now know whether Mark can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronda","Mark","Sandra"],"index":38180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999710381,"difficulty":0.000289619}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marianela's card is shown to Marianela. Marianela's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Marianela knows whether Marianela 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) ] (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) ] 0","hypothesis":"Pauline can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marianela","Pauline","Edwin"],"index":48671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9444442987,"difficulty":0.0555557013}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kaye's card is shown to Emilio. Ronald's card is shown to Emilio. Ronald's card is shown to Marianne. Kaye'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:2,4 Agentb:4 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:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marianne can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emilio","Kaye","Marianne","Ronald"],"index":34908,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997683167,"difficulty":0.0002316833}
-{"premise":"There are four persons. Everyone is visible 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 knows whether Damon'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 4) ] [ ! (Agenta 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) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Damon can now know that Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maria","Scott","Samuel","Damon"],"index":21847,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9380642772,"difficulty":0.0619357228}
-{"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 Betty is thirsty. It is publicly announced that Sheila does not know whether Crystal is thirsty. It is publicly announced that Betty knows whether Betty is thirsty. It is publicly announced that Betty 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)) ] (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) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Betty can now know that Betty is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Crystal","Sheila","Lucille"],"index":51146,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8419784904,"difficulty":1.8419784904}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Kristie can now know that Stephanie can know that Kristie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristie","Lindsay","Stephanie"],"index":50939,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9025651813,"difficulty":0.0974348187}
-{"premise":"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 (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":"Paula can now know whether Beulah can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Beulah","Henry","Paula"],"index":17113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985249639,"difficulty":0.0014750361}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelle knows whether Erica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 2) ] 0","hypothesis":"Kelle can now know that Andrew can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Erica","Andrew","Kelle"],"index":41625,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984446168,"difficulty":0.0015553832}
-{"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 Shanell is thirsty.","smcdel_problem":"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 (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":"Michael can now know that Esteban can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shanell","Richard","Esteban","Michael"],"index":2105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984818101,"difficulty":0.0015181899}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Pamela's card is shown to Jesse. Ann's card is shown to Ann. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Pamela does not know whether Jesse 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 (Agenta knows that 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":"Pamela can now know whether Jesse can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Ann","Pamela"],"index":56345,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9140103459,"difficulty":0.0859896541}
-{"premise":"There are four persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Carl can now know whether Beatrice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irma","Jill","Carl","Beatrice"],"index":50267,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999720037,"difficulty":0.000279963}
-{"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. Eleanor's card is shown to James. Hubert's card is shown to James. James's card is shown to Eleanor. Eleanor's card is shown to Eleanor. Cassie's card is shown to Eleanor. Hubert's card is shown to Eleanor. James's card is shown to Cassie. Hubert's card is shown to Cassie. James's card is shown to Hubert. It is publicly announced that someone picked a red card. It is publicly announced that Hubert does not know whether Eleanor picked a red card. It is publicly announced that Hubert does not know whether Cassie picked a red card. It is publicly announced that James does not know whether Cassie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Eleanor can now know that Cassie can know whether Eleanor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Eleanor","Cassie","Hubert"],"index":36379,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8722646832,"difficulty":0.1277353168}
-{"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 Ruby 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 (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 3) ] 0","hypothesis":"Michael can now know whether Christopher can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Michael","Ruby"],"index":63997,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9754188657,"difficulty":0.0245811343}
-{"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 Otis. Julian's card is shown to Julian. John's card is shown to John. John's card is shown to Kerry. 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) ] Agenta knows that (Agentd knows that 2)","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":"Otis can now know that Kerry can know that Julian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Otis","Julian","John","Kerry"],"index":63237,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981086254,"difficulty":0.0018913746}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charmaine 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 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":"Charmaine can now know that Charmaine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Charmaine","Travis"],"index":41742,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5917797685,"difficulty":1.5917797685}
-{"premise":"There are four 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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know that Barry can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Barry","Peggy","William"],"index":8566,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9914585948,"difficulty":0.0085414052}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone 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) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Peter can now know that George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Peter","George","Helen"],"index":5464,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.850910008,"difficulty":0.149089992}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_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 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":"Jacquelyn can now know that Janice can know whether Jacquelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jacquelyn","Janice","Maureen"],"index":17446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997416139,"difficulty":0.0002583861}
-{"premise":"There are two persons. Everyone is visible 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 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":"David can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Theodore"],"index":31860,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997745156,"difficulty":0.0002254844}
-{"premise":"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 Charles 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) ] [ ! (~(1&2&3)) ] [ ! (Agenta 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) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Robert","Michael"],"index":62717,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959237576,"difficulty":0.0040762424}
-{"premise":"There are 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)","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":"Chong can now know that Thomas can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Chong","Dolores","Geneva"],"index":7505,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985226989,"difficulty":0.0014773011}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Marie can now know that Warren can know that Marie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Warren","Marie","Tori","Alice"],"index":4042,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981476068,"difficulty":0.0018523932}
-{"premise":"There are three persons. Everyone is visible 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 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 3)","n_announcements":1,"pbcheck":"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":"Janet can now know whether Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roger","James","Janet"],"index":8968,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982984662,"difficulty":0.0017015338}
-{"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 Manuel. Manuel's card is shown to Robert. Loren's card is shown to Robert. Arthur's card is shown to Robert. Robert's card is shown to Arthur. 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 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:2 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:2 Agentb:1,3,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (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":1,"names":["Manuel","Robert","Loren","Arthur"],"index":32384,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9939919114,"difficulty":0.0060080886}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Roy. 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 that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Roy can now know that Roy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roy","Andrea"],"index":50116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978969097,"difficulty":0.0021030903}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Becky'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 (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) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know that Nathan can know whether Nathan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Nathan","Becky","Robert"],"index":23568,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9683747292,"difficulty":0.0316252708}
-{"premise":"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. It is publicly announced that Glenn 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)) ] (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) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Raymond","Glenn"],"index":21475,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998113513,"difficulty":0.001886487}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela 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 (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":"Mamie can now know whether Angela can know whether Martin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martin","Angela","Mamie"],"index":15678,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999186933,"difficulty":0.000813067}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly 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 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Beverly can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Wendell","Beverly"],"index":43565,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985380173,"difficulty":0.0014619827}
-{"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 Anthony does not know whether Ronald is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Ronald does not know whether Lori 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 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 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lori","Ronald","Anthony"],"index":67524,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986248016,"difficulty":0.0013751984}
-{"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 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 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":"William can now know whether Charles can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Charles","William"],"index":39814,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997056127,"difficulty":0.0002943873}
-{"premise":"There are three persons. Everyone is visible 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 muddy. It is publicly announced that Leslie knows whether Leslie's forehead is muddy.","smcdel_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 (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 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Leslie can now know whether Peter can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorraine","Peter","Leslie"],"index":3211,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995700717,"difficulty":0.0004299283}
-{"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 Venus. Charise's card is shown to Venus. Charise's card is shown to Lorraine. Venus's card is shown to Jesus. Charise's card is shown to Charise. 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&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":"Venus can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Venus","Lorraine","Jesus","Charise"],"index":3618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9922229648,"difficulty":0.0077770352}
-{"premise":"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 knows whether or not everyone's forehead is muddy. It is publicly announced that Lauren does not know whether Lauren's forehead 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) ] 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) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stan can now know that Lauren can know that Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lauren","Stan","Gloria"],"index":21037,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7319129705,"difficulty":1.7319129705}
-{"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) ] [ ! (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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Anthony can now know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anthony","Mila","Debra"],"index":50213,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9951198101,"difficulty":0.0048801899}
-{"premise":"There are three persons. Everyone is visible 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 not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Laura'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":"Grant can now know that Laura can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grant","Laura","Robert"],"index":19548,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997833371,"difficulty":0.0002166629}
-{"premise":"There are 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":"Theresa can now know whether Danny can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Greta","Sherri","Danny","Theresa"],"index":7835,"s-l":"forehead_mirror-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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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)","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":"Suzan can now know whether Taylor can know whether Suzan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Suzan","Sheila","Taylor","Willis"],"index":64522,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981356859,"difficulty":0.0018643141}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gaylene does not know whether or not everyone is thirsty. It is publicly announced that Debra does not know whether Ruth is thirsty. It is publicly announced that Debra does not know whether or not everyone is thirsty. It is publicly announced that Gaylene does not know whether Ruth 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 (1&2&3)) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ruth can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gaylene","Debra","Ruth"],"index":63667,"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 Robyn 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 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":"Robyn can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vincent","Tyra","Robyn"],"index":61673,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912988544,"difficulty":0.0087011456}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wm's card is shown to Charles. Michael's card is shown to Charles. Charles's card is shown to Wm. Wm's card is shown to Wm. Wm's card is shown to Michael. 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:1,2 Agentc: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:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Michael can now know whether Wm picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Wm","Michael"],"index":65729,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7320919633,"difficulty":0.2679080367}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"Margaret can now know that Cory can know that Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Margaret","David","Cory"],"index":63126,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984070659,"difficulty":0.0015929341}
-{"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 John. Craig's card is shown to John. Mary's card is shown to Mary. 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:2,3 Agentb: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:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that Craig picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Mary","Craig"],"index":12787,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996113658,"difficulty":0.003886342}
-{"premise":"There are four persons. Everyone is visible 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 ] (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":"Mimi can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bonnie","Gail","Mimi","Carol"],"index":51780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997858405,"difficulty":0.0002141595}
-{"premise":"There are four persons. Everyone is visible 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'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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Kevin can now know that Jose can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Todd","Kevin","Kristi","Jose"],"index":7415,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961124063,"difficulty":0.0038875937}
-{"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 Lester. Katherine's card is shown to Lester. Lester's card is shown to Katherine. Katherine's card is shown to Katherine. Christy's card is shown to Katherine. Lester's card is shown to Christy. Jackie's card is shown to Christy. It is publicly announced that someone picked a red card. It is publicly announced that Lester picked a black card. It is publicly announced that Jackie does not know whether Katherine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jackie can now know whether Katherine can know whether Christy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lester","Katherine","Jackie","Christy"],"index":21955,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997615695,"difficulty":0.002384305}
-{"premise":"There are four persons. Everyone is visible 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":"Alice can now know that Rebecca can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alice","Rebecca","Charles","William"],"index":50059,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983891249,"difficulty":0.0016108751}
-{"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 Jennifer. Jennifer's card is shown to Michelle. 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. It is publicly announced that Michelle knows whether Michelle 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) ] 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) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Michelle can now know whether Jennifer can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Michelle"],"index":15741,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8952473402,"difficulty":0.1047526598}
-{"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 Kenneth 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) ] [ ! ~(Agenta knows whether 2) ] Agentc 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|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dewey can now know whether Mark can know that Dewey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Mark","Dewey"],"index":28115,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9194491506,"difficulty":0.0805508494}
-{"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 Jessica 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 (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 2) ] 0","hypothesis":"Jessica can now know whether John can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Jessica","Timothy"],"index":18725,"s-l":"internal-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). Florence's card is shown to Florence. Glenn's card is shown to Florence. Glenn's card is shown to Glenn. Michael's card is shown to Edgar. 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 Agentc:3 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Glenn can now know that Florence can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florence","Glenn","Michael","Edgar"],"index":4576,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998385787,"difficulty":0.001614213}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shana's card is shown to Shana. Shana's card is shown to Annie. It is publicly announced that someone picked a red card. It is publicly announced that Shana does not know whether Annie picked a red card. It is publicly announced that Shana does not know whether Annie picked a red card. It is publicly announced that Annie does not know whether or not everyone picked a red card. It is publicly announced that Shana does not know whether Annie 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 whether (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 (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Annie can now know whether Shana can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shana","Annie"],"index":65700,"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 Julius does not know whether Mark 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Rachel can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachel","Julius","Mark","Mary"],"index":13005,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9249823689,"difficulty":0.0750176311}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alex does not know whether or not everyone's forehead is muddy. It is publicly announced that Pauline knows whether someone's forehead is muddy. It is publicly announced that Alex 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 (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":"Pauline can now know whether Melissa can know that Pauline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melissa","Alex","Pauline","Robert"],"index":62567,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7932018042,"difficulty":0.2067981958}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alvina knows whether Ronald 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":"Alvina can now know that Ronald can know whether Ronald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alvina","Ronald"],"index":22353,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99874264,"difficulty":0.00125736}
-{"premise":"There are two persons. Everyone is visible 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'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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Ruby can now know that Gloria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gloria","Ruby"],"index":16152,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.970664084,"difficulty":0.029335916}
-{"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 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":"Dwayne can now know that Benjamin can know whether Harold is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Benjamin","Harold","Dwayne","James"],"index":49031,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972616434,"difficulty":0.0027383566}
-{"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 Charles is thirsty. It is publicly announced that Nancy 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))) ] Agentd 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) ] [ ! (1&2&3&4) ] [ ! 3 ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Nancy can now know whether Charles can know that Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Ruth","Charles","Nancy"],"index":16906,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963861704,"difficulty":0.0036138296}
-{"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 Pamela. Mae's card is shown to Pamela. Pamela's card is shown to Mae. Mae's card is shown to Mae. It is publicly announced that someone picked a red card. It is publicly announced that Pamela knows whether Mae 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) ] 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Pamela can now know whether Mae can know that Mae picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pamela","Mae"],"index":41378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8772711754,"difficulty":0.1227288246}
-{"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 Beverley. Franklin's card is shown to Beverley. Franklin's card is shown to Cynthia. Beverley's card is shown to Franklin. It is publicly announced that someone picked a red card. It is publicly announced that Beverley picked a red card. It is publicly announced that Franklin does not know whether or not everyone picked a red card. It is publicly announced that Franklin does not know whether Cynthia 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) ] 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:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Beverley can now know whether Franklin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverley","Cynthia","Franklin"],"index":32537,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9792366028,"difficulty":0.0207633972}
-{"premise":"There are four persons. Everyone is visible 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 Ilse's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Mark can now know that Ilse can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ilse","Mark","Katherine","Frances"],"index":823,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984195232,"difficulty":0.0015804768}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Marlene. Mary's card is shown to Marlene. Oscar's card is shown to Mary. Mary's card is shown to Oscar. It is publicly announced that someone picked a red card. It is publicly announced that Marlene 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 whether (Agenta knows that (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":"Mary can now know whether Marlene can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marlene","Mary","Oscar"],"index":469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999768436,"difficulty":0.000231564}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"James can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","James","Patricia","Larry"],"index":8918,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976922274,"difficulty":0.0023077726}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(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:1,2,3,4 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":"Alma can now know whether Ivan can know whether Ivan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alma","Ivan","Shannon","Anita"],"index":52180,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999673605,"difficulty":0.000326395}
-{"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 Gloria. Gloria's card is shown to Elizabeth. Mandy'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: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 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mandy can now know that Gloria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Mandy","Elizabeth"],"index":31997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983488321,"difficulty":0.0016511679}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karyn does not know whether Carla is thirsty. It is publicly announced that Karyn knows whether Karyn is thirsty. It is publicly announced that Carla does not know whether Karyn is thirsty. It is publicly announced that Carolyn does not know whether Karyn 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 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 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Carla can now know that Carolyn can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carla","Karyn","Carolyn"],"index":41053,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997839332,"difficulty":0.0002160668}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Candice does not know whether Dorothy is thirsty. It is publicly announced that Candice knows whether or not everyone is thirsty. It is publicly announced that Candice does not know whether Regina 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 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 (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Candice can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Candice","Dorothy","Regina"],"index":63811,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984657764,"difficulty":0.0015342236}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (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":"Pat can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shirley","Pat","Jean"],"index":43166,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997568727,"difficulty":0.0002431273}
-{"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. Darrell's card is shown to Suzanne. 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 Clarence does not know whether Suzanne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Clarence can now know whether Clarence picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Clarence","Nicholas","Suzanne"],"index":2332,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9977194667,"difficulty":1.9977194667}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harrison does not know whether Charlotte is thirsty. It is publicly announced that Caroline 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 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 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Andrew can now know whether Caroline can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Caroline","Charlotte","Harrison"],"index":56520,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993937016,"difficulty":0.0006062984}
-{"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)","n_announcements":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":"Jennie can now know that Anna can know whether Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Jennie","Eugene","Anna"],"index":30221,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9918923378,"difficulty":0.0081076622}
-{"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 Marcelle. Rosalie's card is shown to Jane. Margo's card is shown to Jane. Marcelle's card is shown to Rosalie. Jane's card is shown to Margo. Rosalie's card is shown to Margo. 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 Agentd: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 Agentb:3,4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jane can now know that Marcelle can know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcelle","Jane","Rosalie","Margo"],"index":66965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9763529897,"difficulty":0.0236470103}
-{"premise":"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 Eric knows whether or not nobody's forehead is muddy. It is publicly announced that Eric knows whether Roy'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 whether 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":"Eric can now know whether Roy can know whether Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roy","Eric"],"index":56720,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9935786724,"difficulty":0.0064213276}
-{"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. Dorothy's card is shown to Kimberly. Katherine's card is shown to Dorothy. Kimberly'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 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 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:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Katherine can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kimberly","Dorothy","Katherine"],"index":62444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997189641,"difficulty":0.0002810359}
-{"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 Scott. Scott's card is shown to Faye. Faye's card is shown to Faye. Scott's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Scott knows whether Faye picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Faye can now know that Christopher can know whether Faye picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Scott","Faye","Christopher","Guadalupe"],"index":45606,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9017184377,"difficulty":1.9017184377}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Angelica. Ralph's card is shown to Ralph. Cecile's card is shown to Ralph. Angelica's card is shown to Cecile. It is publicly announced that someone picked a red card. It is publicly announced that Cecile 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 (1|2|3|4))","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":"Ralph can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angelica","Roy","Ralph","Cecile"],"index":6993,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
-{"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 Carl. Charity's card is shown to Carl. Carl's card is shown to Charity. Charity's card is shown to Charity. 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 (Agenta 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":"Terry can now know that Carl can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carl","Terry","Charity"],"index":14112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984098673,"difficulty":0.0015901327}
-{"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. Fred's card is shown to James. Dale's card is shown to Joseph. James's card is shown to Dale. Dale's card is shown to Dale. James's card is shown to Fred. Dale'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 Fred does not know whether Joseph 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 (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:1,3 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Joseph can now know that Fred can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Joseph","Dale","Fred"],"index":30820,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9259734154,"difficulty":0.0740265846}
-{"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 Brenda. Louise's card is shown to Brenda. Kenneth's card is shown to Kenneth. Gary's card is shown to Kenneth. Brenda's card is shown to Louise. Louise's card is shown to Louise. Brenda's card is shown to Gary. Louise's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Louise 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) ] Agentb knows whether (Agentd 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":"Kenneth can now know whether Gary can know that Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Kenneth","Louise","Gary"],"index":33772,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9527429342,"difficulty":1.9527429342}
-{"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 Patrick. Victoria's card is shown to Patrick. Patrick's card is shown to Todd. Denise's card is shown to Todd. Denise's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Todd does not know whether Todd 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 whether 2) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patrick can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Todd","Victoria","Denise"],"index":66661,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8080064058,"difficulty":0.1919935942}
-{"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 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":"Jerry can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Todd","Jerry"],"index":40160,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986126423,"difficulty":0.0013873577}
-{"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 Teresa. Michael's card is shown to Teresa. Teresa's card is shown to Alice. Michael's card is shown to Alice. Teresa's card is shown to Michael. 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 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) ] 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 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Michael can now know whether Teresa can know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresa","Alice","Michael"],"index":22083,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978466034,"difficulty":0.0021533966}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henrietta knows whether Henrietta's forehead 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 (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":"Irene can now know whether Henrietta can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Irene","Nestor","Henrietta"],"index":63025,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997352958,"difficulty":0.0002647042}
-{"premise":"There are three persons. Everyone is visible 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'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 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) ] 0","hypothesis":"Clyde can now know whether David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clyde","David","Edward"],"index":26375,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995036125,"difficulty":0.0004963875}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (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":"Manuel can now know whether Danny can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Danny","Stephen","Manuel"],"index":59306,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997090697,"difficulty":0.0002909303}
-{"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.","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 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":"Ron can now know whether Javier can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ned","Javier","Ron"],"index":16232,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995575547,"difficulty":0.0004424453}
-{"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 Steve. Gretta's card is shown to Gretta. 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 (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":"Gretta can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Steve","Gretta","Annie"],"index":6272,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985067248,"difficulty":0.0014932752}
-{"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. Herminia's card is shown to Herminia. Marcia's card is shown to Herminia. Herminia's card is shown to Marcia. Herminia'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 Agentb:2,3 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 2)","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":"Billy can now know whether Marcia can know whether Herminia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Herminia","Marcia","Billy"],"index":46378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981842637,"difficulty":0.0018157363}
-{"premise":"There are four persons. Everyone is visible 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 Wesley's forehead is muddy. It is publicly announced that Wesley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 3) ] [ ! 3 ] 0","hypothesis":"Wesley can now know that Brian can know that Wesley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tina","Brian","Wesley","Sandra"],"index":63272,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.5938202143,"difficulty":0.4061797857}
-{"premise":"There are four persons. Everyone is visible 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 Margaret knows whether Monte's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Margaret can now know that Monte can know that Melba's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Monte","Melba","Margaret","Lesley"],"index":52327,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975845814,"difficulty":0.0024154186}
-{"premise":"There are four persons. Everyone is visible 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 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":"Monica can now know that Alice can know whether Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Daniel","Alice","Monica"],"index":23383,"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. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Alice. Shannon's card is shown to Lashawnda. Alice's card is shown to Shannon. Lashawnda's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Alice does not know whether Alice 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) ] Agentb knows that (Agentc knows that 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":"Lashawnda can now know that Shannon can know that Shannon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Lashawnda","Shannon"],"index":30184,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9363413453,"difficulty":0.0636586547}
-{"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 (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":"Julio can now know that Ruth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Julio","Barbara"],"index":34112,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997476935,"difficulty":0.0002523065}
-{"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 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) ] [ ! ~(Agenta 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Vicki can now know that Juanita can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Juanita","Vicki","Daniel"],"index":20044,"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 Jacquelin knows whether or not nobody is thirsty. It is publicly announced that Jacquelin is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(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|2))) ] [ ! ~(2) ] 0","hypothesis":"Wesley can now know whether Jacquelin can know whether Wesley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Wesley","Jacquelin"],"index":3871,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998072505,"difficulty":0.001927495}
-{"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 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 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":"Matthew can now know that Lloyd is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margaret","Michael","Matthew","Lloyd"],"index":51312,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984362721,"difficulty":0.0015637279}
-{"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. Latoya's card is shown to Sam. Mary's card is shown to Latoya. Sam'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:2 Agentb:4 Agentc:1,3 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:2 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sam can now know that Louis can know whether Latoya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Louis","Sam","Latoya"],"index":25073,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8213190436,"difficulty":1.8213190436}
-{"premise":"There are two persons. Everyone is visible 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 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 (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":"Deborah can now know whether Gail can know that Deborah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Deborah","Gail"],"index":14255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994878769,"difficulty":0.0005121231}
-{"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 William. William's card is shown to Aaron. It is publicly announced that someone picked a red card. It is publicly announced that Victor picked a black 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)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 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":["Victor","William","Aaron"],"index":3481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997254014,"difficulty":0.0002745986}
-{"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 Betty. Sheila's card is shown to Jose. Sheila's card is shown to Sandy. 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 (Agentb knows whether 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":"Sandy can now know whether Jose can know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Jose","Sandy","Sheila"],"index":66609,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987257123,"difficulty":0.0012742877}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kara 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 (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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Carolyn can now know that Kara can know whether Kara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chris","Peggy","Carolyn","Kara"],"index":38682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995884299,"difficulty":0.0004115701}
-{"premise":"There are four persons. Everyone is visible 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 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 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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Mary can now know whether Madeline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Nicholas","Barbara","Madeline"],"index":3532,"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 Ryan knows whether Ryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Michael can now know that Ryan can know that Ryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Thomas","Ryan","Peggy"],"index":26239,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974309802,"difficulty":0.0025690198}
-{"premise":"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's forehead is muddy. It is publicly announced that Barbara 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 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":"Barbara can now know that Edward can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Edward","Barbara"],"index":29835,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859879613,"difficulty":0.0140120387}
-{"premise":"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 not muddy. It is publicly announced that Timothy 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 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":"Timothy can now know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Timothy","Gail"],"index":16626,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9743767381,"difficulty":0.0256232619}
-{"premise":"There are three persons. Everyone is visible 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 knows whether Brian's forehead is muddy. It is publicly announced that Esther's forehead is not muddy. 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 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)","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":"Brian can now know that Marlon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marlon","Brian","Esther"],"index":26822,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937858582,"difficulty":0.0062141418}
-{"premise":"There are three persons. Everyone is visible 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 Craig 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)","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":"Monica can now know that Craig's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Craig","William","Monica"],"index":30014,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947815537,"difficulty":0.0052184463}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christin's card is shown to Christin. George's card is shown to Christin. Christin's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Christin 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 (1&2&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":"Warren can now know that Christin can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Warren","Christin","George"],"index":1381,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9779734015,"difficulty":0.0220265985}
-{"premise":"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. It is publicly announced that Linda 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 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":"Vicki can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robin","Vicki","Linda"],"index":51448,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hope is thirsty. It is publicly announced that William 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))) ] Agentb 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) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Audrey can now know that William can know that Audrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Audrey","Hope","Vanessa"],"index":64066,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9710908532,"difficulty":0.0289091468}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cecil's card is shown to Anna. Cecil's card is shown to Cecil. Cecil'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. 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)) ] Agentb knows whether (Agenta 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":"Cecil can now know whether Anna can know whether Cecil picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anna","Cecil","James"],"index":5280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986197948,"difficulty":0.0013802052}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick'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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Victor can now know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joe","Frederick","Frances","Victor"],"index":2752,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966337085,"difficulty":0.0033662915}
-{"premise":"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'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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Paula can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paula","James"],"index":30767,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5290341377,"difficulty":0.4709658623}
-{"premise":"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)","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 Sherilyn can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Sherilyn"],"index":44699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988534451,"difficulty":0.0011465549}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hoa does not know whether Hoa's forehead 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 3)","n_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":"Richard can now know that Hoa can know that Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Hoa","Joanne"],"index":9866,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974631071,"difficulty":0.0025368929}
-{"premise":"There are 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":"Herbert can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Herbert","Nancy","Pat","Pete"],"index":44876,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999771893,"difficulty":0.000228107}
-{"premise":"There are three 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.","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 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":"Alicia can now know that Eric can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Alicia","Karen"],"index":29942,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980624318,"difficulty":0.0019375682}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cory does not know whether Irma is thirsty. It is publicly announced that Vicente does not know whether Beverly is thirsty. It is publicly announced that Beverly does not know whether Cory is thirsty. It is publicly announced that Cory 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)) ] (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) ] [ ! ~(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 whether Cory is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vicente","Irma","Cory","Beverly"],"index":13451,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8057928085,"difficulty":0.1942071915}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances 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 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) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tony can now know that Larry can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Larry","Tony","Marcus"],"index":57159,"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's forehead is muddy. It is publicly announced that Beatriz knows whether or not nobody's forehead is muddy. It is publicly announced that Beatriz 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)) ] (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 (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Beatriz can now know whether Beatriz's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Max","Kenneth","Sharon","Beatriz"],"index":17897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6257203221,"difficulty":0.3742796779}
-{"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 David 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether Billy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","John","Billy","Dawn"],"index":15001,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9911876917,"difficulty":0.0088123083}
-{"premise":"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 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 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":"Israel can now know that David can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Israel","David","Joseph","Charles"],"index":64681,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997839272,"difficulty":0.002160728}
-{"premise":"There are three persons. Everyone is visible to others. 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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 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) ] [ ! 2 ] 0","hypothesis":"Richard can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Vernon","Marcus"],"index":64320,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5140815973,"difficulty":1.5140815973}
-{"premise":"There are three persons. Everyone is visible 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 Melanie's forehead is muddy.","smcdel_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 (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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Melanie can now know that Jean can know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","Mary","Melanie"],"index":53817,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984219074,"difficulty":0.0015780926}
-{"premise":"There are four 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 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 (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":"Jong can now know that Carol can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jong","Pearl","Paul","Carol"],"index":12241,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7184535861,"difficulty":1.7184535861}
-{"premise":"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's forehead is not muddy. It is publicly announced that Ann 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)) ] (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) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Micah","Daniel","Susan","Ann"],"index":19744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982705116,"difficulty":0.0017294884}
-{"premise":"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 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 (~(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":"Mary can now know that Joseph can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Charles","Mary"],"index":47821,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
-{"premise":"There are three persons. Everyone is visible 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 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":"George can now know that Charles can know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Charles","Marie"],"index":51408,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9909415841,"difficulty":0.0090584159}
-{"premise":"There are two persons. Everyone is visible 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 Joseph'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 ] 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) ] [ ! 1 ] 0","hypothesis":"Lynn can now know whether Joseph can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Lynn"],"index":42496,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997448325,"difficulty":0.0002551675}
-{"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 Eleanor is thirsty. It is publicly announced that Eleanor 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Paul can now know whether Maria can know that Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Paul","Eleanor","Juan"],"index":57038,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.989251554,"difficulty":0.010748446}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allen'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 whether (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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ronald can now know whether Andrew can know that Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Andrew","Ronald","James"],"index":57850,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996896982,"difficulty":0.0003103018}
-{"premise":"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 James'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 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 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":"Lisa can now know that Linda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Lisa","Linda"],"index":4834,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9916709661,"difficulty":0.0083290339}
-{"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 Bertha 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(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: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":"Charles can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","John","Bertha","Joyce"],"index":65611,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9184778333,"difficulty":0.0815221667}
-{"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 Cheryl. Cheryl'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 Dorothy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 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:1 Agentb:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Cheryl can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Cheryl","William","Adam"],"index":54266,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6850787997,"difficulty":1.6850787997}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ollie does not know whether Ollie's forehead is muddy. It is publicly announced that Boris knows whether Ollie's forehead is muddy. It is publicly announced that Boris does not know whether Boris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nick can now know that Diane can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nick","Diane","Boris","Ollie"],"index":7305,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983496666,"difficulty":0.0016503334}
-{"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 Erik is thirsty. It is publicly announced that Stephen does not know whether Tina 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 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":"Stephen can now know whether Stephen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Erik","Tina","Stephen"],"index":60871,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986770749,"difficulty":0.0013229251}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deann 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)) ] 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 (1|2|3|4)) ] 0","hypothesis":"Gail can now know whether Deann can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deann","Stephen","Gail","Joseph"],"index":14776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894633293,"difficulty":0.0105366707}
-{"premise":"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 does not know whether Michelle'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)","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":"Michelle can now know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michelle","Tina"],"index":40776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944185019,"difficulty":0.0055814981}
-{"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 (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":"Frederick can now know that Christopher can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Frederick","Francis","Candy"],"index":44069,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997141957,"difficulty":0.0002858043}
-{"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 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 (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":"Terrance can now know whether Esther can know whether Terrance is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terrance","Esther","Elisa","George"],"index":49273,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978262782,"difficulty":0.0021737218}
-{"premise":"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 does not know whether Edward'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) ] [ ! ~(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 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Edward can now know that Billy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Billy","Vera","Edward"],"index":52662,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984437823,"difficulty":0.0015562177}
-{"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 Lesley 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 (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":"Gayle can now know whether Mary can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lesley","Mary","Gayle"],"index":15002,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995019436,"difficulty":0.0004980564}
-{"premise":"There are two 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 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":"Francisco can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kathleen","Francisco"],"index":19746,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955703616,"difficulty":0.0044296384}
-{"premise":"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) ] 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) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Holly can now know that Robert can know that Wendy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Robert","Roger","Holly"],"index":11710,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979288578,"difficulty":0.0020711422}
-{"premise":"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 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) ] [ ! (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":"Marjorie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Marjorie","Teresa"],"index":51175,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996830225,"difficulty":0.0003169775}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie is thirsty. It is publicly announced that Waylon 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)) ] (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) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nancy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Annie","Linda","Waylon"],"index":31614,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5853280425,"difficulty":1.5853280425}
-{"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 Diana. Diana's card is shown to Tracie. Ann's card is shown to Tracie. 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) ] (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tracie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diana","Tracie","Ann"],"index":15526,"s-l":"explicit-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 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 Wayne 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 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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mark can now know that Michael can know whether Wayne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Wayne","Michael"],"index":4000,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8926370144,"difficulty":0.1073629856}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fannie does not know whether or not everyone is thirsty. It is publicly announced that Fannie knows whether Fannie 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) ] Agentc knows whether (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)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jolene can now know whether Fannie can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Fannie","Jolene"],"index":21424,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9931384921,"difficulty":0.0068615079}
-{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that William'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 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) ] [ ! 1 ] 0","hypothesis":"William can now know whether Evelyn can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Evelyn"],"index":15446,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995378256,"difficulty":0.0004621744}
-{"premise":"There are four persons. Everyone is visible 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 Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Mildred can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mildred","Deborah","Hae","Maria"],"index":50986,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997532964,"difficulty":0.0002467036}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marla's card is shown to Candace. Marla's card is shown to Dawn. Jeffrey's card is shown to Jeffrey. Jeffrey's card is shown to Marla. 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 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:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dawn can now know that Marla can know whether Candace picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Candace","Dawn","Jeffrey","Marla"],"index":49651,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8734132648,"difficulty":0.1265867352}
-{"premise":"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 Nettie knows whether Nettie'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 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 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nettie can now know that Sharon can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Nettie","Dana"],"index":36822,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8604218364,"difficulty":1.8604218364}
-{"premise":"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 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 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":"Jerome can now know that Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tiffany","Jacqueline","Willie","Jerome"],"index":16924,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983152151,"difficulty":0.0016847849}
-{"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 (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":"Bryan can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pauline","William","Bryan"],"index":20426,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971513152,"difficulty":0.0028486848}
-{"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 or not everyone is thirsty. It is publicly announced that Linda is thirsty. It is publicly announced that Rosemary 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)) ] (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 (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jarrod can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jarrod","Rosemary","Linda","Rose"],"index":64521,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9360585809,"difficulty":1.9360585809}
-{"premise":"There are three persons. Everyone is visible 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|2|3)))","n_announcements":1,"pbcheck":"VARS 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 nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Kathy","Dustin"],"index":66307,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9933986664,"difficulty":0.0066013336}
-{"premise":"There are four persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Marion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Sara","Dorothy","Virgil"],"index":13997,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9581347704,"difficulty":0.0418652296}
-{"premise":"There are four persons. Everyone is visible 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 Robert's forehead is muddy. It is publicly announced that Ronnie knows whether Robert's forehead is muddy. It is publicly announced that Robert knows whether 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) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentd knows that (Agentc knows that 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) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Roger can now know that Robert can know that Roger's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronnie","Janelle","Robert","Roger"],"index":27824,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973733425,"difficulty":0.0026266575}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone'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: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":"Benjamin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elvira","James","In","Benjamin"],"index":60117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997727275,"difficulty":0.0002272725}
-{"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 Emilee is thirsty.","smcdel_problem":"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 (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":"Amanda can now know whether Andres can know that Amanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Andres","Emilee","Amanda"],"index":15139,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9648160934,"difficulty":0.0351839066}
-{"premise":"There are four persons. Everyone is visible 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)) ] Agentd 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Carson can now know whether April can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","April","Rodrick","Carson"],"index":56112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996752739,"difficulty":0.0003247261}
-{"premise":"There are four persons. Everyone is visible 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 Joy'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 4) ] [ ! ~(2) ] (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 4) ] [ ! ~(2) ] 0","hypothesis":"Julia can now know that Joy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Julia","Maria","Joy"],"index":58739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9908117056,"difficulty":0.0091882944}
-{"premise":"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's forehead is muddy. It is publicly announced that Amanda'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) ] (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) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amanda","Kenneth","Maria","Stephan"],"index":55767,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6324570179,"difficulty":1.6324570179}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Stanley. Stanley's card is shown to Daniel. Daniel's card is shown to Daniel. Stanley's card is shown to Francis. 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 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 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether Stanley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stanley","Daniel","Helen","Francis"],"index":14660,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8716275692,"difficulty":1.8716275692}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beth 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))) ] (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":"Philip can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Philip","Awilda","Beth"],"index":46704,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929056168,"difficulty":0.0070943832}
-{"premise":"There are four persons. Everyone is visible 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 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 (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":"William can now know that Joan can know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joan","Esther","William","Teresa"],"index":52601,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999710381,"difficulty":0.000289619}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Moises knows whether Moises'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 (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":"Moises can now know that Alicia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alicia","Moises"],"index":37240,"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. Each person draws a card, face unrevealed (red or black). Russell's card is shown to Heidi. Michelle's card is shown to Russell. Robert's card is shown to Russell. Michelle's card is shown to Michelle. Robert's card is shown to Michelle. Russell's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Michelle does not know whether Russell picked a red card. It is publicly announced that Michelle does not know whether Russell 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: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)) ] Agentc knows that (Agentb knows whether 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":"Michelle can now know that Russell can know whether Russell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heidi","Russell","Michelle","Robert"],"index":16068,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9274314046,"difficulty":0.0725685954}
-{"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.","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 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":"Edna can now know whether Mary can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edna","John","Mary"],"index":15690,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9755858183,"difficulty":0.0244141817}
-{"premise":"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 does not know whether Earl's forehead 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":"Christopher can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Earl","Christopher","Shirley"],"index":3602,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
-{"premise":"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 knows whether or not everyone's forehead is muddy. It is publicly announced that Tina knows whether someone's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 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:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Tina can now know that Garry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Garry","Tina"],"index":23867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wynona does not know whether Wayne is thirsty. It is publicly announced that Wynona does not know whether James is thirsty. It is publicly announced that Wynona 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) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Wynona can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wayne","James","Wynona"],"index":2738,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985153079,"difficulty":0.0014846921}
-{"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. Max's card is shown to James. James's card is shown to Maryellen. Maryellen's card is shown to Maryellen. Max's card is shown to Maryellen. Maryellen's card is shown to Max. It is publicly announced that someone picked a red card. It is publicly announced that Max knows whether someone picked a red card. It is publicly announced that Maryellen 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) ] Agentc knows that (Agenta knows whether (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":"Max can now know that James can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Maryellen","Max"],"index":34597,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6938930154,"difficulty":1.6938930154}
-{"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. Thelma's card is shown to Susan. Rachelle's card is shown to Rachelle. Susan's card is shown to Thelma. Thelma's card is shown to Thelma. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether Thelma picked a red card. It is publicly announced that Brandon 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 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know that Rachelle can know whether Brandon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandon","Susan","Rachelle","Thelma"],"index":63837,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.589143157,"difficulty":1.589143157}
-{"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 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 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":"Matthew can now know that Ralph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ralph","David","Matthew","Donna"],"index":64839,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982646108,"difficulty":0.0017353892}
-{"premise":"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 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":"Lois can now know whether Priscilla can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lois","Priscilla","Robert"],"index":28510,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9970040917,"difficulty":1.9970040917}
-{"premise":"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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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 (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Arturo can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Charles","James","Arturo"],"index":6138,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6753363609,"difficulty":0.3246636391}
-{"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 Nichole. Genaro's card is shown to Bobby. Nichole's card is shown to Genaro. Genaro's card is shown to Genaro. It is publicly announced that someone picked a red card. It is publicly announced that Bobby does not know whether Nichole 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) ] (Agentb 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":"Bobby can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nichole","Bobby","Genaro"],"index":2746,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984788299,"difficulty":0.0015211701}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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 ] (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 ] 0","hypothesis":"Linda can now know whether Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pamela","Linda","Virginia","Donald"],"index":45079,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978801012,"difficulty":0.0021198988}
-{"premise":"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 Kathleen's forehead is muddy. It is publicly announced that Kathleen 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) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 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) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kathleen can now know that Linda can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Robert","Kathleen","Andra"],"index":42817,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970415235,"difficulty":0.0029584765}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeannette does not know whether Charles is thirsty. It is publicly announced that Bertha does not know whether Jeannette is thirsty. It is publicly announced that Bertha 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 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Charles can now know that Jeannette can know whether Bertha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeannette","Bertha","Charles"],"index":22408,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9905784726,"difficulty":0.0094215274}
-{"premise":"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 does not know whether Melissa's forehead is muddy. It is publicly announced that Robert 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) ] (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)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melissa can now know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Melissa","William","Ray"],"index":63367,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970672727,"difficulty":0.0029327273}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Gary can now know that Penny can know that Penny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Penny","Joel","Gary","Eric"],"index":36330,"s-l":"forehead_mirror-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). Linda's card is shown to Elizabeth. Irene's card is shown to David. David's card is shown to Linda. Irene's card is shown to Linda. Elizabeth's card is shown to Irene. David's card is shown to Irene. 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 (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irene can now know that Linda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","David","Linda","Irene"],"index":43704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bryan 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) ] 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 2) ] 0","hypothesis":"Bryan can now know whether Mark can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryan","Mark","Arthur"],"index":39436,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994149208,"difficulty":0.0005850792}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elsa's card is shown to Elsa. Steven's card is shown to Daniel. Elsa's card is shown to Raymond. Steven's card is shown to Raymond. Raymond'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:1 Agentb:4 Agentc:1,4 Agentd: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:1 Agentb:4 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know that Elsa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elsa","Daniel","Raymond","Steven"],"index":65805,"s-l":"explicit-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). Christopher's card is shown to Christopher. Christopher's card is shown to Branden. Branden's card is shown to Ronald. Ronald's card is shown to Ronald. Christopher's card is shown to Jaclyn. Jaclyn's card is shown to Jaclyn. 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 Christopher picked a red card. It is publicly announced that Christopher 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)) ] Agentd knows that (Agentb knows whether 3)","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":"Jaclyn can now know that Branden can know whether Ronald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Branden","Ronald","Jaclyn"],"index":23760,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9142730832,"difficulty":1.9142730832}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harry does not know whether Danny is thirsty. It is publicly announced that Harry does not know whether or not everyone is thirsty. It is publicly announced that Harry does not know whether or not everyone is thirsty. It is publicly announced that Danny 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 that (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)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Danny can now know that Harry can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Danny","Harry"],"index":58228,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980808496,"difficulty":0.0019191504}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether or not nobody's forehead is muddy. It is publicly announced that Lawrence's forehead is muddy. It is publicly announced that Lawrence knows whether Lawrence'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 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))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lawrence can now know whether Francisco can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lawrence","Francisco"],"index":32010,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8470034599,"difficulty":0.1529965401}
-{"premise":"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 knows whether or not nobody'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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb 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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Andrew"],"index":34949,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9940299988,"difficulty":1.9940299988}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gina's card is shown to Patricia. Gina's card is shown to Lori. Patricia's card is shown to Gina. Lori's card is shown to Gina. Gina's card is shown to Gina. It is publicly announced that someone picked a red card. It is publicly announced that Lori does not know whether or not everyone picked a red card. It is publicly announced that Lori does not know whether Lori picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know whether Lori picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Lori","Gina"],"index":36277,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.805817306,"difficulty":1.805817306}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monique 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 (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":"Helen can now know that Bianca can know that Delia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Delia","Helen","Bianca","Monique"],"index":7002,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985047579,"difficulty":0.0014952421}
-{"premise":"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 Robert knows whether Allison's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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) ] Agenta 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)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Robert can now know whether Richard can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Thomas","Richard","Allison"],"index":28301,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9960816503,"difficulty":0.0039183497}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Greg'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 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) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Greg can now know that Douglas can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terry","Douglas","Greg"],"index":59373,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
-{"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 John. Anna's card is shown to Anna. Larry's card is shown to Anna. John'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:4 Agentb:3,4 Agentc:1 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:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norman can now know that Norman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Norman","Anna","Larry"],"index":54678,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982378483,"difficulty":0.0017621517}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Anne. Anna's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Anne does not know whether Anna picked a red card.","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":"Anna can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anne","Anna"],"index":61287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bethany 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 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":"Mary can now know that Bethany can know whether Bethany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bethany","Mary"],"index":37164,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960617423,"difficulty":0.0039382577}
-{"premise":"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 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) ] [ ! (Agentd knows whether 3) ] 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) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Christopher can now know that Lisa can know that Hector's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hector","Michael","Christopher","Lisa"],"index":14574,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983820915,"difficulty":0.0016179085}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roseann 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":"Arturo can now know that James can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roseann","Arturo","James"],"index":63061,"s-l":"forehead-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 Judith 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)","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":"Marvin can now know that Judith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Judith","Marvin"],"index":53821,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983814955,"difficulty":0.0016185045}
-{"premise":"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 Della 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 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&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Valerie can now know whether John can know whether Valerie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Della","Valerie"],"index":43175,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987536669,"difficulty":0.0012463331}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (~(1&2&3)) ] [ ! 3 ] Agentc 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)) ] [ ! 3 ] 0","hypothesis":"Lauren can now know that Barbara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Jose","Lauren"],"index":11801,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978112578,"difficulty":0.0021887422}
-{"premise":"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 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ryan can now know whether Timothy can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Ryan","Timothy"],"index":42297,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984592199,"difficulty":0.0015407801}
-{"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 Eloise is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Douglas can now know that Douglas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Douglas","Eloise"],"index":4185,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9777070284,"difficulty":1.9777070284}
-{"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 Helen. Helen's card is shown to Allan. Allan's card is shown to Philip. Helen's card is shown to Michael. Allan's card is shown to Michael. Philip'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 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 1)","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":"Michael can now know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Allan","Philip","Michael"],"index":12,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.935559988,"difficulty":0.064440012}
-{"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 Christine. Mary's card is shown to Christine. Lisa's card is shown to Mary. Christine's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether or not everyone picked a red card. It is publicly announced that Christine does not know whether Mary 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) ] (Agenta 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":"Lisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Christine","Mary"],"index":62240,"s-l":"explicit-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). Dianne's card is shown to Dianne. Elena's card is shown to Dianne. Marlene's card is shown to Dianne. Elena's card is shown to Elena. Marlene's card is shown to Marlene. It is publicly announced that someone picked a red card. It is publicly announced that Elena does not know whether Marlene 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 (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":"Marlene can now know whether Elena can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dianne","Elena","Marlene"],"index":21322,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9946846366,"difficulty":0.0053153634}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vance's card is shown to Vance. Margaret's card is shown to Margaret. 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 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":"Margaret can now know that Vance can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Vance","Margaret"],"index":66116,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9875427485,"difficulty":0.0124572515}
-{"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 Paul. William's card is shown to William. William'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 William picked a black card. It is publicly announced that Gladys 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 ] Agentc 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":"Gladys can now know that Paul can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","William","Gladys"],"index":8961,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5100713968,"difficulty":1.5100713968}
-{"premise":"There are four persons. Everyone is visible 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. 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) ] [ ! (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":"Evelyn can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sarah","Willy","Gregory","Evelyn"],"index":13033,"s-l":"forehead_mirror-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 Edith'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":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Edith"],"index":53547,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967632294,"difficulty":0.0032367706}
-{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Christine knows whether Christine's forehead is muddy. It is publicly announced that Ernest 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 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Brenda can now know whether Christine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christine","Brenda","Ernest"],"index":35938,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
-{"premise":"There are two persons. Everyone is visible 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 William knows whether Joseph'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 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 2) ] [ ! (1&2) ] 0","hypothesis":"William can now know whether Joseph can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Joseph"],"index":32740,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997366071,"difficulty":0.0002633929}
-{"premise":"There are two persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that Marie'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)","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":"Brent can now know that Marie can know whether Marie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marie","Brent"],"index":50706,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996687174,"difficulty":0.0003312826}
-{"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 Carolyn. Carolyn'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 Carolyn picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 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 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Carolyn can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carolyn","Karen"],"index":64903,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985153079,"difficulty":0.0014846921}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle'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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Kimberly can now know that Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesus","Kimberly","Margaret","Danielle"],"index":24747,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9713203311,"difficulty":0.0286796689}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Naomi's card is shown to Essie. Essie's card is shown to Helen. Helen's card is shown to Helen. Naomi's card is shown to Helen. Essie'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 Helen does not know whether David 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 that 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":"Naomi can now know that Helen can know that Naomi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Essie","Helen","Naomi","David"],"index":52679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9883104563,"difficulty":0.0116895437}
-{"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. It is publicly announced that 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 (1&2&3)) ] [ ! 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)) ] [ ! 2 ] 0","hypothesis":"Steven can now know that Troy can know that Garfield is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Garfield","Steven","Troy"],"index":20309,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5792368054,"difficulty":1.5792368054}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Margaret'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: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 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":"David can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","David","Judith","Margaret"],"index":52129,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Penni'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":"Penni can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edward","Penni"],"index":31723,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997897744,"difficulty":0.0002102256}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nelson's forehead is not 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) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentb 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) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sharon can now know whether Randy can know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nelson","Sharon","Randy"],"index":30848,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5281413794,"difficulty":1.5281413794}
-{"premise":"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 Roberto'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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"David can now know whether Roberto can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roberto","David"],"index":44927,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996721745,"difficulty":0.0003278255}
-{"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. Jacquelyn's card is shown to Jacquelyn. It is publicly announced that someone picked a red card. It is publicly announced that Jacquelyn 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 (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":"John can now know that Jerry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Jerry","John","Jacquelyn"],"index":23476,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
-{"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 Aaron. Traci's card is shown to Aaron. Aaron's card is shown to Traci. Jeff's card is shown to Keith. Traci'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:2,3 Agentb:2 Agentc:1,3,4 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:2,3 Agentb:2 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeff can now know whether Aaron can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeff","Aaron","Traci","Keith"],"index":67105,"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's forehead is muddy. It is publicly announced that April knows whether someone's forehead is muddy. 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 (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Eli","April"],"index":51716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983347058,"difficulty":0.0016652942}
-{"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 Ramon is thirsty. It is publicly announced that Ramon does not know whether John is thirsty. It is publicly announced that Scott does not know whether or not everyone is thirsty. It is publicly announced that Ramon 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 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"John can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ramon","John","Scott"],"index":48835,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949702621,"difficulty":0.0050297379}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Ruth can now know whether Hayley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hayley","Kimberly","Ruth","Marisol"],"index":39481,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995908141,"difficulty":0.0004091859}
-{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Kathryn knows whether Kathryn's forehead is muddy. It is publicly announced that Nellie 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 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)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Nellie can now know that Paula's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Paula","Nellie"],"index":1700,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974595904,"difficulty":0.0025404096}
-{"premise":"There are four persons. Everyone is visible 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)) ] 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Arthur can now know that Mary can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Joseph","Nina","Arthur"],"index":58260,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99845469,"difficulty":0.00154531}
-{"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 Neal is thirsty. It is publicly announced that Wilbert knows whether Wilbert is 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 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":"Tony can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Neal","Wilbert","Samuel","Tony"],"index":25517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9891947508,"difficulty":0.0108052492}
-{"premise":"There are two 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 Judith 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 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 (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Judith can now know whether Norman can know whether Judith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Norman","Judith"],"index":16196,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970911741,"difficulty":0.0029088259}
-{"premise":"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 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)) ] (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":"Joseph can now know that Randall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bruce","Joseph","Randall"],"index":38832,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5650698543,"difficulty":1.5650698543}
-{"premise":"There are two 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. It is publicly announced that Pauline 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 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":"Pauline can now know that Pauline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Betty","Pauline"],"index":19297,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9690208435,"difficulty":1.9690208435}
-{"premise":"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 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 (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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kathleen can now know whether Danielle can know whether Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kyle","Danielle","Kathleen"],"index":64184,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6338926554,"difficulty":0.3661073446}
-{"premise":"There are three persons. Everyone is visible 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 Phillip's forehead is muddy.","smcdel_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 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":"Charles can now know that Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Samuel","Phillip"],"index":61846,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984570742,"difficulty":0.0015429258}
-{"premise":"There are four persons. Everyone is visible 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 muddy. It is publicly announced that Danny 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))) ] 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) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Danny can now know that Jacqueline can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Victor","Danny","Jacqueline","Alma"],"index":175,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984642267,"difficulty":0.0015357733}
-{"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 Willie. John's card is shown to John. 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 that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Willie can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Willie","John"],"index":11966,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976844788,"difficulty":0.0023155212}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Morgan 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 (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":"Betty can now know that Shoshana can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Morgan","Andrea","Shoshana"],"index":16452,"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 Tina does not know whether Heidi is thirsty. It is publicly announced that Arthur does not know whether John is thirsty. It is publicly announced that Arthur does not know whether Heidi is thirsty.","smcdel_problem":"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) ] (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 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Heidi","John","Tina"],"index":12818,"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 Harold knows 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 1,2,3,4 LAW Top OBS Agenta: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 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":"James can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bridgett","Harold","Brent","James"],"index":20403,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6949520707,"difficulty":0.3050479293}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Royce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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)) ] [ ! 1 ] 0","hypothesis":"Royce can now know that Marjorie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Royce","Robert","Marjorie","Alice"],"index":61624,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6042386293,"difficulty":0.3957613707}
-{"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 Charlotte is thirsty.","smcdel_problem":"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)","n_announcements":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":"Kristi can now know whether Shannon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Kristi","Charlotte","Edward"],"index":39250,"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 is thirsty. It is publicly announced that Jack 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) ] [ ! ~(Agentd 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) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jack can now know whether William can know that Jack is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Manuel","Sarah","Jack"],"index":42731,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9950704575,"difficulty":0.0049295425}
-{"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 Chelsea is thirsty. It is publicly announced that Dorothy does not know whether Chelsea is thirsty.","smcdel_problem":"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) ] (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 2) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Kathy can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Crystal","Chelsea","Kathy","Dorothy"],"index":33372,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986277819,"difficulty":0.0013722181}
-{"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 Krystyna. Krystyna's card is shown to Matthew. Matthew's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether Matthew picked a red card. It is publicly announced that Matthew does not know whether Brian 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) ] (Agentc knows that (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":"Brian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Krystyna","Matthew","Brian"],"index":11503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986097813,"difficulty":0.0013902187}
-{"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)) ] 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":"Ida can now know that Christopher can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ida","Christopher","Dorothy","Thomas"],"index":31729,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997469783,"difficulty":0.0002530217}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! ~(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":"Christina can now know that Serita can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christina","Serita","George"],"index":44628,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983413219,"difficulty":0.0016586781}
-{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Charles knows whether Sophia's forehead is muddy. It is publicly announced that Charles 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&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":"Sophia can now know that Charles can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charles","Sophia"],"index":3565,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961947203,"difficulty":0.0038052797}
-{"premise":"There are two persons. Everyone is visible 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 Jessica'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|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":"Ruth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jessica","Ruth"],"index":62560,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984351993,"difficulty":0.0015648007}
-{"premise":"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 Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Ruth can now know whether Colleen can know that Colleen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Colleen","Reginald","Ruth"],"index":32899,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9509444237,"difficulty":1.9509444237}
-{"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 Mickey is thirsty.","smcdel_problem":"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 4)","n_announcements":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":"Mickey can now know that Kenneth can know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Ruby","Mickey","Kenneth"],"index":1914,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9903552532,"difficulty":0.0096447468}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adalberto does not know whether Jennifer is thirsty. It is publicly announced that Adalberto 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 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":"Adalberto can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Adalberto","Jennifer"],"index":36458,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7585542798,"difficulty":1.7585542798}
-{"premise":"There are three persons. Everyone is visible 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 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 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 3) ] 0","hypothesis":"Virginia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frankie","Virginia","James"],"index":27842,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983139038,"difficulty":0.0016860962}
-{"premise":"There are four persons. Everyone is visible 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 Terry's forehead is muddy. It is publicly announced that Tyler 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 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":"Brenda can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Brenda","Tyler","Doris"],"index":40586,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983832836,"difficulty":0.0016167164}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniela knows whether Edith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 4) ] 0","hypothesis":"Edith can now know that Todd can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniela","Mary","Todd","Edith"],"index":12179,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984492064,"difficulty":0.0015507936}
-{"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 Mary. Angela's card is shown to Mary. Mary's card is shown to Joseph. Joseph's card is shown to Angela. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Joseph picked a black card. It is publicly announced that Joseph picked a black card. It is publicly announced that Paula knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Paula can know that Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Joseph","Paula","Angela"],"index":53971,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9775505066,"difficulty":1.9775505066}
-{"premise":"There are four 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 Lee does not know whether Thomas is thirsty. It is publicly announced that Jeniffer does not know whether Bradley 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)) ] Agentd 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeniffer can now know whether Lee can know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Bradley","Lee","Jeniffer"],"index":45899,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984770417,"difficulty":0.0015229583}
-{"premise":"There are two persons. Everyone is visible 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 Jeremy knows whether someone's forehead is muddy. It is publicly announced that Jeremy knows whether Jeremy'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":"Ada can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Ada"],"index":42286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997578263,"difficulty":0.0002421737}
-{"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. Jacob's card is shown to Jacob. 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 Jacob 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 (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|2)) ] 0","hypothesis":"Jacob can now know that Catherine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Catherine","Jacob"],"index":1608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9797567725,"difficulty":0.0202432275}
-{"premise":"There are two persons. Everyone is visible 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 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":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Kevin"],"index":50461,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998344183,"difficulty":0.001655817}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry knows whether Henry is thirsty. It is publicly announced that Rosie 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 1) ] [ ! ~(Agentb 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rosie can now know that Henry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Henry","Rosie","Helen"],"index":7058,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969944954,"difficulty":0.0030055046}
-{"premise":"There are three persons. Everyone is visible 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 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 (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 3) ] 0","hypothesis":"George can now know that Sue can know that Sue's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sue","Isaac","George"],"index":54037,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984631538,"difficulty":0.0015368462}
-{"premise":"There are two 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 Raymond does not know whether Raymond'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 that (Agentb knows whether 1)","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":"Raymond can now know that Brian can know whether Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Brian"],"index":16548,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983276725,"difficulty":0.0016723275}
-{"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. 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 (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Keith can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Richard","James","Martha"],"index":26354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997609258,"difficulty":0.0002390742}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse does not know whether Alice is thirsty. It is publicly announced that Melissa does not know whether Jesse is thirsty. It is publicly announced that Melissa 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jesse can now know whether Alice can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesse","Melissa","Alice"],"index":65815,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
-{"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 Helen. Cassandra's card is shown to William. Helen's card is shown to Cassandra. 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":"Charlie can now know that Helen can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Charlie","William","Cassandra"],"index":67130,"s-l":"explicit-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 is thirsty. It is publicly announced that Timothy 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 (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) ] [ ! 2 ] 0","hypothesis":"Renate can now know that Timothy can know that Renate is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Renate","Timothy","Kathleen"],"index":26995,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8850822449,"difficulty":0.1149177551}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karyn does not know whether Karyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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 4) ] 0","hypothesis":"Karyn can now know whether Dwight can know that Karyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Simone","Dwight","Karyn"],"index":55670,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8710438609,"difficulty":0.1289561391}
-{"premise":"There are three persons. Everyone is visible 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 Leandra'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 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) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Barbara can now know whether Keri can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keri","Leandra","Barbara"],"index":14863,"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). Rosalie's card is shown to Barbara. Rosalie's card is shown to Patricia. Debra's card is shown to Rosalie. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Barbara can now know that Patricia can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debra","Barbara","Patricia","Rosalie"],"index":53095,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7921487689,"difficulty":0.2078512311}
-{"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 Theresa is thirsty. It is publicly announced that James does not know whether Samuel is thirsty. It is publicly announced that Samuel 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&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":"James can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Samuel","Theresa","Kevin"],"index":38442,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973965883,"difficulty":0.0026034117}
-{"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 Adam. Forrest's card is shown to Forrest. Forrest's card is shown to Jennifer. Adam'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:2 Agentd:1 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:2 Agentd:1 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":["Adam","Forrest","Jennifer","James"],"index":10777,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981065989,"difficulty":0.0018934011}
-{"premise":"There are three persons. Everyone is visible 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 Nisha's forehead is muddy.","smcdel_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 (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 3) ] 0","hypothesis":"Juanita can now know that Nisha can know whether Juanita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juanita","Mary","Nisha"],"index":59836,"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). Geraldine's card is shown to Geraldine. Laurie's card is shown to Laurie. Christine's card is shown to Laurie. Laurie's card is shown to Christine. 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) ] (Agentb knows whether 2)","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":"Laurie can now know whether Laurie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geraldine","Laurie","Christine"],"index":38108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9793435335,"difficulty":0.0206564665}
-{"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 John 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)) ] (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)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lillian can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lillian","John"],"index":23444,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8912635446,"difficulty":1.8912635446}
-{"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 Raymond knows whether Robert 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)","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":"Raymond can now know that Robert can know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymond","Robert"],"index":25140,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9850177169,"difficulty":0.0149822831}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecile 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 (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":"Sherman can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Cecile","Sherman"],"index":10338,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977241158,"difficulty":0.0022758842}
-{"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 someone is thirsty. It is publicly announced that Cassandra does not know whether John is thirsty. It is publicly announced that Cassandra is thirsty. It is publicly announced that Luis 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 (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (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 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Luis can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betsy","Cassandra","John","Luis"],"index":46367,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9453080893,"difficulty":0.0546919107}
-{"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. Kenneth's card is shown to Stephen. Kimberly's card is shown to Stephen. Kenneth's card is shown to Kenneth. Kimberly'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:1,2,3 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:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kimberly can now know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephen","Kenneth","Kimberly"],"index":39880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979659319,"difficulty":0.0020340681}
-{"premise":"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. It is publicly announced that Charles 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 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":"Timothy can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Lorretta","Timothy","Paula"],"index":33753,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5354222655,"difficulty":1.5354222655}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Ross 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":["Rita","Robert","Ross"],"index":12248,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997605681,"difficulty":0.0002394319}
-{"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 Jesse. Tom's card is shown to Jesse. 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 Jesse knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Jesse can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jesse","Tom"],"index":28513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961621761,"difficulty":0.0038378239}
-{"premise":"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's forehead is not muddy. It is publicly announced that Jane 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 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":"Alvina can now know that Alvina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alvina","Thomas","Sam","Jane"],"index":60052,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992251575,"difficulty":0.007748425}
-{"premise":"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 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) ] (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":"Catherine can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Catherine","James","Chris","Steven"],"index":22600,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9902362227,"difficulty":1.9902362227}
-{"premise":"There are three persons. Everyone is visible 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 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) ] (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) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Leslie can now know whether Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leslie","Angela","Ralph"],"index":3297,"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's forehead is muddy. It is publicly announced that Nina knows whether Mark'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 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&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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Norma can now know that Nina can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Mark","Nina"],"index":7694,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9651437998,"difficulty":0.0348562002}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pam's card is shown to Thomas. Joan's card is shown to Joan. Thomas's card is shown to Barbara. Thomas's card is shown to Pam. Joan's card is shown to Pam. 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 (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":"Thomas can now know that Joan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Joan","Barbara","Pam"],"index":14960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9778617024,"difficulty":0.0221382976}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Thomas can now know that Kathryn can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Thomas","Kathryn","Cecilia"],"index":63968,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984480143,"difficulty":0.0015519857}
-{"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. Helen's card is shown to Jill. Frederick's card is shown to Jill. Beverly's card is shown to Beverly. Jill's card is shown to Frederick. 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) ] (Agentd knows that 3)","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":"Frederick can now know that Beverly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Jill","Beverly","Frederick"],"index":62675,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998263061,"difficulty":0.001736939}
-{"premise":"There are two persons. Everyone is visible 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":"Connie can now know that Cathy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cathy","Connie"],"index":45084,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983643889,"difficulty":0.0016356111}
-{"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. Frances's card is shown to Charles. Frances's card is shown to Frances. Antonio'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:1,2 Agentb:2 Agentc:3 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:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonio can now know whether Frances can know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Frances","Antonio","Nancy"],"index":34247,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8565730453,"difficulty":0.1434269547}
-{"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 Joseph. James's card is shown to Rick. Rick's card is shown to Rick. 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 Joseph does not know whether Joseph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Joseph can know that Joseph picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","James","Rick"],"index":17344,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.861337781,"difficulty":0.138662219}
-{"premise":"There are four 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 Roberto. Gloria's card is shown to Roberto. Anne's card is shown to Gloria. Donald's card is shown to Gloria. Roberto'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 Agentb:1,4 Agentc:1,2,3 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:1,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Roberto picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anne","Donald","Roberto","Gloria"],"index":41661,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5753680468,"difficulty":0.4246319532}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lavonne knows whether Lavonne's forehead is muddy. It is publicly announced that Brian'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 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) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Brian can now know that Lavonne can know whether Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnnie","Lavonne","Brian"],"index":13746,"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. 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) ] [ ! (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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Dollie can now know that Tamara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dollie","Tamara","Keith","Christopher"],"index":28505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985510707,"difficulty":0.0014489293}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether Tony is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Alisha is not thirsty. It is publicly announced that Tony 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)) ] (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 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Tony can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Douglas","Alisha","Tony","Jesse"],"index":12410,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997226596,"difficulty":0.0002773404}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn's forehead is muddy. It is publicly announced that Lori'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 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) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Doris can now know that Dawn can know whether Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Dawn","Lori","Doris"],"index":46723,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992077947,"difficulty":0.0007922053}
-{"premise":"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 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) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Gary can now know whether Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Gary","Jack"],"index":47790,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9650467634,"difficulty":0.0349532366}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie 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 (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":"Mary can now know that Jackie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Jackie"],"index":65674,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982973933,"difficulty":0.0017026067}
-{"premise":"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) ] [ ! ~(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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Michelle","Michael"],"index":67543,"s-l":"forehead-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 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) ] [ ! ~(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":"Darryl can now know that Darryl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Cindy","John","Darryl"],"index":67064,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9935045242,"difficulty":0.0064954758}
-{"premise":"There are 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 (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":"Erica can now know whether Jim can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jim","Jeffrey","Erica"],"index":13891,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997692704,"difficulty":0.0002307296}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Man 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 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 (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&2&3)) ] 0","hypothesis":"Frederick can now know whether James can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frederick","Man","James"],"index":39530,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982829094,"difficulty":0.0017170906}
-{"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":"William can now know whether Frank can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Frank","Timmy","Irene"],"index":4617,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996972084,"difficulty":0.0003027916}
-{"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 Michael. Sylvia's card is shown to Maria. Beverly's card is shown to Maria. Beverly's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Michael picked a red card. It is publicly announced that Sylvia does not know whether Michael 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) ] (Agentc 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:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maria can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sylvia","Michael","Maria","Beverly"],"index":3523,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997207522,"difficulty":0.0002792478}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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 (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":"Jacqueline can now know that Robert can know whether Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Barbara","Jacqueline"],"index":23428,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997320771,"difficulty":0.0002679229}
-{"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 John is thirsty. It is publicly announced that John does not know whether 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sandy can now know whether Ralph can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandy","Ralph","John","Adam"],"index":13719,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9891428351,"difficulty":0.0108571649}
-{"premise":"There are three persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Shelia 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|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":"Helen can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Shelia","Andrew"],"index":44491,"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 Walter 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) ] Agentb 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 3) ] 0","hypothesis":"Gayle can now know that Walter can know that Cleo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cleo","Gayle","James","Walter"],"index":16217,"s-l":"internal-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 Norman knows whether or not everyone's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Mark can now know that Alfredo can know that Alfredo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Robert","Norman","Alfredo"],"index":20794,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.62946558,"difficulty":0.37053442}
-{"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&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":"Richard can now know that John can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Jimmie","Minnie","Richard"],"index":59453,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9945703149,"difficulty":0.0054296851}
-{"premise":"There are three persons. Everyone is visible 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'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 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) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jeffery can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeremiah","Jeffery","Adam"],"index":24644,"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. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Sarah's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether Sarah 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) ] (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 1) ] [ ! (1|2) ] 0","hypothesis":"Mark can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sarah","Mark"],"index":32684,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986147881,"difficulty":0.0013852119}
-{"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 Vernon 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)","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":"Joel can now know that Vernon can know whether Mattie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mattie","Joel","Vernon"],"index":15581,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951475263,"difficulty":0.0048524737}
-{"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 Richard. Coy's card is shown to Coy. Richard's card is shown to Kimberly. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that Coy does not know whether Richard 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) ] Agenta knows that (Agentb 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":"Richard can now know that Coy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Coy","Kimberly"],"index":6670,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981321692,"difficulty":0.0018678308}
-{"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. Benton's card is shown to Joseph. May's card is shown to Joseph. Benton's card is shown to Benton. May's card is shown to Benton. Benton's card is shown to May. 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) ] (Agenta 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:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Benton","May"],"index":53116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997279048,"difficulty":0.0002720952}
-{"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 David. Kevin's card is shown to David. Vincent's card is shown to Kevin. David'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 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 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:1,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jill can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vincent","Jill","David","Kevin"],"index":52994,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997264743,"difficulty":0.0002735257}
-{"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. Jessica's card is shown to Thomas. Thomas'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:1,3 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:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robin can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Robin","Jessica"],"index":57847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997728467,"difficulty":0.0002271533}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colleen does not know whether Colleen's forehead is muddy. It is publicly announced that Colleen 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 that 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":"Patricia can now know that Colleen can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Colleen","Patricia"],"index":18794,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8000805974,"difficulty":0.1999194026}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keri's card is shown to Karl. Karl's card is shown to Keri. Keri's card is shown to Keri. Keri's card is shown to Monica. 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) ] (Agentb knows whether (~(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":"Keri can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karl","Keri","Monica"],"index":64370,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997234941,"difficulty":0.0002765059}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adrian 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)) ] 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) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know that Christopher can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Mario","Adrian","William"],"index":13832,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9653632641,"difficulty":0.0346367359}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerome knows whether Jerome's forehead is muddy. It is publicly announced that Anthony knows whether Ellen's forehead is muddy.","smcdel_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 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":"Ellen can now know that Anthony can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ellen","Jerome","Anthony"],"index":45669,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980129004,"difficulty":0.0019870996}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Craig does not know whether Kathryn is thirsty. It is publicly announced that Craig 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 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":"Gary can now know that Kathryn can know that Craig is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Craig","Gary"],"index":67442,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8752559423,"difficulty":0.1247440577}
-{"premise":"There are four persons. Everyone is visible 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 Patrick's forehead is muddy. It is publicly announced that Gene 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) ] [ ! (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":"Enrique can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Enrique","Patrick","Gene"],"index":4256,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982805252,"difficulty":0.0017194748}
-{"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. Suzan's card is shown to Suzan. Rueben's card is shown to Suzan. Rueben's card is shown to Rueben. Richard'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 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":"Janet can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Suzan","Rueben","Janet"],"index":26172,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9486598372,"difficulty":0.0513401628}
-{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jessica knows 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 (1|2|3|4)) ] [ ! (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: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":"Stanley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Betty","Stanley","Jessica"],"index":62182,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924713373,"difficulty":0.0075286627}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 2) ] Agentd knows whether (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 2) ] 0","hypothesis":"Grace can now know whether Kimberley can know whether Kimberley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Virginia","Kimberley","Grace"],"index":23596,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995986819,"difficulty":0.0004013181}
-{"premise":"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. It is publicly announced that 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] (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 (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Christopher can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","John","Christopher"],"index":29311,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9545680881,"difficulty":0.0454319119}
-{"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&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":"Lois can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrance","Fred","Sonny","Lois"],"index":16671,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984656572,"difficulty":0.0015343428}
-{"premise":"There are four persons. Everyone is visible 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 Marc 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 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":"Thomas can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Thomas","Marc","Kimberly"],"index":26449,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983774424,"difficulty":0.0016225576}
-{"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 Eric. Eric's card is shown to Sunday. It is publicly announced that someone picked a red card. It is publicly announced that Sunday 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) ] (Agentb knows whether 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":"Sunday can now know whether Sunday picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eric","Sunday"],"index":17080,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9716620445,"difficulty":1.9716620445}
-{"premise":"There are four persons. Everyone is visible 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 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":"Amber can now know that Salvador can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fay","Estelle","Amber","Salvador"],"index":2143,"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's forehead is muddy. It is publicly announced that Daina does not know whether Daina'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 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) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ralph can now know that Joe can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joe","Daina","Ralph"],"index":22794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9449759126,"difficulty":0.0550240874}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dyan does not know whether Teri is thirsty. It is publicly announced that Kathleen 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)) ] Agentb 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) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kathleen can now know that Dyan can know whether Teri is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teri","Kathleen","Kevin","Dyan"],"index":6581,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8113541603,"difficulty":0.1886458397}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Belinda's card is shown to Lisa. Donald's card is shown to Lisa. Belinda's card is shown to Beatrice. Beatrice's card is shown to Beatrice. Beatrice'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 Belinda 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 whether 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":"Belinda can now know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Belinda","Beatrice","Donald"],"index":49842,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9631119967,"difficulty":0.0368880033}
-{"premise":"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 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 (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 (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dan can now know that Clint can know whether Dan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clint","Dan","Diane"],"index":4517,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999327302,"difficulty":0.000672698}
-{"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 Joanne. Scott's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Patricia 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 3) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Joanne can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","Linda","Patricia","Scott"],"index":61327,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917572141,"difficulty":0.0082427859}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Francis can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","Helen","Robert","Thomas"],"index":37306,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984412789,"difficulty":0.0015587211}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tomas's card is shown to Kristin. Ashley's card is shown to Kristin. Kristin's card is shown to Tomas. 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:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 1)","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":"Kristin can now know that Ashley can know whether Kristin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kristin","Tomas","Ashley"],"index":25731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6652867198,"difficulty":0.3347132802}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nichole's card is shown to Betty. Betty's card is shown to Nichole. It is publicly announced that someone picked a red card. It is publicly announced that Nichole does not know whether or not everyone picked a red card. It is publicly announced that Nichole knows whether or not nobody picked a red card. It is publicly announced that Betty 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 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))) ] [ ! 1 ] 0","hypothesis":"Nichole can now know whether Betty can know that Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betty","Nichole"],"index":26766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9311510921,"difficulty":0.0688489079}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor does not know whether Eleanor's forehead is muddy. It is publicly announced that 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 (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 ] 0","hypothesis":"Eleanor can now know whether Mary can know whether Eleanor's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eleanor","Mary"],"index":15087,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979196191,"difficulty":0.0020803809}
-{"premise":"There are four persons. Everyone is visible 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 Harold's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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) ] (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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jason can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roland","Harold","Jason","Eloise"],"index":19192,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9933614731,"difficulty":0.0066385269}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Candida's card is shown to Bruce. Bruce's card is shown to Candida. Morris's card is shown to Candida. Bruce's card is shown to Morris. Candida's card is shown to Morris. Morris's card is shown to Timmy. It is publicly announced that someone picked a red card. It is publicly announced that Timmy 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 whether (Agenta knows that 2)","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":"Candida can now know whether Bruce can know that Candida picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bruce","Candida","Morris","Timmy"],"index":58653,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8544653058,"difficulty":1.8544653058}
-{"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 Francine. George's card is shown to George. George's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Francine picked a red card. It is publicly announced that Francine 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":"Richard can now know whether George can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francine","George","Richard"],"index":11648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
-{"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 Harry is thirsty. It is publicly announced that Doris 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 (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 (1&2&3&4)) ] 0","hypothesis":"Edward can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Doris","Harry","Edward","Betty"],"index":56240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
-{"premise":"There are three persons. Everyone is visible 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. 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":"Sarah can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Margaret","Elizabeth","Sarah"],"index":30463,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997010827,"difficulty":0.0002989173}
-{"premise":"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 Sharita'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 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Sharita can now know whether Christopher can know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Sharita","Christopher"],"index":63302,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9841775894,"difficulty":0.0158224106}
-{"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. Lynn's card is shown to Robin. Mario's card is shown to Robin. Robin's card is shown to Lynn. Dana's card is shown to Lynn. Robin's card is shown to Mario. Dana'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:1,2,3 Agentb:1,4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dana can now know that Robin can know that Mario picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robin","Lynn","Mario","Dana"],"index":22679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974621534,"difficulty":0.0025378466}
-{"premise":"There are three 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 Alice 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&2&3)) ] [ ! ~(Agentc knows whether 1) ] (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 (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Stacey can now know whether Alice is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Stacey","Alice"],"index":5924,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9740472436,"difficulty":0.0259527564}
-{"premise":"There are three persons. Everyone is visible 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 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&2&3) ] [ ! 1 ] Agentb knows whether (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) ] [ ! 1 ] 0","hypothesis":"Marcia can now know whether James can know that Marcia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Marcia","Michelle"],"index":59503,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992732406,"difficulty":0.0007267594}
-{"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 Ruby. Betty's card is shown to Ruby. Ruby'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 Betty knows whether someone picked a red card. It is publicly announced that Betty 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 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)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Betty can now know whether Ruby can know whether Ruby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ruby","Betty"],"index":20240,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942494631,"difficulty":0.0057505369}
-{"premise":"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. 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) ] [ ! (Agentd knows whether 2) ] [ ! 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) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] 0","hypothesis":"Anna can now know that Anna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","James","Ross","Kevin"],"index":42411,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8322613239,"difficulty":0.1677386761}
-{"premise":"There are two persons. Everyone is visible 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'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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Sabrina can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sabrina","Juanita"],"index":59798,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997890592,"difficulty":0.0002109408}
-{"premise":"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 does not know 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 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":"Addie can now know whether Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Ann","Christina","Addie"],"index":29387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996019006,"difficulty":0.0003980994}
-{"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 (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":"Dorothy can now know that Jennifer can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Jennifer","Joyce"],"index":34322,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997244477,"difficulty":0.0002755523}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (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:1,2,3,4 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":"Louise can now know whether Joseph can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Connie","Maria","Louise","Joseph"],"index":14317,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997506738,"difficulty":0.0002493262}
-{"premise":"There are three persons. Everyone is visible 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 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 Laura can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryan","Laura","Kevin"],"index":25586,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996993542,"difficulty":0.0003006458}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ella does not know whether or not everyone's forehead is muddy. It is publicly announced that Ella 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 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":"Amanda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amanda","Ella"],"index":51705,"s-l":"forehead-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 Jacqueline is not thirsty. It is publicly announced that Amy does not know whether Penny is 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 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) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jacqueline can now know whether Amy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pedro","Penny","Amy","Jacqueline"],"index":13984,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977216125,"difficulty":0.0022783875}
-{"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. Anthony's card is shown to Mark. Susie's card is shown to Mark. Susie's card is shown to Susie. 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) ] Agenta knows that (Agentb knows that 1)","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":"Anthony can now know that Mark can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Mark","Susie"],"index":43582,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973657727,"difficulty":0.0026342273}
-{"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 Frances is thirsty. It is publicly announced that Rosemarie 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 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 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Wendy can now know whether Tom can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tom","Wendy","Frances","Rosemarie"],"index":10834,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994848967,"difficulty":0.0005151033}
-{"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 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) ] 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"James can now know whether Roland can know that Roland is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Roland","James"],"index":7586,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5807293653,"difficulty":1.5807293653}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcella 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Barbara can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tonya","Rita","Marcella","Barbara"],"index":65310,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983803034,"difficulty":0.0016196966}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria 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 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":"Maria can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Maria"],"index":29944,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994313121,"difficulty":0.0005686879}
-{"premise":"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 Karen'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) ] 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) ] [ ! (1&2) ] 0","hypothesis":"Karen can now know that Tiffany can know whether Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tiffany","Karen"],"index":15028,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.990378499,"difficulty":0.009621501}
-{"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 Frank is thirsty. It is publicly announced that Frank 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 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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know that Frank is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bessie","Frank","Donald","Sam"],"index":14679,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7260351777,"difficulty":1.7260351777}
-{"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 Timothy. Winifred's card is shown to Timothy. Timothy's card is shown to Issac. Issac's card is shown to Issac. Winifred's card is shown to Winifred. Winifred'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 Timothy picked a red card. It is publicly announced that Timothy knows whether or not nobody picked a red card. It is publicly announced that Winifred does not know whether Jason picked a red card. It is publicly announced that Issac 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)) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","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":"Winifred can now know whether Timothy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Issac","Winifred","Jason"],"index":5045,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997076392,"difficulty":0.0002923608}
-{"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 Stacy. Stacy's card is shown to Mark. Evelyn's card is shown to Mark. Patricia's card is shown to Evelyn. Evelyn'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:2 Agentb:1,4 Agentc:2,4 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:1,4 Agentc:2,4 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":["Stacy","Patricia","Mark","Evelyn"],"index":10312,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985166192,"difficulty":0.0014833808}
-{"premise":"There are 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":"Ted can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julie","Ted","Francisca"],"index":31966,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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":"Jeremy can now know whether Mildred can know that Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremy","Bradley","Mildred","Maria"],"index":42405,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996808767,"difficulty":0.0003191233}
-{"premise":"There are four persons. Everyone is visible 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 Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Everett can now know that Laura can know that Laura's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marc","Everett","Barbara","Laura"],"index":50545,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980936646,"difficulty":0.0019063354}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aubrey does not know whether Shirley is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Shirley knows whether Aubrey 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 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)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Shirley can now know whether Aubrey can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shirley","Aubrey"],"index":66808,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993258715,"difficulty":0.0006741285}
-{"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 Maureen. Kasey's card is shown to Christopher. Christopher's card is shown to Christopher. Maureen's card is shown to Thomas. Christopher'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 Agentb:1,3 Agentc: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:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kasey can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kasey","Maureen","Christopher","Thomas"],"index":20086,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6049044132,"difficulty":0.3950955868}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosetta does not know whether Rosetta's forehead is muddy. It is publicly announced that not everyone'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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 ] Agentd knows that (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) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Sandra can now know that Rosetta can know whether Rosetta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Dorothy","Rosetta","Sandra"],"index":60622,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7801039219,"difficulty":1.7801039219}
-{"premise":"There are two persons. Everyone is visible 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 Frank 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)","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":"Frank can now know that Frank's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frank","Betty"],"index":342,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975073934,"difficulty":0.0024926066}
-{"premise":"There are 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":"Stephen can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Carol","Stephen"],"index":59232,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983142614,"difficulty":0.0016857386}
-{"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 Thomas is thirsty. It is publicly announced that Scott 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 (~(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":"Carmen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Carmen","Scott","Thomas"],"index":8783,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998232305,"difficulty":0.001767695}
-{"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 thirsty. It is publicly announced that Dorothy is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! 1 ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Teresa can now know whether Dorothy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Dorothy","Teresa"],"index":29006,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9928998947,"difficulty":0.0071001053}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felix's card is shown to Felix. Debbie's card is shown to Felix. Louis's card is shown to Felix. Debbie's card is shown to Debbie. Louis's card is shown to Debbie. Felix's card is shown to Louis. Victor's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Debbie does not know whether Victor 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) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Debbie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Felix","Debbie","Louis","Victor"],"index":57750,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984540939,"difficulty":0.0015459061}
-{"premise":"There are two persons. Everyone is visible 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 Juliette 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))) ] [ ! (Agentb knows whether 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) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Michael can now know that Juliette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Juliette"],"index":182,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976668358,"difficulty":0.0023331642}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida knows whether 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(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: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":"Seth can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Seth","Bill","Patricia"],"index":60439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vonda's forehead is muddy.","smcdel_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":"Carmen can now know whether Vonda can know whether Vonda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Irene","Carmen","Vonda"],"index":20860,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996891022,"difficulty":0.0003108978}
-{"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 Roy. Catherine's card is shown to Freddy. Denita's card is shown to Catherine. Freddy'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:4 Agentb:4 Agentc:1,3 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:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Freddy can now know whether Denita can know that Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denita","Roy","Freddy","Catherine"],"index":38567,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9268438816,"difficulty":1.9268438816}
-{"premise":"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) ] [ ! (Agentd knows whether 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) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Eric can now know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eric","Sherry","Patrick","Michele"],"index":318,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999566257,"difficulty":0.000433743}
-{"premise":"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 does not know whether Timothy'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 does not know whether Michael's forehead is muddy. It is publicly announced that Libby knows whether 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Libby can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Michael","Libby"],"index":35262,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995112419,"difficulty":0.0004887581}
-{"premise":"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) ] [ ! (Agentd 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that Janet can know whether Janet's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Janet","Rex","Robert"],"index":65122,"s-l":"forehead-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). Whitney's card is shown to Thomas. Shirley's card is shown to Whitney. Jodie's card is shown to Whitney. Thomas's card is shown to Shirley. Whitney's card is shown to Jodie. Shirley's card is shown to Jodie. 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 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 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shirley can now know that Jodie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Whitney","Shirley","Jodie"],"index":52990,"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. It is publicly announced that Demetrius's forehead is not muddy. It is publicly announced that Milan knows whether Milan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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) ] (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) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Milan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Demetrius","Sylvia","Milan","Gary"],"index":54443,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998481214,"difficulty":0.001518786}
-{"premise":"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 Robin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Robin can now know whether Tommy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dolores","Phyllis","Tommy","Robin"],"index":30194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994723201,"difficulty":0.0005276799}
-{"premise":"There are three persons. Everyone is visible 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 knows whether Louis's forehead is muddy.","smcdel_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 (1|2|3))","n_announcements":1,"pbcheck":"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":"Lori can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lori","Louis","Gladys"],"index":38203,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997614026,"difficulty":0.0002385974}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicitas's card is shown to Monica. Steve's card is shown to Felicitas. Delmar's card is shown to Felicitas. Monica's card is shown to Steve. Felicitas's card is shown to Steve. Felicitas's card is shown to Delmar. Steve's card is shown to Delmar. 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) ] Agentd knows whether (Agenta knows whether 3)","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":"Delmar can now know whether Monica can know whether Steve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Felicitas","Steve","Delmar"],"index":15503,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981880784,"difficulty":0.0018119216}
-{"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 Deanna. Christopher's card is shown to Christopher. John's card is shown to Christopher. Harold's card is shown to Christopher. John's card is shown to John. 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:2,3,4 Agentc:3 Agentd: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:4 Agentb:2,3,4 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know that John can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deanna","Christopher","John","Harold"],"index":32553,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9900394082,"difficulty":0.0099605918}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anneliese knows whether Anneliese's forehead 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 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":"Nancy can now know whether Stacy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Stacy","Anneliese"],"index":53397,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995927215,"difficulty":0.0004072785}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Verna'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 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":"Eric can now know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Walter","Eric","Verna"],"index":30595,"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's forehead is muddy. It is publicly announced that Wayne does not know whether Wayne's forehead is muddy. It is publicly announced that Lori's forehead is 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: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)) ] (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) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Wayne can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Carmen","Margaret","Wayne"],"index":43978,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981302619,"difficulty":0.0018697381}
-{"premise":"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) ] 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":"Daniel can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Javier","Daniel","John"],"index":13954,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999706924,"difficulty":0.000293076}
-{"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. 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 Gary 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 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":"Gary can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","David"],"index":3950,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6536402702,"difficulty":1.6536402702}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tabatha does not know whether or not everyone is thirsty. It is publicly announced that Tabatha does not know whether 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 (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Paula can now know whether Tabatha can know that Johnny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnny","Paula","Tabatha"],"index":43350,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9912455678,"difficulty":0.0087544322}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Juanita. Noah's card is shown to Juanita. Juanita's card is shown to Noah. 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) ] Agentb knows that (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":"Noah can now know that Juanita can know that Noah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juanita","Noah","Carolyn"],"index":54080,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972617626,"difficulty":0.0027382374}
-{"premise":"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) ] [ ! ~(Agenta 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: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 Krystyna can know whether Krystyna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Krystyna","David","Rene"],"index":65264,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6618156433,"difficulty":1.6618156433}
-{"premise":"There are two persons. Everyone is visible 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":"Mark can now know that Lorraine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mark","Lorraine"],"index":49296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984690547,"difficulty":0.0015309453}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Garrett's card is shown to Garrett. Mimi's card is shown to Mimi. 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 whether (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":"Phyllis can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Lavonna","Garrett","Mimi"],"index":41657,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999768436,"difficulty":0.000231564}
-{"premise":"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 Isidro does not know whether Isidro's forehead 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) ] (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 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Isidro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clifford","James","Isidro"],"index":58591,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9888640642,"difficulty":0.0111359358}
-{"premise":"There are two persons. Everyone is visible 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 Scott'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 ] 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) ] [ ! 1 ] 0","hypothesis":"Faye can now know that Scott can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Scott","Faye"],"index":33324,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997541308,"difficulty":0.0002458692}
-{"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 Bonnie knows whether Helen 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 (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":"Helen can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Helen","Bonnie"],"index":37137,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9923747182,"difficulty":0.0076252818}
-{"premise":"There are three persons. Everyone is visible 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 Chelsea knows whether Dexter's forehead is muddy.","smcdel_problem":"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 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":"Chelsea can now know whether Chelsea's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dexter","Chelsea","Frances"],"index":48300,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992728829,"difficulty":0.0007271171}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoine knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Dena knows whether Dena's forehead is muddy. It is publicly announced that Antoine knows 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Dena can now know whether Lois can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lois","Dena","Antoine"],"index":2030,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997040629,"difficulty":0.0002959371}
-{"premise":"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 does not know whether Pedro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Mark can now know whether Pedro can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Lorraine","Misty","Pedro"],"index":23654,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996911287,"difficulty":0.0003088713}
-{"premise":"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 knows whether Elliott's forehead 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 (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":"Roy can now know that Elliott can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Elliott","Roy"],"index":8014,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9915456176,"difficulty":0.0084543824}
-{"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 Ricardo 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 (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) ] [ ! ~(2) ] 0","hypothesis":"Kathy can now know that Ricardo can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harry","Ricardo","Chad","Kathy"],"index":33284,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998069942,"difficulty":0.001930058}
-{"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 Tony. Tuan's card is shown to Tony. Tony's card is shown to Charles. Betty's card is shown to Charles. Tuan's card is shown to Charles. Betty's card is shown to Betty. Tuan's card is shown to Betty. Tony's card is shown to Tuan. Tuan's card is shown to Tuan. 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 that (~(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":"Tuan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tony","Charles","Betty","Tuan"],"index":59271,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983782768,"difficulty":0.0016217232}
-{"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.","smcdel_problem":"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 (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":"Melissa can now know that Karla can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wendell","Karla","Melissa","Edward"],"index":8826,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathaniel's forehead 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)","n_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":"Nathaniel can now know whether Brendan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nathaniel","Brendan","Sherri"],"index":63558,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994904995,"difficulty":0.0005095005}
-{"premise":"There are three persons. Everyone is visible 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 Floyd's forehead is muddy.","smcdel_problem":"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)","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":"Joshua can now know that Charles can know that Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Charles","Floyd"],"index":66268,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9780797958,"difficulty":0.0219202042}
-{"premise":"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 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|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Christine can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","David","Sarah","Christine"],"index":9640,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980667233,"difficulty":0.0019332767}
-{"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. Jefferson's card is shown to Jefferson. Mary's card is shown to Stephen. Jefferson's card is shown to Dorris. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Jefferson picked a red card. It is publicly announced that Dorris knows whether Jefferson picked a red card. It is publicly announced that Mary does not know whether Stephen picked a red card. It is publicly announced that Jefferson 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)) ] Agentd knows whether (Agentb 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":"Dorris can now know whether Jefferson can know whether Stephen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Jefferson","Stephen","Dorris"],"index":17158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978547692,"difficulty":0.0021452308}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynette'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":"Philip can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lynette","Philip"],"index":49003,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998509109,"difficulty":0.001490891}
-{"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 or not everyone is thirsty.","smcdel_problem":"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":"Florence can now know that Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Florence","Carlos","Brandon","Maria"],"index":28560,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5428491831,"difficulty":0.4571508169}
-{"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 Beulah 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)","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":"Beulah can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Beulah","Robert"],"index":29464,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9756469727,"difficulty":0.0243530273}
-{"premise":"There are three persons. Everyone is visible 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 Mario's forehead is muddy. It is publicly announced that Marianne's forehead is not 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) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 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":"Marianne can now know that Marianne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicholas","Marianne","Mario"],"index":28561,"s-l":"forehead_mirror-0","deberta_pred":1,"deberta_confidence":0.7233409882,"difficulty":1.7233409882}
-{"premise":"There are three persons. Everyone is visible 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 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 (1&2&3))","n_announcements":1,"pbcheck":"VARS 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":"Lajuana can now know whether Shirley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willie","Shirley","Lajuana"],"index":547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996157885,"difficulty":0.0003842115}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leona 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 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":"Leona can now know that Leona is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Leona","Jennifer"],"index":3946,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9910982251,"difficulty":0.0089017749}
-{"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 Patricia. Marie's card is shown to Sandra. 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 (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":"Patricia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Marie","Sandra"],"index":22638,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985376596,"difficulty":0.0014623404}
-{"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 Susan. Susan's card is shown to Randy. 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 LAW Top OBS Agenta:2 Agentb:1 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Randy can now know that Susan can know that Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susan","Randy"],"index":8746,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9515817761,"difficulty":0.0484182239}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nina knows whether William's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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":"Kimberly can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nina","Kimberly","William"],"index":51442,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975976348,"difficulty":0.0024023652}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florine 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 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) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Florine can now know that Letha can know that Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Florine","Francis","Letha","James"],"index":48964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985039234,"difficulty":0.0014960766}
-{"premise":"There are three persons. Everyone is visible 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 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":"Shelly can now know that Trina can know that Floyd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shelly","Floyd","Trina"],"index":20762,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983964562,"difficulty":0.0016035438}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Clayton can now know that Clayton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clayton","Michael","Ralph"],"index":47368,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.889522016,"difficulty":0.110477984}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angeles knows whether Keisha's forehead is muddy. It is publicly announced that Angeles knows whether Keisha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Keisha can now know whether Angeles can know that Angeles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angeles","Keisha","Susan","Deidre"],"index":17989,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996615648,"difficulty":0.0003384352}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Marjorie. Mildred's card is shown to Gary. Gary's card is shown to Mildred. Mildred'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:1 Agentb:3 Agentc:2,3 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:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gary can now know whether Mildred can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","Gary","Mildred"],"index":47508,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997057319,"difficulty":0.0002942681}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb 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:1,2,3,4 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":"Paul 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":["Charlene","Donald","Paul","Kyle"],"index":38677,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999761045,"difficulty":0.000238955}
-{"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) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Willie can now know whether Sergio can know whether Sergio is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Willie","Lindsey","Sergio"],"index":40481,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954214692,"difficulty":0.0045785308}
-{"premise":"There are three 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 someone's forehead is muddy. It is publicly announced that Carmine does not know whether Carmine's forehead 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 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)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Amy can now know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmine","Sylvia","Amy"],"index":36645,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9768291116,"difficulty":0.0231708884}
-{"premise":"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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Lino can now know whether Eduardo can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lino","Eduardo","Peter","David"],"index":51568,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995415211,"difficulty":0.0004584789}
-{"premise":"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 Robin's forehead is muddy. It is publicly announced that Kenneth'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) ] (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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Lucia can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Kenneth","Robin","Lucia"],"index":67564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996092916,"difficulty":0.0003907084}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronnie 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 (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":"Allen can now know whether Seth can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronnie","Allen","Seth"],"index":18361,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997186065,"difficulty":0.0002813935}
-{"premise":"There are four persons. Everyone is visible 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's forehead is muddy. It is publicly announced that Pauline 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 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 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Pauline can now know that Barbara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Harrison","Laurie","Barbara"],"index":45242,"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. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Christopher. Victor's card is shown to Christopher. Yvonne's card is shown to Yvonne. Christopher's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Yvonne does not know whether Christopher 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 whether (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":"Victor can now know whether Christopher can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Yvonne","Victor"],"index":36053,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994655252,"difficulty":0.0005344748}
-{"premise":"There are three persons. Everyone is visible 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 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 (~(1|2|3)))","n_announcements":1,"pbcheck":"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":"Jose can now know that Rafael can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Rafael","Jose"],"index":18876,"s-l":"forehead_mirror-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 is thirsty. It is publicly announced that Carl 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 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Carl can now know that Roderick can know that Roderick is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Roderick","Carl"],"index":31812,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9299849868,"difficulty":0.0700150132}
-{"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 Austin. Tamar's card is shown to Austin. Arthur's card is shown to Austin. Tamar's card is shown to Robert. Tamar's card is shown to Arthur. Arthur'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:2,3,4 Agentb:3 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:2,3,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tamar can now know that Robert can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Austin","Robert","Tamar","Arthur"],"index":65793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997140765,"difficulty":0.0002859235}
-{"premise":"There are 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 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":"Robert can now know that Muriel can know that Javier's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Muriel","Javier","Robert"],"index":52455,"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). Raymond's card is shown to Blanch. Martha's card is shown to Marcelino. Raymond's card is shown to Marcelino. Raymond's card is shown to Martha. Martha'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:4 Agentb:3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 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":"Marcelino can now know that Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Blanch","Marcelino","Martha","Raymond"],"index":51072,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978573918,"difficulty":0.0021426082}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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":"Virginia can now know whether Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virginia","Thomas","Kathy","Teresa"],"index":49645,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994192123,"difficulty":0.0005807877}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ferdinand knows whether or not nobody'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:1,2,3,4 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 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":"Sammy can now know whether Ferdinand's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sammy","Marie","Ferdinand","Ryan"],"index":15516,"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. It is publicly announced that someone is thirsty. It is publicly announced that Arthur knows whether Tiffany is thirsty. It is publicly announced that Tiffany is thirsty. It is publicly announced that Tiffany 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))) ] 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 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Tiffany can now know whether Arthur can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Tiffany"],"index":53486,"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 is thirsty. It is publicly announced that Carlos knows whether someone is thirsty. It is publicly announced that Charles knows whether or not nobody is thirsty. It is publicly announced that Carole knows whether Carole is thirsty. It is publicly announced that Charles does not know whether Carlos is thirsty.","smcdel_problem":"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) ] (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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Carlos can now know that Phyllis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","Carole","Charles","Phyllis"],"index":623,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970378876,"difficulty":0.0029621124}
-{"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 Oscar. Tara's card is shown to Oscar. Blanche's card is shown to Blanche. Gregory's card is shown to Tara. It is publicly announced that someone picked a red card. It is publicly announced that Gregory does not know whether Tara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Gregory can now know whether Blanche can know that Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Oscar","Blanche","Gregory","Tara"],"index":40862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9626654387,"difficulty":0.0373345613}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Gerald can now know whether Jerry can know whether Ruby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Ruby","Jerry","Elizabeth"],"index":47422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997224212,"difficulty":0.0002775788}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica knows whether Jessica is thirsty. It is publicly announced that Jessica does not know whether George 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) ] 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 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"George can now know that Jessica can know whether Jessica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Jessica"],"index":52345,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991698265,"difficulty":0.0008301735}
-{"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 Mary. Mary's card is shown to Ruth. Robert'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:4 Agentb: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:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Clifford can now know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clifford","Mary","Robert","Ruth"],"index":59896,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983752966,"difficulty":0.0016247034}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ulysses 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)","n_announcements":1,"pbcheck":"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":"Roger can now know that Ulysses's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ulysses","Roger","Karen"],"index":24712,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9238554835,"difficulty":0.0761445165}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Alfred can now know that Christian can know that Christian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christian","Alfred","Barbara"],"index":27102,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985287189,"difficulty":0.0014712811}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Rita can now know whether Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kevin","Rita","Juan","Arnold"],"index":65563,"s-l":"forehead_mirror-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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Lawrence can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nan","Eloise","Janet","Lawrence"],"index":59252,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985914826,"difficulty":0.0014085174}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cyril knows whether Cyril's forehead 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 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":"Cyril can now know that Danielle can know that Cyril's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Danielle","Bradley","Cyril"],"index":30057,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9973831773,"difficulty":1.9973831773}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kate 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 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":"Tania can now know that Young's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Young","Nancy","Tania","Kate"],"index":27388,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.795085907,"difficulty":0.204914093}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alyssa's forehead is 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":"Alyssa can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Russell","Alyssa"],"index":49803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frankie'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 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":"Janice can now know whether Frankie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frankie","Janice"],"index":1606,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997486472,"difficulty":0.0002513528}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Ronnie knows whether or not nobody's forehead is muddy. It is publicly announced that Ronnie knows whether Thomas's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy.","smcdel_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)","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":"Thomas can now know that Timothy can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Timothy","Ronnie"],"index":21121,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965625405,"difficulty":0.0034374595}
-{"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) ] (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) ] [ ! ~(1) ] 0","hypothesis":"David can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Elizabeth","Xavier","Scott"],"index":456,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990736246,"difficulty":0.0009263754}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marvin knows whether Marvin 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 (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":"Henry can now know whether Marvin can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kay","Marvin","Henry"],"index":61544,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7333520651,"difficulty":0.2666479349}
-{"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 Cynthia. Steven's card is shown to Steven. 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 Steven 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)) ] 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) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Cynthia can now know whether Steven can know that Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Steven"],"index":10138,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9213355184,"difficulty":1.9213355184}
-{"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 Kelly. William's card is shown to Kelly. Kelly's card is shown to Bonnie. Bonnie's card is shown to Bonnie. William's card is shown to William. Kelly's card is shown to Melanie. Bonnie's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Kelly does not know whether Melanie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Kelly can now know that Melanie can know whether Melanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Bonnie","William","Melanie"],"index":51708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6372243166,"difficulty":0.3627756834}
-{"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 Eddie. 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 Michael knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! 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:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Eddie can now know that Michael can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Eddie"],"index":61221,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9109556675,"difficulty":0.0890443325}
-{"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 Willie 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 (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 2) ] 0","hypothesis":"Willie can now know whether Gary can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Willie","Antone"],"index":64600,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997091889,"difficulty":0.0002908111}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanine knows whether someone is thirsty. It is publicly announced that Joel 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)","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":"Jeanine can now know that Joel can know whether Jeanine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeanine","Joel"],"index":18130,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9888355136,"difficulty":0.0111644864}
-{"premise":"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 muddy. It is publicly announced that Stephanie does not know whether Stephanie's forehead 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 (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) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donna can now know that James can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephanie","Donna","James"],"index":58480,"s-l":"forehead-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 Sandra 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 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":"Sandra can now know that Rose can know that Lester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lester","Sandra","Rose"],"index":8212,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981684685,"difficulty":0.0018315315}
-{"premise":"There are four persons. Everyone is visible 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'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 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) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Juanita can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Brett","Juanita","Dorothy"],"index":20728,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9809984565,"difficulty":0.0190015435}
-{"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 Latonya. Clarence's card is shown to Latonya. George's card is shown to George. Latonya's card is shown to Clarence. It is publicly announced that someone picked a red card. It is publicly announced that Latonya 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 that (Agentb 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":"Latonya can now know that George can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Latonya","George","Clarence"],"index":5960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9886277318,"difficulty":0.0113722682}
-{"premise":"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 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) ] [ ! 3 ] [ ! ~(Agenta knows whether 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) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debrah can now know that William can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Debrah","William"],"index":28410,"s-l":"forehead-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). Donald's card is shown to Donald. Etta's card is shown to Etta. Rowena's card is shown to Etta. Donald's card is shown to Rowena. Etta's card is shown to Rowena. 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 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Rowena picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Etta","Rowena"],"index":58769,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.842869401,"difficulty":0.157130599}
-{"premise":"There are four persons. Everyone is visible 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 Loren's forehead is muddy. It is publicly announced that Geraldine knows whether Geraldine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"William can now know whether Geraldine can know whether Geraldine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Loren","William","Frank","Geraldine"],"index":33856,"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 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 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":"Joseph can now know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Catherine","Joseph","Reginald"],"index":3084,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977262616,"difficulty":0.0022737384}
-{"premise":"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 Lillian 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 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":"Jean can now know that Mariela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mariela","Lillian","Jean"],"index":53304,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6589118242,"difficulty":0.3410881758}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Mark can now know that Lester can know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Gerald","Lesley","Lester"],"index":4300,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985185266,"difficulty":0.0014814734}
-{"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. Fredrick's card is shown to James. Fredrick's card is shown to Vernita. James'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 Nancy does not know whether Fredrick picked a red card. It is publicly announced that Vernita does not know whether Nancy 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 whether (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":"Vernita can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Vernita","Nancy","Fredrick"],"index":44089,"s-l":"explicit-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's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. 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: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)) ] Agentb 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) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know whether Alvaro can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Michael","Alvaro"],"index":40768,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986365438,"difficulty":0.0013634562}
-{"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 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":"Monique can now know whether Theresa can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Monique","Theresa"],"index":57054,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9459977746,"difficulty":0.0540022254}
-{"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 Deborah is thirsty. It is publicly announced that Victor does not know whether Deborah 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 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(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: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":"Victor can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Victor","Michael","Deborah","Joseph"],"index":18466,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997186065,"difficulty":0.0002813935}
-{"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 Sheila. Fred's card is shown to Sheila. Sheila's card is shown to David. David's card is shown to David. Fred's card is shown to David. Sheila's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Sheila does not know whether Sheila 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 that 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":"Fred can now know that Fred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheila","David","Fred"],"index":34547,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9638840556,"difficulty":0.0361159444}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Virginia knows whether or not everyone's forehead is muddy. It is publicly announced that Margarite'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 (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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Juliet can now know that Virginia can know that Margarite's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margarite","Juliet","Virginia","Grace"],"index":40238,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8862134814,"difficulty":0.1137865186}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernadette 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 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":"Leonard can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gwen","Leonard","Bernadette"],"index":32926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983295798,"difficulty":0.0016704202}
-{"premise":"There are four persons. Everyone is visible 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 Lorene'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) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (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 3) ] [ ! 2 ] 0","hypothesis":"Chelsea can now know whether Chelsea's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chelsea","Melissa","Lorene","Mary"],"index":827,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995397329,"difficulty":0.0004602671}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommy does not know whether Tommy's forehead is muddy. It is publicly announced that Gregory 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)) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know that Tommy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tommy","Gregory","Erika","Archie"],"index":39020,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.791200757,"difficulty":0.208799243}
-{"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 Richard. Efrain's card is shown to Richard. Richard's card is shown to Ruth. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that Ruth 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 whether (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":"Ruth can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Ruth","Rosa","Efrain"],"index":7823,"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 Marjorie is not 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) ] [ ! ~(4) ] [ ! 1 ] 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) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Marjorie can now know whether Helen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Earnest","Charles","Marjorie"],"index":43808,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963046312,"difficulty":0.0036953688}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory knows whether someone is thirsty. It is publicly announced that Gregory does not know whether Michael 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":"Gregory can now know whether Michael can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Gregory"],"index":58378,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
-{"premise":"There are two persons. Everyone is visible 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":"Gail can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gail","Jose"],"index":53186,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998344183,"difficulty":0.001655817}
-{"premise":"There are four persons. Everyone is visible 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. 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) ] [ ! (Agentc 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:1,2,3,4 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":"Elizabeth can now know that Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Margaret","Elizabeth","Mary"],"index":35212,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.979475379,"difficulty":0.020524621}
-{"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 Pamela. Pamela'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: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":"John can now know that Pamela can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","John"],"index":321,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984429479,"difficulty":0.0015570521}
-{"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 Todd. Yolanda's card is shown to William. Todd's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Todd 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) ] [ ! 1 ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Todd can now know that William can know whether Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Todd","William","Kevin","Yolanda"],"index":6478,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9848970175,"difficulty":1.9848970175}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobbie 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 (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&2&3&4)) ] 0","hypothesis":"Bobbie can now know that Monica can know whether Bobbie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Santos","Armand","Monica","Bobbie"],"index":19775,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruben knows whether Ruben's forehead is muddy. It is publicly announced that Inell 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (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 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ruben can now know that Inell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolyn","Ruben","Inell","Christa"],"index":11492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977485538,"difficulty":0.0022514462}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Cecil. Eldon's card is shown to Joy. Joy's card is shown to Joy. 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 Cecil does not know whether Jeff picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb 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:3 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eldon can now know that Cecil can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eldon","Cecil","Jeff","Joy"],"index":60763,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997164607,"difficulty":0.0002835393}
-{"premise":"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'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 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":"Shane can now know that Shane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Robert","Shane","Kevin"],"index":67349,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.849301517,"difficulty":0.150698483}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Devon 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) ] 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 3) ] 0","hypothesis":"Elizabeth can now know whether Devon can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Devon","Ronnie"],"index":5334,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7735514045,"difficulty":0.2264485955}
-{"premise":"There are four persons. Everyone is visible 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 Florence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 2) ] 0","hypothesis":"Craig can now know whether Florence can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Florence","Craig","Robert"],"index":51258,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996774197,"difficulty":0.0003225803}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genevieve knows whether someone's forehead is muddy. It is publicly announced that Heather knows whether Joseph's forehead is muddy. It is publicly announced that Joseph 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)) ] 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Heather can now know that Joseph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Genevieve","Heather","Hortensia","Joseph"],"index":27123,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984334111,"difficulty":0.0015665889}
-{"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 Kenneth. Kenneth's card is shown to Doris. 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. It is publicly announced that Kenneth 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)) ] Agentb knows that (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 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Doris can now know that Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Doris"],"index":28250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
-{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Diana 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) ] Agenta knows that (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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Gloria can now know that Diana can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Melvin","Diana"],"index":36619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mercedes's card is shown to Angela. Angela's card is shown to Chester. Mercedes's card is shown to Chester. Angela's card is shown to Mercedes. 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) ] (Agentc knows whether 1)","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":"Mercedes can now know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angela","Chester","Mercedes"],"index":66803,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6854445934,"difficulty":1.6854445934}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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":"Saul can now know that Michele can know that Saul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Michele","Saul"],"index":35407,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983922839,"difficulty":0.0016077161}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Karri. Karri's card is shown to Regina. 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) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lucy can now know whether Karri can know that Karri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karri","Lucy","Regina"],"index":6121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6235328317,"difficulty":0.3764671683}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonita 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 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":"Joshua can now know that Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bonita","Joshua","Renae","Maria"],"index":13943,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981675148,"difficulty":0.0018324852}
-{"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 Stanley. Mark's card is shown to Mark. Norma's card is shown to Norma. It is publicly announced that someone picked a red card. It is publicly announced that Norma does not know whether Mark picked a red card. It is publicly announced that Mark does not know whether Norma 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 that (Agenta knows whether (1|2|3))","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":"Norma can now know that Stanley can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stanley","Mark","Norma"],"index":37129,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
-{"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. Lawrence's card is shown to Victoria. Deanna's card is shown to Gregory. Victoria's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that Lawrence does not know whether Lawrence picked a red card. It is publicly announced that Victoria 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)) ] (Agentc knows that 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":"Gregory can now know that Deanna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Lawrence","Gregory","Deanna"],"index":26481,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7216499448,"difficulty":0.2783500552}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Polly knows whether Agnes's forehead is muddy. It is publicly announced that Polly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Donna can now know that Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Polly","Agnes","Nicholas"],"index":48382,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9330176711,"difficulty":0.0669823289}
-{"premise":"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 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 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":"Letitia can now know whether William can know whether Letitia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Letitia"],"index":66066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958484173,"difficulty":0.0041515827}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Audrey'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)","n_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":"Audrey can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Dewey","Audrey"],"index":22244,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944387674,"difficulty":0.0055612326}
-{"premise":"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 Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Jamie can now know whether Angela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Lottie","Jamie","Felica"],"index":29461,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954990745,"difficulty":0.0045009255}
-{"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.","smcdel_problem":"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":"Kyle can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronnie","Sherie","Bethanie","Kyle"],"index":38206,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6474044919,"difficulty":1.6474044919}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kirsten does not know whether Keith 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)","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":"Kirsten can now know that Keith can know that Kirsten is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kirsten","Keith"],"index":17881,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9919449687,"difficulty":1.9919449687}
-{"premise":"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 knows 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) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Chad can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Marian","Chad"],"index":21819,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982414246,"difficulty":0.0017585754}
-{"premise":"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 knows 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Brian can now know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynn","Brian","Darrell"],"index":57553,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927154183,"difficulty":0.0072845817}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paulette 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 (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":"Charles can now know whether Russell can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Paulette","Russell"],"index":13608,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9629603028,"difficulty":0.0370396972}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Megan's card is shown to Jackie. Edward's card is shown to Megan. Elsa's card is shown to Megan. Megan's card is shown to Edward. Elsa's card is shown to Elsa. 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) ] Agentb knows whether (Agenta knows that 4)","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":"Megan can now know whether Jackie can know that Elsa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jackie","Megan","Edward","Elsa"],"index":65445,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9024967551,"difficulty":0.0975032449}
-{"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 Joe. Joe's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Joe knows whether 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 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 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) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Heather can now know that Joe can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joe","Heather"],"index":57802,"s-l":"explicit-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 Ron knows whether Ron's forehead is muddy. It is publicly announced that Stephen'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 (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) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Terri can now know whether Stephen can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Terri","Ron","Stephen"],"index":43945,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996159077,"difficulty":0.0003840923}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bertha does not know whether James is thirsty. It is publicly announced that Penny is thirsty.","smcdel_problem":"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 (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) ] [ ! 3 ] 0","hypothesis":"Ricky can now know that James can know whether Bertha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Bertha","Penny","Ricky"],"index":38263,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948239326,"difficulty":0.0051760674}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isabelle 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)","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":"Ericka can now know that Ericka's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ericka","Isabelle"],"index":26548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9207749963,"difficulty":0.0792250037}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd does not know whether Todd's forehead is muddy. It is publicly announced that Justin'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 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":"Justin can now know that Todd can know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Justin","Todd"],"index":38552,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7830030918,"difficulty":0.2169969082}
-{"premise":"There are four persons. Everyone is visible 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 Carol's forehead is muddy. It is publicly announced that Tom knows whether Tom's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (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) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Tom can now know whether Carol can know whether Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Matthew","Alexia","Tom"],"index":20211,"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 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) ] [ ! (Agentb knows whether (1&2&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 (1&2&3)) ] 0","hypothesis":"Troy can now know that Lolita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Troy","Kevin","Lolita"],"index":60580,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9883893728,"difficulty":0.0116106272}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Andrew can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Angie","Charles","Calvin"],"index":58746,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984325767,"difficulty":0.0015674233}
-{"premise":"There are two 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. It is publicly announced that Jeff knows whether Jeff 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":"Kenneth can now know that Jeff can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kenneth","Jeff"],"index":36069,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986370206,"difficulty":0.0013629794}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ona does not know whether Ona's forehead 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 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":"Ona can now know whether Helen can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Ona","John"],"index":58865,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9499140382,"difficulty":1.9499140382}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnetta does not know whether Johnetta's forehead 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 (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":"Travis can now know whether Johnetta can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Travis","Johnetta"],"index":45898,"s-l":"forehead-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). William's card is shown to Charles. Charles's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that William picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 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 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"William can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Charles","Donna"],"index":17035,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5931307077,"difficulty":1.5931307077}
-{"premise":"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 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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lee can now know whether Mildred can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Richard","Mildred","Hobert"],"index":9326,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9791101813,"difficulty":0.0208898187}
-{"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 or not everyone is thirsty. It is publicly announced that Robert knows whether Mary is thirsty. It is publicly announced that Robert 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) ] Agenta knows whether (Agentb knows that 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":"Robert can now know whether Mary can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Mary"],"index":15049,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9930019975,"difficulty":0.0069980025}
-{"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. Terrell's card is shown to Olivia. Olivia's card is shown to Terrell. Michael's card is shown to George. Olivia'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:3 Agentc:2 Agentd:1,2 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:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether George can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Olivia","Terrell","George"],"index":32856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Noelle 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":"Noelle can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Julia","Noelle"],"index":50120,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997517467,"difficulty":0.0002482533}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony 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) ] [ ! ~(Agenta knows whether 3) ] 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Nancy can now know that Tara can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tony","Tara","Nancy","Dawna"],"index":16446,"s-l":"internal-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's forehead is muddy. It is publicly announced that Jesus knows whether Barry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] (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 2) ] 0","hypothesis":"Barry can now know that Dortha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesus","Barry","Dortha","Caroline"],"index":15595,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983022213,"difficulty":0.0016977787}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! 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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Bennie can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bennie","Frank","Richard"],"index":13935,"s-l":"forehead_mirror-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 Sanford 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 (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)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeanne can now know whether Calvin can know that Brandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sanford","Jeanne","Brandy","Calvin"],"index":26020,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979793429,"difficulty":0.0020206571}
-{"premise":"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 Gregory's forehead is not muddy. It is publicly announced that Dwight 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) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta 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) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Dwight can now know that April's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwight","April","Gregory"],"index":17345,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9194930792,"difficulty":0.0805069208}
-{"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 Stella knows whether Stella is 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) ] (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 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jules can now know that Stella is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stella","David","Jules","Alberto"],"index":12208,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8283897638,"difficulty":0.1716102362}
-{"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 Brian. Brian'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 Agentb: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:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know that Karen can know that Elva picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Karen","Elisa","Elva"],"index":67036,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984871149,"difficulty":0.0015128851}
-{"premise":"There are two persons. Everyone is visible 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 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 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":"Kevin can now know whether Pamela can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Pamela"],"index":3977,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995402098,"difficulty":0.0004597902}
-{"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 Jessica is thirsty. It is publicly announced that Carol 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Carol can now know that Jessica can know that Jessica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessica","Carol","Catherine"],"index":43089,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9647224545,"difficulty":0.0352775455}
-{"premise":"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'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 (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":"Arthur can now know that Yvonne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Cristy","John","Yvonne"],"index":29893,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979838133,"difficulty":0.0020161867}
-{"premise":"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 Santiago's forehead is muddy. It is publicly announced that Andrew'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) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Santiago can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Santiago","Henry","Andrew","Guillermo"],"index":155,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6964222789,"difficulty":0.3035777211}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stella 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":"Elia can now know whether Stella can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stella","Elia"],"index":59714,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994618297,"difficulty":0.0005381703}
-{"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 Paul. Vida's card is shown to Vida. Eric's card is shown to Vida. Paul's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Vida 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:1 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:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that Vida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Joseph","Vida","Eric"],"index":10145,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7694762349,"difficulty":0.2305237651}
-{"premise":"There are two 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 Lois knows whether someone's forehead is muddy. It is publicly announced that Elijah 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 whether 1)","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":"Elijah can now know whether Elijah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elijah","Lois"],"index":60265,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7262375951,"difficulty":1.7262375951}
-{"premise":"There are four persons. Everyone is visible 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 or not everyone'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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 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)) ] [ ! 1 ] 0","hypothesis":"Jacob can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Amanda","Jacob","Justin"],"index":15379,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Leonel's forehead is muddy. It is publicly announced that Leonel's forehead is muddy.","smcdel_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":"Michael can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Trent","Leonel","Michael"],"index":29314,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
-{"premise":"There are three persons. Everyone is visible 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 Beverly's forehead is muddy.","smcdel_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 (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":"Beverly can now know whether Alan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beverly","Alan","James"],"index":4615,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995549321,"difficulty":0.0004450679}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Preston's card is shown to Catherine. Marian's card is shown to Catherine. Marian's card is shown to Preston. 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 that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Preston can now know that Catherine can know that Preston picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Catherine","Preston","Marian"],"index":61154,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960401058,"difficulty":0.0039598942}
-{"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 Aaron. Hugh's card is shown to Hugh. Aaron's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Benjamin 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) ] 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:1 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Hugh can now know that Aaron can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Aaron","Hugh","Benjamin"],"index":35665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981752634,"difficulty":0.0018247366}
-{"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 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":"Brent can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brent","Rocky"],"index":63760,"s-l":"internal-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 Shawn 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) ] [ ! (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: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":"Mark can now know that Shawn can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shawn","Anna","Stephen","Mark"],"index":40012,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992194176,"difficulty":0.0007805824}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Steve's card is shown to Walter. Steve's card is shown to Steve. 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 Steve knows whether Walter 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 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":"Steve can now know that Steve picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Walter","Steve"],"index":5036,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9972555041,"difficulty":0.0027444959}
-{"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 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 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 that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Lisa","Thomas","John"],"index":1567,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985716343,"difficulty":0.0014283657}
-{"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. Mary's card is shown to Jeffrey. Mark's card is shown to Jeffrey. Mary's card is shown to Mary. Mark's card is shown to Mary. Jeffrey's card is shown to Mark. Mary'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:1,2,3 Agentb:2,3 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:1,2,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mark 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":["Jeffrey","Mary","Mark"],"index":4360,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999705255,"difficulty":0.000294745}
-{"premise":"There are four persons. Everyone is visible 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 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 (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":"Earl can now know whether Jessica can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Shelly","Earl","Wanda"],"index":10499,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999591291,"difficulty":0.000408709}
-{"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 Gwen. Patricia's card is shown to Gwen. Laura'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:2,3 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:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gwen","Laura","Patricia"],"index":50280,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953363538,"difficulty":0.0046636462}
-{"premise":"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|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Joshua can now know that Angela can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Joshua","Patricia","Arlene"],"index":18690,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997529387,"difficulty":0.0002470613}
-{"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 (~(1|2|3|4)))","n_announcements":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":"Adam can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adam","Richard","Mary","Christian"],"index":9698,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983238578,"difficulty":0.0016761422}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elisha 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)) ] 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elisha can now know whether Emily can know whether Emily's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elisha","Idalia","Jackie","Emily"],"index":49483,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996241331,"difficulty":0.0003758669}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynetta does not know whether Archie is thirsty.","smcdel_problem":"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 4)","n_announcements":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":"Rena can now know that Stephen can know whether Rena is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Archie","Lynetta","Stephen","Rena"],"index":62554,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976680875,"difficulty":0.0023319125}
-{"premise":"There are four persons. Everyone is visible 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Jillian can now know whether Angela can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jillian","Angela","Carl","Magdalena"],"index":53532,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
-{"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. Rosemary's card is shown to Holly. Rosemary's card is shown to Rosemary. Cynthia's card is shown to Cynthia. 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) ] Agentd knows whether (Agenta 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":"Cynthia can now know whether Jose can know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Holly","Rosemary","Cynthia"],"index":28260,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977204204,"difficulty":0.0022795796}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Horace's card is shown to Horace. Horace's card is shown to Yvonne. Yvonne'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:1 Agentb:1,3 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:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Horace can now know that Andrew can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Horace","Andrew","Yvonne","Sharon"],"index":19749,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997217059,"difficulty":0.0002782941}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kate knows whether Deann's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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 Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deann","Kate","Robert"],"index":58836,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982156754,"difficulty":0.0017843246}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores's forehead is muddy.","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":"Dolores can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dolores","James"],"index":41865,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984048009,"difficulty":0.0015951991}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lindsay's card is shown to Lindsay. Anne's card is shown to Lindsay. Lindsay's card is shown to William. Anne'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 LAW Top OBS Agenta:1,3 Agentb:1,3 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:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Anne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lindsay","William","Anne"],"index":27065,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
-{"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 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) ] [ ! 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) ] [ ! 3 ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Elizabeth can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kevin","Eloisa","Elizabeth"],"index":49247,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997201562,"difficulty":0.0002798438}
-{"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 Thomas. Joanne's card is shown to Thomas. Joanne's card is shown to Adrienne. Thomas's card is shown to Joanne. 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 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":"Joanne can now know whether Thomas can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Adrienne","Joanne"],"index":58847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
-{"premise":"There are two 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. It is publicly announced that Susan 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 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 (1&2)) ] 0","hypothesis":"Susan can now know that Omar can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Omar","Susan"],"index":43225,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975883961,"difficulty":0.0024116039}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ebony knows whether Harold's forehead is muddy. It is publicly announced that Harold knows whether John's forehead is muddy. It is publicly announced that Ebony'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)","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":"Harold can now know that Ebony can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Harold","Ebony"],"index":47707,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9883188009,"difficulty":0.0116811991}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wenona 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 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":"Bernard can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacob","Wenona","Bernard","James"],"index":33948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999697566,"difficulty":0.000302434}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvette's card is shown to Yvette. David's card is shown to Yvette. William's card is shown to Yvette. William's card is shown to David. 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 or not everyone picked a red card. It is publicly announced that William does not know whether or not everyone picked a red card. It is publicly announced that David does not know whether David picked a red card. It is publicly announced that Yvette 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))) ] (Agenta knows whether 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":"Yvette can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yvette","David","William"],"index":40234,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8562533855,"difficulty":0.1437466145}
-{"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. Mary's card is shown to Ruby. Victor's card is shown to Mary. Darrin'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:4 Agentc:1,2 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:4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Darrin","Ruby","Mary"],"index":18748,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982403517,"difficulty":0.0017596483}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). George's card is shown to Ronald. 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 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)) ] Agentb knows whether (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&2)) ] 0","hypothesis":"George can now know whether Ronald can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronald","George"],"index":4958,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marissa's card is shown to Marissa. Jeremy's card is shown to Marissa. Marissa's card is shown to Jeremy. Jeremy's card is shown to Gayla. Winford's card is shown to Gayla. Gayla's card is shown to Winford. It is publicly announced that someone 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:1,2 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentd knows that 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":"Jeremy can now know that Winford can know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marissa","Jeremy","Gayla","Winford"],"index":4651,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9344180226,"difficulty":0.0655819774}
-{"premise":"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 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 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":"Christie can now know that Christie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Christie","David","Daniel"],"index":15159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7017980814,"difficulty":0.2982019186}
-{"premise":"There are four persons. Everyone is visible 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 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 2) ] 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: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":"Margaret can now know that Amanda can know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Amanda","James","Nicholas"],"index":49936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979102015,"difficulty":0.0020897985}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Michael 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 (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":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronnie","Russell","Michael","Joann"],"index":38317,"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. 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 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":"Robert can now know that Susan can know that Reba's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Priscilla","Reba","Susan","Robert"],"index":66380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986487031,"difficulty":0.0013512969}
-{"premise":"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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"John can now know that Paul can know that Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Paul","John","Hester"],"index":6908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9392620921,"difficulty":0.0607379079}
-{"premise":"There are four persons. Everyone is visible 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 everyone's forehead is muddy. It is publicly announced that Violette'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|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":"Joseph can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roy","Joseph","Violette","Brian"],"index":26031,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
-{"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 Merle. Mattie's card is shown to Mattie. Merle's card is shown to Yolanda. 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 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 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know that Merle can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Merle","Mattie","Rita","Yolanda"],"index":42175,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99836725,"difficulty":0.00163275}
-{"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 Betty. Donald's card is shown to Mildred. Betty's card is shown to James. Betty'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 Agentb:4 Agentc:1 Agentd: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 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Mildred","James","Donald"],"index":48516,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983505011,"difficulty":0.0016494989}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeannie knows whether Jeannie 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 (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":"Judy can now know that Jeannie can know whether Judy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeannie","Richard","Judy"],"index":14396,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.992770493,"difficulty":0.007229507}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Ronald can now know that Myra can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myra","Patrick","Phillip","Ronald"],"index":4189,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997837007,"difficulty":0.002162993}
-{"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 Sammy 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 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":"Frederick can now know whether Robin can know that Robin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Robin","Sammy"],"index":40879,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9699617028,"difficulty":1.9699617028}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erma does not know whether Lisa 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 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) ] [ ! (1|2|3|4) ] 0","hypothesis":"Erma can now know that Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Reva","Erma","Alyssa"],"index":39527,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977945089,"difficulty":0.0022054911}
-{"premise":"There are two persons. Everyone is visible 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 Peggy 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 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":"Alan can now know that Peggy can know that Alan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Peggy","Alan"],"index":8760,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9178383946,"difficulty":0.0821616054}
-{"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 Andrew 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 (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) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lesley can now know whether Helen can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Helen","Lesley"],"index":35921,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9975625277,"difficulty":0.0024374723}
-{"premise":"There are three persons. Everyone is visible 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 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)","n_announcements":1,"pbcheck":"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":"Ida can now know whether Johnny can know whether Ida's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ida","Johnny","Sheila"],"index":1501,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997051358,"difficulty":0.0002948642}
-{"premise":"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's forehead is muddy. It is publicly announced that Stephanie 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 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 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Stephanie can now know that Sherri can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephanie","Sherri"],"index":49320,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.518330276,"difficulty":1.518330276}
-{"premise":"There are four persons. Everyone is visible 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 Judith'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) ] [ ! (Agentd knows whether 1) ] [ ! 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) ] [ ! 3 ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judith","Brenda","Joseph","Sherry"],"index":59988,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984618425,"difficulty":0.0015381575}
-{"premise":"There are two persons. Everyone is visible 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 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) ] [ ! (Agenta knows whether (1|2)) ] [ ! 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|2)) ] [ ! 1 ] 0","hypothesis":"Fred can now know that Clifford can know that Clifford's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Fred","Clifford"],"index":48705,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9127179384,"difficulty":0.0872820616}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlin 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Efrain can know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marlin","Efrain","Melissa","Gregory"],"index":10610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9453071952,"difficulty":0.0546928048}
-{"premise":"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))) ] (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":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Mary"],"index":3762,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997035861,"difficulty":0.0002964139}
-{"premise":"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 James does not know whether James's forehead is muddy. It is publicly announced that Patrick knows whether Marion'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) ] [ ! (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":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Patrick","Paul","James"],"index":18683,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985089898,"difficulty":0.0014910102}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Zoila does not know whether or not everyone is thirsty. It is publicly announced that Timothy knows whether someone is thirsty. It is publicly announced that Gloria does not know whether Timothy 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) ] (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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Zoila can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Gloria","Zoila"],"index":34644,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
-{"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 Rick. Stephanie's card is shown to Rick. Rick's card is shown to Pierre. Rick's card is shown to Stephanie. 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) ] (Agenta knows whether 3)","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":"Jay can now know whether Pierre picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jay","Rick","Pierre","Stephanie"],"index":47482,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9279618263,"difficulty":0.0720381737}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Trevor's card is shown to Trevor. Trevor's card is shown to Michael. Thomas'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 Thomas picked a black card. It is publicly announced that Trevor picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 1 ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Michael can now know that Trevor can know that Trevor picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Trevor","Thomas","Michael","Keith"],"index":13297,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7471942902,"difficulty":0.2528057098}
-{"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 Jane knows whether Darryl 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 that (Agentb knows that 1)","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":"Jane can now know that Darryl can know that Jane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jane","Darryl"],"index":48965,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9823300242,"difficulty":0.0176699758}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Traci's card is shown to Traci. Clayton's card is shown to Clayton. 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.","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":"Traci can now know whether Clayton can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Traci","Clayton"],"index":10054,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997692704,"difficulty":0.0002307296}
-{"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 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":"Timothy can now know that Carmelo can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Karen","Timothy","Carmelo"],"index":46216,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995778203,"difficulty":0.0004221797}
-{"premise":"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.","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":"Omar can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Omar","Dale","Morris"],"index":6464,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997723699,"difficulty":0.0002276301}
-{"premise":"There are four persons. Everyone is visible 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 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":"Darlene can now know whether Barbara can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Darlene","Cathleen","James"],"index":30183,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997343421,"difficulty":0.0002656579}
-{"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 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 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":"Laura can now know that Hazel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francisco","Hazel","Laura","Thomas"],"index":57352,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8991549611,"difficulty":0.1008450389}
-{"premise":"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'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 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) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Jose can now know whether Thomas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Jose","Norma"],"index":25592,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997164607,"difficulty":0.0002835393}
-{"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 Morgan 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Marjorie can now know whether Morgan can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Morgan","Marjorie"],"index":30431,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996979237,"difficulty":0.0003020763}
-{"premise":"There are three persons. Everyone is visible 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 Victor's forehead is muddy. It is publicly announced that John's forehead is not muddy. It is publicly announced that Glenda 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) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (Agenta 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) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"John can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Victor","Glenda"],"index":18059,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996503592,"difficulty":0.0003496408}
-{"premise":"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 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 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":"Josephine can now know whether Jessica can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Jessica","Martha","Josephine"],"index":59710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9952690005,"difficulty":0.0047309995}
-{"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 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 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":"Henry can now know that Lisa can know that Henry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Henry","Norma","Lisa"],"index":39762,"s-l":"internal-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 Karen 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 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":"Helen can now know that Deborah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Helen","Karen","Deborah","Paul"],"index":21231,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985420704,"difficulty":0.0014579296}
-{"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 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) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Ryan can now know that Cheryl can know whether Brandy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sylvester","Cheryl","Brandy","Ryan"],"index":19933,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979727864,"difficulty":0.0020272136}
-{"premise":"There are four persons. Everyone is visible 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":"Juan can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Blanche","Marie","Jesse","Juan"],"index":37201,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9983318448,"difficulty":0.0016681552}
-{"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 Eva. Ronald's card is shown to Ronald. Eva's card is shown to Ilene. Ronald's card is shown to Ilene. 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:2 Agentc:1,2 Agentd: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 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eva","Ronald","Ilene","Patricia"],"index":30479,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919546247,"difficulty":0.0080453753}
-{"premise":"There are three persons. Everyone is visible 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 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":"Charlene can now know whether Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charlene","Monica","Alvin"],"index":40112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999740541,"difficulty":0.000259459}
-{"premise":"There are two 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.","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":"Melissa can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Miguel","Melissa"],"index":3634,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9946973324,"difficulty":0.0053026676}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marian's card is shown to James. Marian's card is shown to Marian. James's card is shown to Olivia. Olivia's card is shown to Olivia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Marian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Marian","Olivia"],"index":57257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5800293088,"difficulty":0.4199706912}
-{"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) ] [ ! ~(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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jesse can now know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Kenneth","Gregory","Bernard"],"index":44834,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.954026401,"difficulty":0.045973599}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nora does not know whether or not everyone is thirsty. It is publicly announced that Nora does not know whether Julio is thirsty. It is publicly announced that Rick knows 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&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! (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 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":"Rick can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rick","Milton","Julio","Nora"],"index":1750,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983702302,"difficulty":0.0016297698}
-{"premise":"There are three persons. Everyone is visible 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 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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Christopher can now know that Mary can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheila","Christopher","Mary"],"index":34287,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984033704,"difficulty":0.0015966296}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Pablo does not know whether or not everyone is thirsty. It is publicly announced that James knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 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":"Ethel can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pablo","Ethel","James","Bobby"],"index":54094,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997754693,"difficulty":0.0002245307}
-{"premise":"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 Andrew 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 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&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Richard can now know that Andrew can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Andrew"],"index":39988,"s-l":"forehead-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's forehead is muddy. It is publicly announced that Benjamin knows whether someone's forehead is muddy. It is publicly announced that Leonor'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 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Benjamin can now know that Kathaleen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Peggy","Kathaleen","Leonor"],"index":12841,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928990602,"difficulty":0.0071009398}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allison's card is shown to Yvonne. Tracy's card is shown to Allison. Yvonne's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Allison does not know whether Allison 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 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Allison can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yvonne","Allison","Tracy"],"index":61108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
-{"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 (~(1|2|3|4)))","n_announcements":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":"Theresa can now know that Timothy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Theresa","Ralph","Gary"],"index":54857,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996829033,"difficulty":0.0003170967}
-{"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 Jeffery. Jeffery's card is shown to Tracey. Concetta's card is shown to Tracey. Jeffery's card is shown to Concetta. Tracey's card is shown to Concetta. 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) ] (Agentc 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":"Concetta can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffery","Tracey","Concetta"],"index":28803,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
-{"premise":"There are two persons. Everyone is visible 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 Kristina knows whether Joseph'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 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 2) ] [ ! (1&2) ] 0","hypothesis":"Kristina can now know that Joseph can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kristina","Joseph"],"index":62755,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962790608,"difficulty":0.0037209392}
-{"premise":"There are two persons. Everyone is visible 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 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":"Albert can now know that Steve can know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Steve","Albert"],"index":56643,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965498447,"difficulty":0.0034501553}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lahoma's card is shown to Justin. Nathaniel's card is shown to Matthew. Lahoma's card is shown to Nathaniel. Nathaniel's card is shown to Lahoma. 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) ] Agenta knows that (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":"Justin can now know that Nathaniel can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Matthew","Nathaniel","Lahoma"],"index":14954,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997133613,"difficulty":0.0002866387}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katrina does not know whether Steven 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) ] (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":"Katrina can now know that Katrina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Steven","Katrina","Chase"],"index":34115,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970340729,"difficulty":0.0029659271}
-{"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. Randy's card is shown to Sally. Phillip's card is shown to Randy. Randy's card is shown to Phillip. 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) ] 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 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Phillip can now know that Randy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arturo","Sally","Randy","Phillip"],"index":23650,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997772574,"difficulty":0.0002227426}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey 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) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Terry can now know that John can know that Gladys's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gladys","Stacey","Terry","John"],"index":45765,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985987544,"difficulty":0.0014012456}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon'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 Joseph 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 whether 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":"Joseph can now know whether Shannon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Shannon"],"index":6939,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6726197004,"difficulty":1.6726197004}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donald knows whether Christine is thirsty. It is publicly announced that Donald knows whether Christine is thirsty. It is publicly announced that Christine knows whether Donald is thirsty. It is publicly announced that Donald 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":"Donald can now know whether Christine can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Christine"],"index":67290,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997882247,"difficulty":0.0002117753}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryne's card is shown to Kathryne. Willie's card is shown to Kathryne. Walter's card is shown to Kathryne. Willie's card is shown to Willie. Grace's card is shown to Willie. Walter's card is shown to Walter. Grace's card is shown to Walter. Willie's card is shown to Grace. 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 whether 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":"Walter can now know whether Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathryne","Willie","Walter","Grace"],"index":59576,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8038173914,"difficulty":1.8038173914}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clayton 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) ] [ ! ~(Agentb knows whether 1) ] 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 1) ] 0","hypothesis":"Yesenia can now know whether Clayton can know whether Clayton is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Clayton","Yesenia","Shera"],"index":12995,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989690781,"difficulty":0.0010309219}
-{"premise":"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 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 (~(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":"Paula can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Paula","Scott"],"index":60094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983152151,"difficulty":0.0016847849}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melanie's card is shown to Melanie. Melanie'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 Agentb:1 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 VALID? [ ! (1|2) ] 0","hypothesis":"Joseph can now know whether Melanie can know whether Melanie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melanie","Joseph"],"index":19261,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964197874,"difficulty":0.0035802126}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 (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":"Janice can now know whether Rona can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Alise","Janice","Rona"],"index":18271,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995922446,"difficulty":0.0004077554}
-{"premise":"There are four persons. Everyone is visible 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 Matthew 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) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Frank can now know whether Edgar can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edgar","Frank","Mark","Matthew"],"index":41798,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997845292,"difficulty":0.0002154708}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gordon knows whether Gordon 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 (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":"Gordon can now know that Kevin can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danielle","Kevin","Gordon"],"index":52807,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998441875,"difficulty":0.001558125}
-{"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 Joseph. Steven's card is shown to Joseph. Steven's card is shown to Jennifer. Jennifer's card is shown to Steven. Steven's card is shown to Steven. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether Jennifer 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) ] (Agentb knows whether (1|2|3))","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":"Jennifer can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Jennifer","Steven"],"index":2865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
-{"premise":"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 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":"John can now know that Christopher can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juana","Johanna","John","Christopher"],"index":3058,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992413521,"difficulty":0.0007586479}
-{"premise":"There are four persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Minnie can now know whether Roger can know that Minnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Roger","Kimberly","Minnie"],"index":24511,"s-l":"forehead_mirror-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's forehead is muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy. It is publicly announced that Jerome knows whether Christopher's forehead is muddy. It is publicly announced that Jerome does not know 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 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 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) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jerome can now know that Dale can know that Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeanne","Dale","Jerome","Christopher"],"index":36333,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898236394,"difficulty":0.0101763606}
-{"premise":"There are two persons. Everyone is visible 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 knows whether or not nobody's forehead is muddy. It is publicly announced that Alan 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 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))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Alan can now know whether Gertrude can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alan","Gertrude"],"index":41518,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997723699,"difficulty":0.0002276301}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maxine does not know whether Robert is thirsty. It is publicly announced that Tessa does not know whether Maxine 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 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 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Tessa can now know whether Maxine can know that Maxine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tessa","Maxine","Robert"],"index":5391,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9266935587,"difficulty":1.9266935587}
-{"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. Patricia's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether someone picked a red card. It is publicly announced that Anthony knows whether someone picked a red card. It is publicly announced that Patricia 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)) ] [ ! 2 ] (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)) ] [ ! (Agenta knows whether (1|2)) ] [ ! 2 ] 0","hypothesis":"Anthony can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anthony","Patricia"],"index":32557,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999783814,"difficulty":0.000216186}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Helen can now know that Matthew can know that Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Dorothy","Joseph","Matthew"],"index":14928,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964795709,"difficulty":0.0035204291}
-{"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 Jeffrey. Jeffrey'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 someone picked a red card. It is publicly announced that Jeffrey picked a red card. It is publicly announced that Joseph picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","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":"Jeffrey can now know whether Joseph can know whether Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeffrey","Joseph"],"index":44060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970641732,"difficulty":0.0029358268}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jerry knows whether Jerry's forehead is muddy. It is publicly announced that Wayne 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) ] [ ! (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":"Wayne can now know whether Jerry can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Jerry","Wayne"],"index":57246,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9959962368,"difficulty":0.0040037632}
-{"premise":"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's forehead is muddy. It is publicly announced that Rebecca'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 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 ] [ ! ~(3) ] 0","hypothesis":"Richard can now know whether Angela can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Angela","Rebecca","Richard"],"index":18571,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7322888374,"difficulty":0.2677111626}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elton knows whether or not everyone's forehead is muddy. It is publicly announced that Trevor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Elton can now know that Bradley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bradley","Donald","Elton","Trevor"],"index":52842,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978121519,"difficulty":0.0021878481}
-{"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 Donald knows whether David is thirsty. It is publicly announced that Donald does not know whether Chris is thirsty.","smcdel_problem":"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) ] [ ! ~(Agentc knows whether 4) ] Agenta 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&2&3&4)) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Daniel can now know that David can know whether Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","David","Donald","Chris"],"index":39202,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7806939483,"difficulty":0.2193060517}
-{"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 Karen. Charles's card is shown to Theodore. Theodore's card is shown to Michelle. Michelle's card is shown to Michelle. Karen's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Charles picked a red card. It is publicly announced that Theodore 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) ] (Agentd 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":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Theodore","Michelle","Charles"],"index":46422,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984351993,"difficulty":0.0015648007}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Florence's card is shown to Florence. Andrew's card is shown to Florence. Andrew's card is shown to Andrew. Daniel'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:1,2 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:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Florence can now know that Andrew can know whether Florence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Andrew","Daniel"],"index":9785,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7570416927,"difficulty":0.2429583073}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucia knows whether someone's forehead is muddy. It is publicly announced that Lucia knows whether David'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) ] Agentb 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Katie can now know whether Ana can know that Ana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ana","Katie","David","Lucia"],"index":2962,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5881006718,"difficulty":0.4118993282}
-{"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 Richard. Richard's card is shown to Nicole. Rita's card is shown to Nicole. Richard's card is shown to Rita. Nicole's card is shown to Rita. 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 that (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":"Nicole can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Nicole","Rita"],"index":29207,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997729659,"difficulty":0.0002270341}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Sally. Sally'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 or not everyone picked a red card. It is publicly announced that Sally knows whether Sally 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) ] 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 (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sally can now know that Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sally","Deborah"],"index":22645,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5625312924,"difficulty":0.4374687076}
-{"premise":"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'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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Paula can now know that Haywood's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Haywood","Brenda","Charles","Paula"],"index":36414,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927500486,"difficulty":0.0072499514}
-{"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. Andrew's card is shown to Esther. Esther's card is shown to Dean. Dean'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:1 Agentc:2 Agentd: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 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dean can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Esther","Dean","John"],"index":12557,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982642531,"difficulty":0.0017357469}
-{"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 Janet does not know whether Hellen is thirsty. It is publicly announced that Hellen 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|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":"Hellen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","Hellen","Janet"],"index":7904,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984903336,"difficulty":0.0015096664}
-{"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. It is publicly announced that 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)) ] [ ! 3 ] Agentc 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) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Jimmy can now know whether Mary can know that Jimmy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cesar","Mary","Jimmy"],"index":9074,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9849354029,"difficulty":0.0150645971}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Emily can now know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Emily","Margaret","Nancy"],"index":20595,"s-l":"forehead_mirror-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 Edward'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 (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":"Edward can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ava","Edward"],"index":16394,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys does not know whether Gladys's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy. It is publicly announced that Larry 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)","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":"Larry can now know that Gladys's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gladys","Larry"],"index":64806,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.595692873,"difficulty":0.404307127}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie knows whether or not everyone's forehead is muddy. It is publicly announced that Harry 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":"Bonnie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jerry","Harry","Bonnie"],"index":1900,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997197986,"difficulty":0.0002802014}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wendy's card is shown to Wendy. Ali's card is shown to Wendy. Wendy's card is shown to Ali. Ali's card is shown to Ali. 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 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":"Wendy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Wendy","Ali"],"index":36319,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6185434461,"difficulty":0.3814565539}
-{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that Shelby'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 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":"Shelby can now know whether Timothy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelby","Sharon","Timothy"],"index":67276,"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 Rosetta does not know whether Jack is thirsty. It is publicly announced that Vernell 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] (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 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Rosetta can now know whether Jack is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vernell","Jack","Rosetta","Hazel"],"index":9848,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9885441661,"difficulty":0.0114558339}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Francisco's card is shown to Patricia. Mary's card is shown to Francisco. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Francisco knows whether Mary 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 someone 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 3) ] [ ! ~(Agentc knows whether (1&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:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Francisco can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Francisco","Mary"],"index":27487,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999481976,"difficulty":0.000518024}
-{"premise":"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 not muddy. It is publicly announced that Cynthia knows whether Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 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) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jessie can now know whether Katherine can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Katherine","Jessie","Helen"],"index":10321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983987212,"difficulty":0.0016012788}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hillary's card is shown to Walter. Karen's card is shown to Karen. Walter's card is shown to Hillary. 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 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":"Hillary can now know that Karen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Walter","Karen","Hillary"],"index":45982,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984278679,"difficulty":0.0015721321}
-{"premise":"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 Daniel's forehead is muddy. It is publicly announced that Reid knows whether Reid'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 that 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":"Daniel can now know whether Reid can know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Reid","Daniel"],"index":7186,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5839731097,"difficulty":0.4160268903}
-{"premise":"There are four persons. Everyone is visible 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 James knows whether James's forehead is muddy. It is publicly announced that Clyde knows whether Clyde's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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) ] (Agentb 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) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Clyde can now know whether Joan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Clyde","Laura","Joan"],"index":49255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996978045,"difficulty":0.0003021955}
-{"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 Carol. Carol's card is shown to Carol. Latoya's card is shown to Carol. Jean'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:1,3,4 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:1,3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chester can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jean","Chester","Carol","Latoya"],"index":25229,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997715354,"difficulty":0.0002284646}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melissa's card is shown to Teresa. Teresa's card is shown to Melissa. Teresa's card is shown to Mark. Melissa'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:2 Agentb:1 Agentc: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:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresa can now know that Melissa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Teresa","Melissa","Mark"],"index":27335,"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). Roland's card is shown to Charles. Roland's card is shown to Eric. Charles's card is shown to Roland. 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:1 Agentd: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:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Michael can know whether Roland picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Eric","Roland","Michael"],"index":32453,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7374662757,"difficulty":0.2625337243}
-{"premise":"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. It is publicly announced that Ashley 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)) ] 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ashley can now know that Jack can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Ashley","Jack"],"index":65963,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978430271,"difficulty":0.0021569729}
-{"premise":"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 everyone's forehead is muddy. It is publicly announced that Xiao'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) ] Agentb 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&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Xiao can now know whether Susan can know that Xiao's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Xiao","Susan"],"index":58211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8466256857,"difficulty":0.1533743143}
-{"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) ] [ ! (Agenta 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Virginia can now know whether Ronald can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Virginia","Barry","Dagmar"],"index":45060,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973592162,"difficulty":0.0026407838}
-{"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 Michelle. Anna's card is shown to Michelle. Michelle's card is shown to Amanda. Amanda's card is shown to Amanda. Amanda'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 Anna does not know whether Michelle 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 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 (Agenta knows that 1)","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":"Amanda can now know whether Michelle can know that Michelle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Amanda","Anna"],"index":51536,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9229752421,"difficulty":0.0770247579}
-{"premise":"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 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 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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Loretta can now know whether Jeffrey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loretta","Kathy","Jeffrey"],"index":3860,"s-l":"forehead-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's forehead is muddy. It is publicly announced that Zachary 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 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":"Michael can now know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristie","Eric","Zachary","Michael"],"index":34877,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983307719,"difficulty":0.0016692281}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice 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 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Dale can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Janice","Mary"],"index":38192,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
-{"premise":"There are four persons. Everyone is visible 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 Sue'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 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Mary can now know that Sue's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Patricia","Mary","Sue"],"index":66452,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8507062197,"difficulty":0.1492937803}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myrna knows whether Emelia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Sara can now know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Kathleen","Myrna","Emelia"],"index":34500,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982321858,"difficulty":0.0017678142}
-{"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. Kris's card is shown to Gina. Gina's card is shown to Kris. Peter's card is shown to Karen. Gina'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:1 Agentb:3 Agentc:2 Agentd:1,2 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 Agentb:3 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gina can now know that Karen can know that Gina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Peter","Gina","Kris","Karen"],"index":58389,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968403578,"difficulty":0.0031596422}
-{"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 Arlene 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 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":"James can now know that Arlene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Arlene","Nancy"],"index":64747,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982555509,"difficulty":0.0017444491}
-{"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 Jason. Jason's card is shown to Beulah. Beulah's card is shown to Beulah. Jason's card is shown to Maria. Beulah'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:3 Agentb:1,2 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:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Beulah can now know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jason","Beulah","Maria"],"index":45585,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7766760588,"difficulty":0.2233239412}
-{"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 Jasper is thirsty. It is publicly announced that Kathy does not know whether Jasper is thirsty. It is publicly announced that Kathy 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)) ] (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 3) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Edward can now know whether Kathy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerald","Edward","Jasper","Kathy"],"index":43028,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.945201993,"difficulty":0.054798007}
-{"premise":"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's forehead is not muddy. It is publicly announced that Glen 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 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":"Avis can now know whether Glen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Avis","Glen","Laura"],"index":31358,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995326996,"difficulty":0.0004673004}
-{"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 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":"Joshua can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joshua","Debra"],"index":7272,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9945253134,"difficulty":0.0054746866}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maurice's card is shown to Maureen. Bonnie's card is shown to Maureen. It is publicly announced that someone picked a red card. It is publicly announced that Maurice does not know whether Maureen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Maurice can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maurice","Bonnie","Maureen"],"index":53479,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997197986,"difficulty":0.0002802014}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scotty does not know whether Scotty's forehead is muddy. It is publicly announced that Lisa 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 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) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lisa can now know that Scotty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Scotty","Lisa"],"index":20161,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5191722512,"difficulty":1.5191722512}
-{"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 Roy is thirsty. It is publicly announced that Roy is thirsty. It is publicly announced that Roy 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 (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 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mary can now know whether Roy can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Roy","Robert"],"index":13867,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983167648,"difficulty":0.0016832352}
-{"premise":"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. It is publicly announced that Kimberly 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)) ] (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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Donald","Kimberly"],"index":23855,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5306899548,"difficulty":1.5306899548}
-{"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. Earl's card is shown to Raymond. Donald's card is shown to Raymond. Raymond's card is shown to Earl. Donald's card is shown to Earl. Raymond'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:1,3,4 Agentb:1,4 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:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Raymond can now know that Earl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Donna","Earl","Donald"],"index":40747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979903698,"difficulty":0.0020096302}
-{"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 Stacy. Philip's card is shown to Stacy. Stacy's card is shown to Brenda. Stacy's card is shown to Jennifer. Brenda's card is shown to Philip. Jennifer's card is shown to Philip. 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) ] 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 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Philip can now know whether Brenda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacy","Brenda","Jennifer","Philip"],"index":16549,"s-l":"explicit-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). Linda's card is shown to Mary. 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 whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Mary can now know whether Linda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Kevin","Linda"],"index":6520,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9972015619,"difficulty":0.0027984381}
-{"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 thirsty. It is publicly announced that Thaddeus 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 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 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thaddeus can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Thaddeus","Jimmy","Terri"],"index":10372,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967058301,"difficulty":0.0032941699}
-{"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 William is thirsty. It is publicly announced that Mario does not know whether or not everyone is thirsty. It is publicly announced that George does not know whether Lynne is thirsty. It is publicly announced that William 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)) ] Agentd knows whether (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 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Lynne can now know whether William can know whether Mario is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","George","Mario","Lynne"],"index":49204,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980916381,"difficulty":0.0019083619}
-{"premise":"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's forehead is muddy. It is publicly announced that Marielle does not know whether or not everyone's forehead is muddy. It is publicly announced that Marielle does not know whether Marielle'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 whether (Agenta knows whether 1)","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":"Marielle can now know whether Paul can know whether Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Marielle"],"index":46476,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9419451356,"difficulty":0.0580548644}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Lynda knows whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Peter can now know that Daniel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lynda","Leon","Daniel","Peter"],"index":28680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978821874,"difficulty":0.0021178126}
-{"premise":"There are two persons. Everyone is visible 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. 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) ] (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":"Diane can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jason","Diane"],"index":47309,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984359145,"difficulty":0.0015640855}
-{"premise":"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 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 (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":"James can now know whether Jessie can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Jessie","James","Keith"],"index":63987,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980211258,"difficulty":0.0019788742}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Lisa. Lisa's card is shown to Lisa. 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:1,2 Agentb: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:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Rosemary can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosemary","Lisa","Steven"],"index":52119,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6996873617,"difficulty":1.6996873617}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randy 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":"Dale can now know that Randy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dale","Randy"],"index":62844,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996727705,"difficulty":0.0003272295}
-{"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 William. Ela's card is shown to Harold. Gertrude's card is shown to Harold. William's card is shown to Ela. Gertrude's card is shown to Ela. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Gertrude picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 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 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"William can now know whether Harold can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Harold","Ela","Gertrude"],"index":56224,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
-{"premise":"There are four persons. Everyone is visible 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 Joan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 3) ] 0","hypothesis":"Nicholas can now know that Roberta can know that Katie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katie","Nicholas","Joan","Roberta"],"index":23984,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998434484,"difficulty":0.001565516}
-{"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 Dewayne 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) ] 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) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dewayne can now know that Calvin can know that Ella is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Calvin","Dewayne","Ella","Barbara"],"index":47344,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979019165,"difficulty":0.0020980835}
-{"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 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 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) ] [ ! ~(2) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Frank can know whether Frank is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","James","Myra","Frank"],"index":47432,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9969033599,"difficulty":0.0030966401}
-{"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 Jean is thirsty. It is publicly announced that Charla does not know whether James 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 (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 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jean can now know whether James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","Charla","James"],"index":41648,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8761732578,"difficulty":1.8761732578}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"Sonya can now know that John can know that Dee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dee","John","Sonya","Marnie"],"index":1782,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.969583571,"difficulty":0.030416429}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bruce's card is shown to Bruce. Christina's card is shown to Bruce. Jake's card is shown to Christina. Bruce's card is shown to Jake. Jake's card is shown to Jake. It is publicly announced that someone picked a red card. It is publicly announced that Jake 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)) ] 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:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bruce can now know whether Jake can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Christina","Jake"],"index":60120,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996808767,"difficulty":0.0003191233}
-{"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.","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 (~(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":"Robert can now know that Doug can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Robert","Doug"],"index":25914,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983810186,"difficulty":0.0016189814}
-{"premise":"There are 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":"Monica can now know that Ronnie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronnie","Hope","John","Monica"],"index":20199,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984635115,"difficulty":0.0015364885}
-{"premise":"There are three 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 Elizabeth's forehead is 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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Emma can now know that Elizabeth can know that Emma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Elizabeth","Emma"],"index":20950,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9790070057,"difficulty":0.0209929943}
-{"premise":"There are four persons. Everyone is visible 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) ] (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)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Dale can now know whether Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dale","Matthew","Shirley","Cynthia"],"index":26986,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997374415,"difficulty":0.0002625585}
-{"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 Paul. Todd's card is shown to Paul. Paul's card is shown to Todd. Todd's card is shown to Todd. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Todd picked a red card. It is publicly announced that Paul 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) ] [ ! 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 2) ] [ ! 1 ] 0","hypothesis":"Paul can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Todd"],"index":21485,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997791648,"difficulty":0.0002208352}
-{"premise":"There are four 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Virginia can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Virginia","Gregory","Lena"],"index":1373,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977982044,"difficulty":0.0022017956}
-{"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 Gustavo. Natasha's card is shown to Gustavo. Gustavo's card is shown to Natasha. Natasha's card is shown to Shannon. It is publicly announced that someone picked a red card. It is publicly announced that Natasha 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) ] [ ! 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:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Natasha can now know whether William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Gustavo","Natasha","Shannon"],"index":43116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995318651,"difficulty":0.0004681349}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frankie's forehead is muddy. It is publicly announced that Lilian knows whether someone's forehead is muddy. It is publicly announced that Frankie 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))) ] Agentb knows that (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) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jeanna can now know that Frankie can know that Lilian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frankie","Jeanna","Lilian"],"index":38735,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9727553129,"difficulty":0.0272446871}
-{"premise":"There are four persons. Everyone is visible to others. 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:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 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) ] [ ! ~(2) ] 0","hypothesis":"Alex can now know that Gina can know whether Gina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilfredo","Alex","Gina","Nancy"],"index":62418,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742544889,"difficulty":0.0257455111}
-{"premise":"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 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) ] [ ! ~(3) ] Agentc 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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether David can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","David","James","Vincent"],"index":36309,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993189573,"difficulty":0.0006810427}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frankie does not know whether Larry is thirsty. It is publicly announced that Larry 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 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":"Frankie can now know whether Frankie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angelica","Larry","Frankie","Charles"],"index":66447,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991040826,"difficulty":0.0008959174}
-{"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 Renee is thirsty. It is publicly announced that Renee 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) ] [ ! ~(Agenta knows whether 3) ] (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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Renee can now know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Renee","Michael","Joseph"],"index":43359,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9816840291,"difficulty":0.0183159709}
-{"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 Bertha. Jennifer's card is shown to Bertha. Alan's card is shown to Alan. Geoffrey's card is shown to Jennifer. Bertha's card is shown to Jennifer. Alan's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Geoffrey picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc: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:3,4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Geoffrey can now know that Alan can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geoffrey","Bertha","Alan","Jennifer"],"index":59101,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997833371,"difficulty":0.0002166629}
-{"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 (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":"Benjamin can now know that Johnnie can know that Benjamin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lillian","Benjamin","Johnnie","Mary"],"index":16198,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985620379,"difficulty":0.0014379621}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raphael's forehead is muddy. It is publicly announced that Ashley does not know 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) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (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) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Raphael can now know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Raphael","Steven","Charles","Ashley"],"index":63579,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994755387,"difficulty":0.0005244613}
-{"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 John. James's card is shown to James. James's card is shown to Molly. 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 that 4)","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":"James can now know that Molly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","John","James","Molly"],"index":8187,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978778362,"difficulty":0.0021221638}
-{"premise":"There are two 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 muddy. 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) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 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":"Michael can now know that Janet's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Janet"],"index":5366,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8237550855,"difficulty":1.8237550855}
-{"premise":"There are four persons. Everyone is visible 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 Steven'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) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Joe can now know whether Randy can know whether Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Clair","Joe","Randy"],"index":364,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997227788,"difficulty":0.0002772212}
-{"premise":"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's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Harry knows 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 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 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) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Peter can now know whether Ralph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Peter","Ralph"],"index":67396,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
-{"premise":"There are four persons. Everyone is visible 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 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 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Nathan can now know whether Fannie can know that Nathan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bruce","Fannie","Emily","Nathan"],"index":62115,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994254112,"difficulty":0.0005745888}
-{"premise":"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 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 (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":"Angelina can now know whether Karen can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Mark","Lisa","Angelina"],"index":27468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999542594,"difficulty":0.000457406}
-{"premise":"There are four persons. Everyone is visible 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'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 (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) ] [ ! ~(2) ] 0","hypothesis":"James can now know whether Helen can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Lisa","Helen","Sean"],"index":7619,"s-l":"forehead_mirror-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 Christa does not know whether Gregory is thirsty. It is publicly announced that Christa 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":"Sharan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christa","Sharan","Gregory"],"index":24563,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982045889,"difficulty":0.0017954111}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather does not know whether Heather's forehead is muddy. It is publicly announced that Heather 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":"Heather can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","James","Heather"],"index":48583,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978017211,"difficulty":0.0021982789}
-{"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. Donald's card is shown to Glenn. Donald's card is shown to Donald. 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 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) ] [ ! (1|2) ] [ ! ~(Agentb 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:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Glenn can now know whether Donald can know that Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Glenn","Donald"],"index":17378,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9679307938,"difficulty":0.0320692062}
-{"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 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) ] (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) ] 0","hypothesis":"Joellen can now know that Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Calvin","Joellen","Tina","Susan"],"index":25350,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983038902,"difficulty":0.0016961098}
-{"premise":"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 Rebecca's forehead is muddy. It is publicly announced that James's forehead is not 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) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agentc 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) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know whether Christopher can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Christopher","Rebecca","James"],"index":54810,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8125815988,"difficulty":1.8125815988}
-{"premise":"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 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 (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":"Anthony can now know that Linda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Phillip","Ralph","Linda"],"index":13474,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997532964,"difficulty":0.0002467036}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Susan can now know whether Roy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Barbara","Susan","Roy"],"index":3765,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5025337338,"difficulty":1.5025337338}
-{"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. Charles's card is shown to Troy. Kristen's card is shown to Troy. Paul's card is shown to Kristen. It is publicly announced that someone picked a red card. It is publicly announced that Paul knows whether Paul 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) ] (Agenta knows that (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":"Paul can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Troy","Charles","Kristen"],"index":2371,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986152649,"difficulty":0.0013847351}
-{"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 Kathy. Kathryn's card is shown to Kathy. Kathy's card is shown to Terry. Terry's card is shown to Terry. Kathryn's card is shown to Terry. Kathy's card is shown to Kathryn. 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 (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 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know that Kathy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathy","Terry","Kathryn"],"index":67607,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981870055,"difficulty":0.0018129945}
-{"premise":"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. It is publicly announced that Jack 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 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 (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Jack can now know that Peggy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Peggy","Charles"],"index":58317,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
-{"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 Mary 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) ] [ ! ~(Agentd knows whether 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) ] [ ! ~(Agentd knows whether 1) ] [ ! (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":["Mary","Michael","William","Patrick"],"index":58771,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997225821,"difficulty":0.002774179}
-{"premise":"There are three persons. Everyone is visible 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 Jennifer's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy. It is publicly announced that Jennifer 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) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (Agentb 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":"James can now know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","James","Jennifer"],"index":21638,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997022748,"difficulty":0.0002977252}
-{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Chris'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 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":"Chris can now know that Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michele","Chris"],"index":22218,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9972110391,"difficulty":0.0027889609}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Myrna's card is shown to Jimmie. Jimmie's card is shown to Myrna. 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 whether (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":"Jimmie can now know whether Myrna can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmie","Myrna","Anthony"],"index":31910,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769628,"difficulty":0.000230372}
-{"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 Richard 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) ] 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Luther can now know that Richard can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benjamin","Thomas","Luther","Richard"],"index":42401,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9917318225,"difficulty":0.0082681775}
-{"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 Amanda is thirsty. It is publicly announced that Robert knows whether Amanda 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":"Amanda can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Amanda"],"index":3232,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997233748,"difficulty":0.0002766252}
-{"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 Brandon. Larry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Brandon knows whether someone picked a red card. It is publicly announced that Brandon does not know whether or not everyone picked a red card. It is publicly announced that Brandon 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 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":"Larry can now know that Brandon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brandon","Larry"],"index":35687,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.639018178,"difficulty":1.639018178}
-{"premise":"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 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 (1&2&3)) ] [ ! ~(Agentc 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)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bertha can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Bertha","Robert"],"index":20145,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9334014654,"difficulty":1.9334014654}
-{"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. Gloria's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Steven 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 that (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":"Gloria can now know that Steven can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Gloria"],"index":29037,"s-l":"explicit-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 Carlos does not know whether or not everyone is thirsty. It is publicly announced that William 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)) ] (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&2)) ] 0","hypothesis":"Carlos can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carlos","William"],"index":23565,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998190105,"difficulty":0.001809895}
-{"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 Leo. Alva's card is shown to Leo. Susann's card is shown to Alva. Susann's card is shown to Susann. 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:1,2 Agentb:3 Agentc:3 Agentd: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 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Melissa can now know that Alva picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leo","Alva","Susann","Melissa"],"index":60202,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980788231,"difficulty":0.0019211769}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christie 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 1) ] (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":"Shirley can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Shirley","Christie","Joe"],"index":42421,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891405106,"difficulty":0.0108594894}
-{"premise":"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 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) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joe can now know whether Rebecca can know that Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Daniel","Joe"],"index":42140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9419466853,"difficulty":0.0580533147}
-{"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. Elizabeth's card is shown to Pauline. Pauline'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 Pauline 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":"Elizabeth can now know that Pauline can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pauline","Elizabeth"],"index":3997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997105002,"difficulty":0.0002894998}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dee does not know whether Soon 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 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":"Walter can now know that Dee is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Soon","Walter","Dee"],"index":25926,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977837205,"difficulty":0.0022162795}
-{"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 Francis. Susan's card is shown to Susan. Susan's card is shown to James. Aaron's card is shown to James. Francis's card is shown to Aaron. Susan'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: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":"James can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Susan","James","Aaron"],"index":48167,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9916439652,"difficulty":0.0083560348}
-{"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 James. James'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. It is publicly announced that James knows whether James picked a red card. It is publicly announced that Jill knows whether Jill 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) ] (Agentb knows that 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":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jill","James"],"index":47943,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928432703,"difficulty":0.0071567297}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delbert does not know whether Delbert's forehead 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 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":"Delbert can now know whether Betty can know whether Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delbert","Betty","Blanca"],"index":30841,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.91276896,"difficulty":1.91276896}
-{"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 Donald. Brian's card is shown to Brian. Paula's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Donald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 1)","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":"Brian can now know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Brian","David","Paula"],"index":27702,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5697490573,"difficulty":1.5697490573}
-{"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 Wayne. Kimberlee's card is shown to Wayne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erin can now know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erin","Wayne","Kimberlee"],"index":52055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9433723092,"difficulty":0.0566276908}
-{"premise":"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 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 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) ] [ ! (~(1&2)) ] 0","hypothesis":"Eula can now know that Nicholas can know that Eula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicholas","Eula"],"index":38217,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9955910444,"difficulty":1.9955910444}
-{"premise":"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 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":"David can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andre","David"],"index":33215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984454513,"difficulty":0.0015545487}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rolando's card is shown to Rolando. James's card is shown to Rolando. Rolando's card is shown to Peter. Kyle's card is shown to Peter. Rolando's card is shown to Kyle. James's card is shown to Kyle. It is publicly announced that someone 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:1,4 Agentb:1,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 1)","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":"Kyle can now know that Rolando can know that Rolando picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rolando","Peter","Kyle","James"],"index":23265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9304373264,"difficulty":0.0695626736}
-{"premise":"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 knows whether Eric's forehead is muddy. It is publicly announced that Eric 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 whether (~(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":"Eric can now know whether Kathryn can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Kathryn"],"index":46721,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994540811,"difficulty":0.0005459189}
-{"premise":"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 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) ] [ ! ~(Agentb knows whether 2) ] [ ! 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: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":"James can now know whether Anne can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Faye","Anne","Jon"],"index":33829,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7107486129,"difficulty":1.7107486129}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Lucy. Jim's card is shown to Lucy. Tuyet's card is shown to Jim. Jim's card is shown to Tuyet. It is publicly announced that someone picked a red card. It is publicly announced that Tuyet does not know whether Tuyet 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) ] (Agenta knows that 2)","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":"Lucy can now know that Jim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lucy","Jim","Tuyet"],"index":22118,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9800134301,"difficulty":0.0199865699}
-{"premise":"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 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 (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":"Harry can now know whether Sarah can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Clara","Sarah","Harry"],"index":57682,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9394689202,"difficulty":0.0605310798}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mariana does not know whether James is thirsty. It is publicly announced that Sylvia does not know whether Melanie is thirsty. It is publicly announced that Mariana does not know whether Sylvia is thirsty.","smcdel_problem":"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) ] 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Melanie can now know whether Mariana can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Melanie","James","Mariana"],"index":63632,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9959141612,"difficulty":0.0040858388}
-{"premise":"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 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":"Joseph can now know that Kenneth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Joseph","Blake","Ryan"],"index":11480,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992123842,"difficulty":0.0007876158}
-{"premise":"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 Claude knows whether Claude's forehead is muddy. It is publicly announced that Robert knows whether Claude'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) ] Agenta knows whether (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 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know whether Claude can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Claude"],"index":8097,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9891377091,"difficulty":0.0108622909}
-{"premise":"There are four persons. Everyone is visible 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 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 (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&2&3&4)) ] 0","hypothesis":"Grover can now know that Lara can know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Grover","Gregory","Dan","Lara"],"index":17287,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974622726,"difficulty":0.0025377274}
-{"premise":"There are two persons. Everyone is visible 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 Olga's forehead is not muddy. It is publicly announced that Marco'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":"Marco can now know that Olga can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marco","Olga"],"index":40503,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989443421,"difficulty":0.0010556579}
-{"premise":"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. It is publicly announced that Richard knows whether 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: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 ] 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|2|3)) ] [ ! 3 ] 0","hypothesis":"Vincent can now know that Thomas can know whether Vincent's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vincent","Thomas","Richard"],"index":30382,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984818101,"difficulty":0.0015181899}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sergio's card is shown to Lorenza. Jason's card is shown to Sergio. Sergio's card is shown to Michele. Jason's card is shown to Michele. Lorenza's card is shown to Jason. Michele'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:2 Agentb:4 Agentc:2,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sergio can now know that Lorenza picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorenza","Sergio","Michele","Jason"],"index":56704,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973312616,"difficulty":0.0026687384}
-{"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 Jimmie. Joan's card is shown to Tom. Tom's card is shown to Joan. Joan's card is shown to Joan. It is publicly announced that someone picked a red card. It is publicly announced that Joan 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 that (Agentc knows that 2)","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":"Tom can now know that Joan can know that Tom picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmie","Tom","Joan"],"index":491,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7127860188,"difficulty":1.7127860188}
-{"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 Leon. Gary's card is shown to Gary. George's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Leon 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":"Leon can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leon","Gary","George"],"index":5447,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985812902,"difficulty":0.0014187098}
-{"premise":"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 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) ] [ ! (Agenta knows whether 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 3) ] 0","hypothesis":"Thelma can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Thelma","William"],"index":16107,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988045692,"difficulty":0.0011954308}
-{"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 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":"Linda can now know whether Stephanie can know that Stephanie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Phillip","Stephanie"],"index":57602,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.898001194,"difficulty":0.101998806}
-{"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 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":"Juana can now know that Connie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Connie","Ann","Juana"],"index":48609,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988325238,"difficulty":0.0011674762}
-{"premise":"There are two persons. Everyone is visible 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 Earl's forehead is muddy. It is publicly announced that Derrick 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 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":"Derrick can now know whether Derrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Earl","Derrick"],"index":21669,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992436171,"difficulty":0.0007563829}
-{"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 Jeremy. Susan's card is shown to Jessica. Susan's card is shown to Susan. Hilda's card is shown to Susan. Susan's card is shown to Hilda. Hilda's card is shown to Hilda. 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) ] Agenta knows whether (Agentd knows that (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":"Jeremy can now know whether Hilda can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremy","Jessica","Susan","Hilda"],"index":22758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999424696,"difficulty":0.000575304}
-{"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 thirsty. It is publicly announced that Juanita 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 (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) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Thomas can now know that Juanita can know whether Juanita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Juanita","Thomas"],"index":23534,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9873235822,"difficulty":0.0126764178}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeremiah does not know whether or not everyone is thirsty. It is publicly announced that Jeremiah knows whether Jeremiah 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) ] Agentc knows whether (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) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"David can now know whether Sandra can know that Jeremiah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Jeremiah","David"],"index":48710,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9903304577,"difficulty":0.0096695423}
-{"premise":"There are three persons. Everyone is visible 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 ] 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":"Joseph can now know that Rosa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Ruth","Rosa"],"index":22764,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989816546,"difficulty":0.0010183454}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel 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 (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":"Samuel can now know whether Hannah can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","Hannah","Samuel"],"index":44686,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993459582,"difficulty":0.0006540418}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentd knows whether 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) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Nancy can now know that Paul can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Jim","Eleanor","Nancy"],"index":40446,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980592132,"difficulty":0.0019407868}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phuong's card is shown to Keith. Keith's card is shown to Phuong. Phuong's card is shown to Phuong. It is publicly announced that someone picked a red card. It is publicly announced that Phuong knows whether someone picked a red card. It is publicly announced that Keith knows whether someone picked a red card. It is publicly announced that Phuong knows whether Keith picked a red card. It is publicly announced that Phuong 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 that (1|2))","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":"Phuong can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Keith","Phuong"],"index":33700,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
-{"premise":"There are four persons. Everyone is visible 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 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Mary can now know that Beatrice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Beatrice","Mary","Erica"],"index":63833,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9782779217,"difficulty":0.0217220783}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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 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 Karyn can know whether Karyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karyn","Amanda","Henry"],"index":49890,"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. Each person draws a card, face unrevealed (red or black). Forrest's card is shown to Forrest. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Forrest 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 that (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":"Deborah can now know that Forrest can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Forrest","Deborah"],"index":58759,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989147186,"difficulty":0.0010852814}
-{"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 Trevor is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Christine does not know whether Marta is thirsty.","smcdel_problem":"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 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Christine can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Trevor","Adolph","Christine","Marta"],"index":32403,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965928197,"difficulty":0.0034071803}
-{"premise":"There are two 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 Maxine knows whether or not everyone's forehead is muddy. It is publicly announced that Amanda'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 that (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":"Amanda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maxine","Amanda"],"index":16884,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976750016,"difficulty":0.0023249984}
-{"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 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) ] 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":"Samuel can now know that James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Samuel"],"index":34356,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9830758572,"difficulty":0.0169241428}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tom 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 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":"Joseph can now know whether Tom is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tom","Joseph","Patricia"],"index":60692,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.975238204,"difficulty":0.024761796}
-{"premise":"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 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":"Clifton can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Clifton","Scott","Sylvia"],"index":14696,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990261793,"difficulty":0.0009738207}
-{"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 Donald is thirsty. It is publicly announced that Donald 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 (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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Cynthia can now know that Jeffrey can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Cynthia","Jeffrey"],"index":55301,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9912419319,"difficulty":0.0087580681}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kate's card is shown to Kate. Penelope's card is shown to Kate. Penelope'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:1,2 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 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kate can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kate","Penelope","Katherine"],"index":32217,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
-{"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 Danny. Danny's card is shown to Thomas. Thomas'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 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:3 Agentb:1 Agentc:2 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":["Danny","Thomas","John"],"index":7853,"s-l":"explicit-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). Michael's card is shown to Michael. James's card is shown to Michael. Michael's card is shown to James. James's card is shown to James. Joseph's card is shown to James. James's card is shown to Joseph. Joseph's card is shown to Martin. 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 4)","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":"Michael can now know that Martin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","James","Joseph","Martin"],"index":65632,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983926415,"difficulty":0.0016073585}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Don 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 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":"Don can now know that Melissa can know that Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Don","Melissa"],"index":21188,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9933634996,"difficulty":0.0066365004}
-{"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 Dianne. Al's card is shown to Dianne. Dianne's card is shown to Lisa. Al's card is shown to Lisa. Kathryn's card is shown to Kathryn. Lisa's card is shown to Al. It is publicly announced that someone picked a red card. It is publicly announced that Dianne knows whether or not nobody picked a red card. It is publicly announced that Dianne 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 ] (Agentc 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":"Kathryn can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dianne","Lisa","Kathryn","Al"],"index":37117,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990420938,"difficulty":0.0009579062}
-{"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 (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":"Joy can now know that Alicia can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Corey","Joy","Alicia","Armida"],"index":19154,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988889098,"difficulty":0.0011110902}
-{"premise":"There are three persons. Everyone is visible 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":"John can now know that Caroline can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Benjamin","Caroline"],"index":52497,"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). Edward's card is shown to James. James's card is shown to Edward. Ericka's card is shown to Ericka. Ericka'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 Edward 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 (Agenta knows whether 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":"Edward can now know that James can know whether Keith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Edward","Ericka","Keith"],"index":12589,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9952581525,"difficulty":0.0047418475}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Viola 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 4)","n_announcements":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":"Greta can now know that Greta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Viola","Grace","Cory","Greta"],"index":30786,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9894382358,"difficulty":0.0105617642}
-{"premise":"There are two persons. Everyone is visible 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 Joan'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|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":"Anne can now know that Joan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joan","Anne"],"index":52382,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989596605,"difficulty":0.0010403395}
-{"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 Cheryl. Kathryn's card is shown to Cheryl. Kathryn's card is shown to Linda. 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:1,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb 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:1,3 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Cheryl can now know that Amanda can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Cheryl","Kathryn","Linda"],"index":1049,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990441203,"difficulty":0.0009558797}
-{"premise":"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 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 (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":"Shirley can now know whether Alice can know whether Alice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Alice","Stephanie"],"index":40322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967036843,"difficulty":0.0032963157}
-{"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 Flora is thirsty. It is publicly announced that Warren does not know whether Flora is thirsty.","smcdel_problem":"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 4)","n_announcements":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":"Flora can now know that Flora is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Rosemary","Warren","Flora"],"index":28497,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9634153843,"difficulty":0.0365846157}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 (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":"Eric can now know that Patricia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Eric","Patricia","Angie"],"index":19351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994887114,"difficulty":0.0005112886}
-{"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. Robyn's card is shown to Jane. Ashley's card is shown to Ashley. Jane's card is shown to Robyn. 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:1,3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","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":"Ashley can now know whether Ashley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jane","Ashley","Robyn"],"index":7396,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5084484816,"difficulty":0.4915515184}
-{"premise":"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.","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":"Robert can now know that Andrew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Andrew","Robert"],"index":27754,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9629219174,"difficulty":0.0370780826}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Herbert can now know whether Janine can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Herbert","Kim","Janine","Linda"],"index":25854,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994313121,"difficulty":0.0005686879}
-{"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 Donna. Donna's card is shown to Brent. Brenda's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that Brenda does not know whether Donna picked a red card. It is publicly announced that Brenda does not know whether Donna 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 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Donna can now know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Brent","Brenda"],"index":63059,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9871698618,"difficulty":0.0128301382}
-{"premise":"There are three 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 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 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":"Jean can now know whether Jean is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joe","Harold","Jean"],"index":19162,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986999035,"difficulty":0.0013000965}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Burton 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 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 3) ] 0","hypothesis":"Susan can now know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Burton","Susan","Charles"],"index":18919,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993008256,"difficulty":0.006991744}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorna knows whether Aaron's forehead is muddy. It is publicly announced that Aaron does not know whether Aaron's forehead is muddy. It is publicly announced that Aaron does not know whether Aaron's forehead is muddy. It is publicly announced that Aaron knows whether Lorna'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 1)","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":"Aaron can now know that Lorna can know that Lorna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lorna","Aaron"],"index":47451,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9007114768,"difficulty":1.9007114768}
-{"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 (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":"Lauren can now know whether Mary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Jeanne","Lauren"],"index":10995,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994056225,"difficulty":0.0005943775}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosa does not know whether Roy is thirsty. It is publicly announced that Marry is 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 (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":"Marry can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bruce","Marry","Rosa","Roy"],"index":57248,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995032549,"difficulty":0.0004967451}
-{"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. Susan's card is shown to Charlotte. Brenda's card is shown to Brenda. Charlotte's card is shown to Susan. 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) ] Agenta knows whether (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":"Charlotte can now know whether Susan can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlotte","Brenda","Susan"],"index":18923,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993456006,"difficulty":0.0006543994}
-{"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 Louise. Michael's card is shown to Louise. Joyce's card is shown to Karen. Louise's card is shown to Michael. Michael's card is shown to Michael. Michael'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:2,3 Agentb:4 Agentc:1,3 Agentd: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:2,3 Agentb:4 Agentc:1,3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Louise can now know that Karen can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louise","Karen","Michael","Joyce"],"index":41480,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993558526,"difficulty":0.0006441474}
-{"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. Neil's card is shown to Louis. Louis's card is shown to Stacey. Stacey's card is shown to Neil. Neil's card is shown to Neil. It is publicly announced that someone picked a red card. It is publicly announced that Louis 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) ] (Agenta 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":"Louis can now know whether Stacey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louis","Stacey","Neil"],"index":9049,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8532918692,"difficulty":1.8532918692}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Milan's card is shown to Milan. Nina's card is shown to Milan. Justin's card is shown to Justin. Nina's card is shown to Justin. Milan's card is shown to Karen. Nina's card is shown to Karen. Nina's card is shown to Nina. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Nina can now know whether Karen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Milan","Justin","Karen","Nina"],"index":5299,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9868761301,"difficulty":0.0131238699}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cornell 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 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 (1|2|3)) ] 0","hypothesis":"Vernon can now know whether Stephan can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vernon","Stephan","Cornell"],"index":58666,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993751645,"difficulty":0.0006248355}
-{"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 Heather. Stephen's card is shown to Stephen. 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 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(1) ] (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":"Stephen can now know whether Stephen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Heather","Stephen"],"index":941,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9852446914,"difficulty":0.0147553086}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Denise can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynn","Denise","William"],"index":51121,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986307025,"difficulty":0.0013692975}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monica 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 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":"Monica can now know that Lynette is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lynette","Robert","Laurence","Monica"],"index":16774,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962800145,"difficulty":0.0037199855}
-{"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 Kattie is thirsty. It is publicly announced that Kattie knows whether Kattie 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 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kattie can now know whether Kattie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Jared","Kattie"],"index":55830,"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'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: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 (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":"Randall can now know that Madeleine can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Madeleine","Randall","David","Delbert"],"index":36497,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993921518,"difficulty":0.0006078482}
-{"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)) ] (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":"Edward can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edward","Darrell"],"index":19206,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993240833,"difficulty":0.0006759167}
-{"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. Everett's card is shown to Daniel. Mark's card is shown to Mark. Mark's card is shown to Johnathan. It is publicly announced that someone picked a red card. It is publicly announced that Mark picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Daniel can now know that Everett can know that Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Mark","Everett","Johnathan"],"index":12156,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9804602265,"difficulty":0.0195397735}
-{"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 or not nobody is thirsty. It is publicly announced that Cynthia 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 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))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Cynthia can now know whether Fernando can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Fernando","Cynthia","Margaret"],"index":21173,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994592071,"difficulty":0.0005407929}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Effie knows whether Effie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Tatum can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tatum","Randy","Effie","Verna"],"index":52591,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993698001,"difficulty":0.0006301999}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Reynaldo does not know whether Logan is thirsty.","smcdel_problem":"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 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":"Reynaldo can now know that Darryl can know that Logan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Reynaldo","David","Logan","Darryl"],"index":57361,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975278974,"difficulty":0.0024721026}
-{"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 Joseph. Alysia's card is shown to Alysia. Leslie's card is shown to Alysia. Leslie's card is shown to Robert. Alysia's card is shown to Leslie. Robert's card is shown to Leslie. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,4 Agentc:4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta 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:3 Agentb:2,4 Agentc:4 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Alysia can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Alysia","Robert","Leslie"],"index":40174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9697844386,"difficulty":0.0302155614}
-{"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. Justin's card is shown to Robert. Carter's card is shown to Robert. Robert's card is shown to Carter. Shane's card is shown to Carter. It is publicly announced that someone picked a red card. It is publicly announced that Justin does not know whether Shane 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)) ] (Agentc knows that 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":"Carter can now know that Shane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Robert","Carter","Shane"],"index":60483,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956160784,"difficulty":0.0043839216}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jean knows whether someone is thirsty. It is publicly announced that Jeana knows whether Jeana 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 (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":"Jean can now know that Jeana can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeana","Jean"],"index":36754,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988805652,"difficulty":0.0011194348}
-{"premise":"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 Harry's forehead is muddy. It is publicly announced that Ignacio 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 whether (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) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Ignacio can now know whether Harry can know that Harry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ignacio","Harry"],"index":3256,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7053913474,"difficulty":0.2946086526}
-{"premise":"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 (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":"Kate can now know whether Tony can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Tony","Jose","Kate"],"index":65119,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984663725,"difficulty":0.0015336275}
-{"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 Terry 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 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|2|3|4) ] 0","hypothesis":"George can now know whether George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Theodore","George","Rita","Terry"],"index":47072,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970431924,"difficulty":0.0029568076}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dwayne knows whether or not everyone is thirsty. It is publicly announced that Jessica 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) ] (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)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jessica","Dwayne","Gloria"],"index":27333,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995112419,"difficulty":0.0004887581}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle'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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] (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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michelle can now know whether Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerald","Melanie","Michelle"],"index":60515,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.81378901,"difficulty":0.18621099}
-{"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 Gwen. Thelma's card is shown to Gwen. Lee's card is shown to Lee. Thelma's card is shown to Thelma. 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":"Lee can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gwen","Lee","Thelma"],"index":40871,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989535809,"difficulty":0.0010464191}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marla's card is shown to Karl. Karl's card is shown to Willie. Marla's card is shown to Willie. Willie's card is shown to Marla. Marla's card is shown to Marla. 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.","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 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 2) ] 0","hypothesis":"Marla can now know whether Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karl","Willie","Marla"],"index":47899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5936346054,"difficulty":0.4063653946}
-{"premise":"There are two persons. Everyone is visible 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 everyone's forehead is muddy. It is publicly announced that Brian'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 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":"Amy can now know whether Brian can know that Amy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","Amy"],"index":35084,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994315505,"difficulty":0.0005684495}
-{"premise":"There are four persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Matthew can now know whether Carl can know that Tami's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tami","Carl","Matthew","Audrey"],"index":8327,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994332194,"difficulty":0.0005667806}
-{"premise":"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 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 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":"Robert can now know whether Anthony can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Anthony"],"index":14079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993548989,"difficulty":0.0006451011}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmela knows whether Carmela's forehead is muddy. It is publicly announced that Susan 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 (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) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Susan can now know whether Cyrus can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmela","Cyrus","Susan"],"index":34920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992540479,"difficulty":0.0007459521}
-{"premise":"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 Douglas knows whether Douglas's forehead is muddy. It is publicly announced that Douglas'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) ] Agentd knows that (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) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Brian can now know that Edward can know that Douglas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Shawn","Douglas","Brian"],"index":46843,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.983716011,"difficulty":0.016283989}
-{"premise":"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 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Brandi can now know that Leon can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jeffrey","Leon","Brandi"],"index":66625,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998927772,"difficulty":0.001072228}
-{"premise":"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 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 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":"Linda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Cynthia","Lulu","Linda"],"index":63532,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9348654747,"difficulty":1.9348654747}
-{"premise":"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 does not know whether Lee'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) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lee can now know that Jerry can know that Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Tammy","Lee"],"index":64311,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9821106791,"difficulty":0.0178893209}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Sidney can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrea","Amy","Andre","Sidney"],"index":29479,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987646341,"difficulty":0.0012353659}
-{"premise":"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 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 (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 (~(1|2|3|4))) ] 0","hypothesis":"Russell can now know that Aaron can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Aaron","Kenneth","Russell"],"index":35763,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970061183,"difficulty":0.0029938817}
-{"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 Juliet. Stephen's card is shown to Juliet. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Aaron picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Susan can now know that Juliet picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Aaron","Stephen","Juliet"],"index":35052,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997887671,"difficulty":0.002112329}
-{"premise":"There are four persons. Everyone is visible 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 (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":"Susan can now know that Darren can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Susan","Suzanne","Darren"],"index":17126,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989262223,"difficulty":0.0010737777}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Thomas can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Thomas","Laura"],"index":59810,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9920588732,"difficulty":0.0079411268}
-{"premise":"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 Cheryl 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 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":"Cheryl can now know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cynthia","Cheryl","Edna"],"index":52594,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.963588655,"difficulty":0.036411345}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Blanche can now know whether Howard can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Blanche","Howard"],"index":24456,"s-l":"forehead_mirror-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 Floyd does not know whether Floyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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 2) ] 0","hypothesis":"Kevin can now know that Lillie can know whether Floyd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lillie","Floyd","Kevin","Betty"],"index":23537,"s-l":"forehead-1","deberta_pred":1,"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. It is publicly announced that Anthony 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) ] [ ! (Agentc knows whether 2) ] Agentc 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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Anthony can now know that Christine can know whether Gina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Timothy","Anthony","Gina"],"index":57877,"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. 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Tonya can now know that Susan can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonnie","Brenda","Susan","Tonya"],"index":20020,"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. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Irene. Elizabeth's card is shown to Irene. Elizabeth's card is shown to Rhonda. Irene's card is shown to Elizabeth. Jean's card is shown to Elizabeth. Jean'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:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Irene","Rhonda","Elizabeth","Jean"],"index":9489,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8300721645,"difficulty":1.8300721645}
-{"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 Jason. Leo's card is shown to Ruben. Leo's card is shown to Leo. 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) ] Agenta knows that (Agentc knows that 1)","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":"Jason can now know that Leo can know that Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Ruben","Leo"],"index":63732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9824202061,"difficulty":0.0175797939}
-{"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 Peter. Roy's card is shown to Kevin. Kevin's card is shown to Robert. Robert's card is shown to Robert. Roy's card is shown to Robert. Kevin'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:3 Agentb:4 Agentc:2,3,4 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:3 Agentb:4 Agentc:2,3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Peter can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Peter","Kevin","Robert","Roy"],"index":66888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
-{"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 Guadalupe 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":"Leona can now know whether Susan can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leona","Susan","Guadalupe"],"index":42059,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9967088699,"difficulty":0.0032911301}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Norma 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) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Norma can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norma","Pamela","Keith"],"index":25884,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994415641,"difficulty":0.0005584359}
-{"premise":"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 Daniel does not know whether Daniel'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 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd 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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Megan can now know that Thomas can know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Laura","Thomas","Megan"],"index":55335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962355494,"difficulty":0.0037644506}
-{"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|2|3|4))","n_announcements":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":"Christopher can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jamie","Sylvia","Bruce","Christopher"],"index":30522,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
-{"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 Brenda. Karen's card is shown to Brenda. Brenda's card is shown to Jose. Ella's card is shown to Jose. Karen's card is shown to Jose. Brenda's card is shown to Ella. Brenda'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:1,3,4 Agentc:1 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:3,4 Agentb:1,3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ella can now know whether Karen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Jose","Ella","Karen"],"index":31853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6353532076,"difficulty":0.3646467924}
-{"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 Geneva. Kerrie's card is shown to Kerrie. Helen's card is shown to Kerrie. 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:2,3 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:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kerrie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Geneva","Kerrie","Helen"],"index":25676,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9914719462,"difficulty":0.0085280538}
-{"premise":"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 Toby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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 3) ] 0","hypothesis":"Carry can now know whether Alan can know that Toby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carry","Alan","Toby","Gwendolyn"],"index":62250,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.943380475,"difficulty":0.056619525}
-{"premise":"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 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":"Craig can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Craig","John"],"index":4785,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994702935,"difficulty":0.0005297065}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Margaret knows whether Samuel's forehead is muddy. It is publicly announced that Ellan 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) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Rhonda can now know that Margaret can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rhonda","Ellan","Margaret","Samuel"],"index":62696,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
-{"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 Newton. Eli's card is shown to Eli. Edward's card is shown to Eli. Newton's card is shown to Edward. 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) ] (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) ] [ ! (1&2&3) ] 0","hypothesis":"Newton can now know that Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Newton","Eli","Edward"],"index":46570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9809897542,"difficulty":0.0190102458}
-{"premise":"There are three persons. Everyone is visible 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 Alice'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&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":"Debra can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Waldo","Alice"],"index":41967,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988142252,"difficulty":0.0011857748}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Berry does not know whether Ethel is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Eileen does not know whether Ethel is thirsty.","smcdel_problem":"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) ] (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 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Eileen can now know that Ethel is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ethel","Berry","Rose","Eileen"],"index":20407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969553947,"difficulty":0.0030446053}
-{"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. Kenneth's card is shown to Michael. Kenneth's card is shown to Sheila. Sheila's card is shown to Sheila. 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:1,2 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:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Kenneth","Sheila"],"index":28188,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994257689,"difficulty":0.0005742311}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Victoria. Mark's card is shown to Mark. 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 whether (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":"Victoria can now know whether Benjamin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Benjamin","Victoria","Mark"],"index":47199,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993641973,"difficulty":0.0006358027}
-{"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 Carl is thirsty. It is publicly announced that Guadalupe knows whether someone is thirsty. It is publicly announced that John 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 1,2,3,4 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)) ] Agentb 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) ] [ ! ~(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":"John can now know whether Martha can know that Guadalupe is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guadalupe","John","Carl","Martha"],"index":8673,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9832693338,"difficulty":0.0167306662}
-{"premise":"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 does not know whether Dan's forehead 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)","n_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 Matthew can know whether Dan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dan","Cody","Matthew"],"index":42996,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991588593,"difficulty":0.0008411407}
-{"premise":"There are 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 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":"Bobby can now know that Edith can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","Kenneth","Bobby","Cassie"],"index":52123,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978860021,"difficulty":0.0021139979}
-{"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 Genevieve is thirsty. It is publicly announced that John does not know whether 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Mike can now know that Genevieve can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Genevieve","Margaret","Mike"],"index":41255,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989842772,"difficulty":0.0010157228}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Buddy 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 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":"Michelle can now know that Buddy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Billy","Buddy","Michelle","Lauren"],"index":65693,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974281192,"difficulty":0.0025718808}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Violet's card is shown to Sharon. Sharon's card is shown to Judy. Violet's card is shown to Judy. Judy's card is shown to Violet. Violet's card is shown to Violet. 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. It is publicly announced that Judy knows whether Violet picked a red card. It is publicly announced that Judy 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)) ] Agentb knows whether (Agenta knows that 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":"Judy can now know whether Sharon can know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Judy","Violet"],"index":54878,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8131505847,"difficulty":0.1868494153}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Therese'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 (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":"Christopher can now know whether Marcene can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marcene","Therese","Christopher"],"index":14223,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992945194,"difficulty":0.0007054806}
-{"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 Tracy. Matthew's card is shown to Tracy. Keith's card is shown to Tracy. Marsha's card is shown to Matthew. Marsha'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:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know that Tracy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Matthew","Marsha","Keith"],"index":40754,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973166585,"difficulty":0.0026833415}
-{"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 Richard. Richard's card is shown to Randy. Richard's card is shown to Gene. 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) ] Agentb knows whether (Agenta knows that 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":"Randy can now know whether Richard can know that Gene picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Randy","Gene"],"index":5026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.887509644,"difficulty":0.112490356}
-{"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 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) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mark can now know whether Raymond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Raymond","Timothy","Mark"],"index":19331,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973096848,"difficulty":0.0026903152}
-{"premise":"There are four persons. Everyone is visible 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 Andrew knows whether or not nobody's forehead is muddy. It is publicly announced that Belinda knows whether Stella's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Andrew can now know that Stella can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Andrew","Stella","Belinda"],"index":20628,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988735318,"difficulty":0.0011264682}
-{"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 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) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Louis can now know whether Clara can know that Clara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Louis","Barbara","Lorraine","Clara"],"index":18067,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9889233112,"difficulty":0.0110766888}
-{"premise":"There are two persons. Everyone is visible 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)) ] (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) ] [ ! (~(1&2)) ] 0","hypothesis":"Timothy can now know whether Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","Timothy"],"index":23114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992536902,"difficulty":0.0007463098}
-{"premise":"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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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 William can know that Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Michael","William","Louise"],"index":7575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9870142937,"difficulty":0.0129857063}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alejandro does not know whether Terrence is thirsty. It is publicly announced that Nathan 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)) ] (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) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Terrence can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alejandro","Nathan","Vera","Terrence"],"index":39491,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959640503,"difficulty":0.0040359497}
-{"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 Jessie. Jessie's card is shown to Bridget. Ervin's card is shown to Bridget. Ervin's card is shown to Andrew. Andrew's card is shown to Ervin. Ervin's card is shown to Ervin. 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) ] Agentc knows whether (Agenta 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":"Andrew can now know whether Jessie can know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessie","Bridget","Andrew","Ervin"],"index":18337,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.647980392,"difficulty":0.352019608}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pennie's card is shown to Pennie. Matt's card is shown to Matt. Jennifer's card is shown to Jennifer. Pennie's card is shown to Ebony. Jennifer's card is shown to Ebony. 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 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:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ebony can now know that Jennifer can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pennie","Matt","Jennifer","Ebony"],"index":27292,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9692741036,"difficulty":0.0307258964}
-{"premise":"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 (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":"Amanda can now know that Martha can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Martha","Thomas","Amanda"],"index":55888,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894743562,"difficulty":0.0105256438}
-{"premise":"There are two persons. Everyone is visible 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 Jeremy'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 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&2)) ] [ ! 1 ] 0","hypothesis":"Jeremy can now know that Barbara can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jeremy","Barbara"],"index":14870,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9779595137,"difficulty":0.0220404863}
-{"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 Ryan. Michael's card is shown to Michael. Ryan's card is shown to Melissa. 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) ] (Agentc 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) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melissa can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Michael","Melissa","Neil"],"index":22288,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9772166014,"difficulty":0.0227833986}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma knows whether or not everyone'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 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 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":"Wilma can now know that Christy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wilma","Christy","Tammy"],"index":41246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807434678,"difficulty":0.0192565322}
-{"premise":"There are four persons. Everyone is visible 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 May's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"May can now know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melvin","May","Debra","Rachel"],"index":56379,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983711839,"difficulty":0.0016288161}
-{"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 Trudi is thirsty. It is publicly announced that Doris 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 2) ] [ ! ~(Agentd knows whether 3) ] 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"David can now know whether Doris can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Trudi","John","Doris"],"index":16470,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937700629,"difficulty":0.0062299371}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jimmy's card is shown to Sara. Rhonda's card is shown to Sara. Rhonda's card is shown to Jimmy. Rhonda's card is shown to Star. It is publicly announced that someone picked a red card. It is publicly announced that Star does not know whether Sara 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) ] Agenta knows that (Agentc knows whether 1)","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":"Sara can now know that Star can know whether Sara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sara","Jimmy","Star","Rhonda"],"index":24206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6030892134,"difficulty":0.3969107866}
-{"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 Byron. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Byron 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 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&2)) ] 0","hypothesis":"Kevin can now know that Byron can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Byron","Kevin"],"index":30495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988942742,"difficulty":0.0011057258}
-{"premise":"There are three persons. Everyone is visible 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 (1|2|3))","n_announcements":1,"pbcheck":"VARS 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":"Johnny can now know whether Autumn can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raul","Autumn","Johnny"],"index":34470,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992532134,"difficulty":0.0007467866}
-{"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. Alice's card is shown to Eugene. 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 Eugene knows whether or not nobody 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))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Eugene can now know that Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alice","Eugene"],"index":44361,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9895964265,"difficulty":0.0104035735}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micaela does not know whether Emily is thirsty. It is publicly announced that Micaela 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 (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 (1&2&3)) ] 0","hypothesis":"Emily can now know that Micaela can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emily","Micaela","Jasper"],"index":54523,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995093346,"difficulty":0.0004906654}
-{"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 Roxanne. 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 that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Roxanne","James","George"],"index":41326,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989697933,"difficulty":0.0010302067}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maurice does not know whether Mitchell 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) ] 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Marcy can now know whether Maurice can know that Marcy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mitchell","Marcy","Maurice","Richard"],"index":1977,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9764816165,"difficulty":0.0235183835}
-{"premise":"There are four persons. Everyone is visible 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 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 1) ] 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joseph can now know that Bradley can know that Tammy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tammy","Bradley","Gloria","Joseph"],"index":66232,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974834323,"difficulty":0.0025165677}
-{"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. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Norma picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb 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":"Wanda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Norma","Wanda","David"],"index":54611,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9314910769,"difficulty":0.0685089231}
-{"premise":"There are four persons. Everyone is visible 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 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":"Kathy can now know whether Valencia can know whether Ruth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathy","Valencia","Ruth","John"],"index":38951,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992846847,"difficulty":0.0007153153}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leigh's card is shown to Leigh. Leigh's card is shown to Chelsea. Chelsea's card is shown to Chelsea. It is publicly announced that someone picked a red card. It is publicly announced that Chelsea knows whether or not nobody picked a red card. It is publicly announced that Chelsea knows whether Leigh 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":"Chelsea can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leigh","Chelsea"],"index":24580,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987180233,"difficulty":0.0012819767}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Tom 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))) ] (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 (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tom can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Helen","Tom","Rex"],"index":14472,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990488887,"difficulty":0.0009511113}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne does not know whether Lillian is thirsty. It is publicly announced that Alan does not know whether Lillian is thirsty. It is publicly announced that Alan 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 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":"Lillian can now know whether Yvonne can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lillian","Yvonne","Alan"],"index":51149,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993870258,"difficulty":0.0006129742}
-{"premise":"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 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 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":"Bradley 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":["Bradley","Robert"],"index":64715,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9754604697,"difficulty":0.0245395303}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa does not know whether Michael is thirsty. 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 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 that (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) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Teresa can now know that Michael can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Jennie","Teresa"],"index":512,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8879603744,"difficulty":0.1120396256}
-{"premise":"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 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)) ] (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":"Willie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrew","Willie","Billie"],"index":42056,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994575381,"difficulty":0.0005424619}
-{"premise":"There are three persons. Everyone is visible 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 Joel's forehead is muddy.","smcdel_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 (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":"Joel can now know that Hazel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hazel","Leonard","Joel"],"index":45044,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989218712,"difficulty":0.0010781288}
-{"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 Lloyd. Mary's card is shown to Christopher. Christopher's card is shown to Christopher. Eric's card is shown to Christopher. Lloyd'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 Christopher 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 that (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":"Christopher can now know that Lloyd can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Lloyd","Christopher","Eric"],"index":54696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.711356461,"difficulty":0.288643539}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Letha 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 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) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Devin can now know that Letha can know that Letha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Letha","Devin","Joycelyn"],"index":41441,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.924038291,"difficulty":0.075961709}
-{"premise":"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 Ronald's forehead is muddy. It is publicly announced that Malika's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 ] 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) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Malika can now know whether Arturo can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arturo","Amanda","Malika","Ronald"],"index":24199,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993374944,"difficulty":0.0006625056}
-{"premise":"There are four persons. Everyone is visible 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Jerry can now know whether Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerry","Glynis","Carol","Helen"],"index":11126,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999425292,"difficulty":0.000574708}
-{"premise":"There are two persons. Everyone is visible 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 everyone's forehead is muddy. It is publicly announced that Kim knows whether Henry's forehead is muddy. It is publicly announced that Kim 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|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":"Henry can now know that Kim can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kim","Henry"],"index":44853,"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. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Mary. Michael's card is shown to Richard. Mary's card is shown to Michael. Richard'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 Richard 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)) ] (Agentb knows that (~(1|2|3)))","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":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Richard","Michael"],"index":26256,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990051389,"difficulty":0.0009948611}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrice'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 (~(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":"Greg can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patrice","Greg"],"index":11338,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988818765,"difficulty":0.0011181235}
-{"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. Lyndsey's card is shown to Julia. Julia's card is shown to Denise. Michael's card is shown to Michael. Denise's card is shown to Lyndsey. Michael's card is shown to Lyndsey. Lyndsey's card is shown to Lyndsey. 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: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:1,4 Agentb:1 Agentc:3 Agentd:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lyndsey can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julia","Denise","Michael","Lyndsey"],"index":49833,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994131327,"difficulty":0.0005868673}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille 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 (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":"Ann can now know that Lucille can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lucille","Ann"],"index":10354,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989834428,"difficulty":0.0010165572}
-{"premise":"There are four persons. Everyone is visible 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 Jordan 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 (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) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Mireya can now know that Jordan can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jordan","Nancy","Richard","Mireya"],"index":7284,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986666441,"difficulty":0.0013333559}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Patricia's forehead is muddy. It is publicly announced that 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) ] [ ! 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":"Linda can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Linda","Amy","Patricia"],"index":20960,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994670749,"difficulty":0.0005329251}
-{"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 Jennifer. Ronald's card is shown to Jennifer. Jennifer's card is shown to Linda. Jennifer'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:1,4 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:1,4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Jennifer","Linda","Ronald"],"index":18760,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989462495,"difficulty":0.0010537505}
-{"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 Mi. Mi's card is shown to Virginia. Virginia'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:4 Agentb:2 Agentc: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:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mi can now know whether Virginia can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Mi","Virginia","Kimberly"],"index":31298,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9443525076,"difficulty":0.0556474924}
-{"premise":"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 Tarah knows whether or not everyone's forehead is muddy. It is publicly announced that Roger knows 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"William can now know that Agustin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tarah","William","Roger","Agustin"],"index":67581,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990353584,"difficulty":0.0009646416}
-{"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 Kevin. Kevin's card is shown to Ana. Ana's card is shown to Ana. Ana'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:1,2 Agentc: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:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Walter can now know that Kevin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Ana","Walter"],"index":33320,"s-l":"explicit-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's forehead is muddy. It is publicly announced that Thomas knows whether Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] 0","hypothesis":"Thomas can now know that Philip can know that Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Timothy","Thomas","Isaac"],"index":19675,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9846950173,"difficulty":0.0153049827}
-{"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 Demetrius. Demetrius's card is shown to Demetrius. Leroy's card is shown to Demetrius. Leroy's card is shown to Leroy. 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 (Agenta 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":"Demetrius can now know whether James can know whether Demetrius picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Demetrius","Leroy"],"index":18071,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973570704,"difficulty":0.0026429296}
-{"premise":"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'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) ] 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) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Jason can now know that Carla can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Carla","Jason"],"index":25511,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999317646,"difficulty":0.000682354}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jesse's card is shown to Jesse. Katie's card is shown to Frank. Jesse's card is shown to Katie. 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 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 1)","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":"Jesse can now know whether Jesse picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jesse","Frank","Katie"],"index":17864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9103828669,"difficulty":0.0896171331}
-{"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 Cynthia is thirsty. It is publicly announced that 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) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 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) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"Joseph can now know whether Margaret can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Derrick","Margaret","Joseph"],"index":2436,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989596605,"difficulty":0.0010403395}
-{"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 Heath. Kristopher's card is shown to Andrew. Heath's card is shown to Kristopher. Andrew's card is shown to Kristopher. Kristopher's card is shown to Kristopher. It is publicly announced that someone picked a red card. It is publicly announced that Andrew 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)) ] (Agentb knows that (1|2|3))","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":"Andrew can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Heath","Andrew","Kristopher"],"index":55949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993946552,"difficulty":0.0006053448}
-{"premise":"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 Victoria's forehead is muddy. It is publicly announced that Jane 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 whether (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) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Victoria can now know whether Jane can know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Victoria","Jane"],"index":61133,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7783370614,"difficulty":0.2216629386}
-{"premise":"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 knows whether or 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) ] [ ! (Agentb knows whether (1&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 (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Frank can now know that Chris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chris","Frank"],"index":34035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994766116,"difficulty":0.0005233884}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jasmin knows whether Jasmin'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":"Stephen can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jasmin","Stephen"],"index":23174,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999363482,"difficulty":0.000636518}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Avril's card is shown to Sandra. David's card is shown to Sandra. Marie's card is shown to Sandra. Sandra's card is shown to David. David's card is shown to David. David'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:2,3,4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","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":"David can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Avril","David","Marie"],"index":17900,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9430911541,"difficulty":0.0569088459}
-{"premise":"There are four persons. Everyone is visible 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 Mary'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 2) ] [ ! (Agentb knows whether 2) ] 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) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know that Thomas can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Mary","Thomas","Jacob"],"index":46249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9923750758,"difficulty":0.0076249242}
-{"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 Judy. Audrey's card is shown to Audrey. Robert's card is shown to Audrey. Judy'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 Robert knows whether Judy 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) ] (Agenta knows whether (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":"Judy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judy","Audrey","Robert"],"index":10179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9316136241,"difficulty":0.0683863759}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"Jill can now know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Jill","Thomas","James"],"index":63628,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971154928,"difficulty":0.0028845072}
-{"premise":"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 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":"Reba can now know that Antonio's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Michael","Antonio","Reba"],"index":5636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963650703,"difficulty":0.0036349297}
-{"premise":"There are four persons. Everyone is visible 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 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":"Dennis can now know whether Judith can know that Dennis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Robert","James","Judith"],"index":28955,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992672801,"difficulty":0.0007327199}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margie 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) ] [ ! ~(Agentc 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Andrea can now know whether Margie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Scott","Andrea","Margie"],"index":31503,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9934270382,"difficulty":0.0065729618}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Seymour knows whether or not everyone's forehead is muddy. It is publicly announced that Seymour does not know whether Seymour's forehead 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 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":"Janice can now know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Seymour","Steven","Janice"],"index":32131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9847220778,"difficulty":0.0152779222}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bridget does not know whether Bridget's forehead 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 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":"Kelly can now know whether Bridget can know that Bridget's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bridget","Ann","Kelly"],"index":61536,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.670168817,"difficulty":1.670168817}
-{"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. Joe'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: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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Grant can now know whether Joe can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grant","Joe","Joseph"],"index":53834,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994334579,"difficulty":0.0005665421}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pearly 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 3)","n_announcements":1,"pbcheck":"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":"Trevor can now know whether Trevor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Pearly","Trevor"],"index":29050,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993784428,"difficulty":0.0006215572}
-{"premise":"There are 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 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":"Lakisha can now know that Marjorie can know that Lakisha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marjorie","Donald","Lakisha"],"index":33010,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981020093,"difficulty":0.0018979907}
-{"premise":"There are 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":"Theresa can now know that Ramon can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ramon","Theresa","Betty"],"index":36734,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99927634,"difficulty":0.00072366}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mitchell's card is shown to Mitchell. Bruce's card is shown to Mitchell. Edward's card is shown to George. Bruce's card is shown to Edward. 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: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:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know that George can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mitchell","George","Edward","Bruce"],"index":2433,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981922507,"difficulty":0.0018077493}
-{"premise":"There are three persons. Everyone is visible 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 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 (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 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":"Kimberly can now know whether Dorothy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Kimberly","Shawn"],"index":60412,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994643331,"difficulty":0.0005356669}
-{"premise":"There are four persons. Everyone is visible 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 Tamika'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|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":"James can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Mark","Carol","Tamika"],"index":64914,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994043112,"difficulty":0.0005956888}
-{"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 Arianne 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 (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":"Randall can now know whether Michael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arianne","Randall","Michael"],"index":13079,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993931055,"difficulty":0.0006068945}
-{"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 Sharon. Sharon's card is shown to Roy. Sharon's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Sharon knows whether or not everyone picked a red card. It is publicly announced that Sylvia does not know whether Roy 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 that (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":"Sharon can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharon","Roy","Sylvia","Jason"],"index":64864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994775653,"difficulty":0.0005224347}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilber knows whether 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) ] [ ! (Agenta knows whether 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Wilber can now know that Niki can know that Wilber's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wilber","Angela","Niki"],"index":22022,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974488616,"difficulty":0.0025511384}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria is thirsty. It is publicly announced that Marilyn does not know whether Marianne is thirsty. It is publicly announced that Marilyn 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) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gloria can now know that Marianne can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marilyn","Evelyn","Marianne","Gloria"],"index":48777,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996516943,"difficulty":0.003483057}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Delbert does not know whether or not everyone is thirsty. It is publicly announced that Clara does not know whether Daisy is thirsty. It is publicly announced that Clara does not know whether or not everyone is thirsty. It is publicly announced that Delbert does not know whether Daisy 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 (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Daisy can now know that Clara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Delbert","Clara","Daisy"],"index":40189,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9876547456,"difficulty":1.9876547456}
-{"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) ] [ ! ~(1) ] 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) ] [ ! ~(1) ] 0","hypothesis":"Mike can now know whether Jodi can know whether Mike is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mike","Manuel","Ruben","Jodi"],"index":48402,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991059899,"difficulty":0.0008940101}
-{"premise":"There are two persons. Everyone is visible 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 Elizabeth 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":"Elizabeth can now know that David can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elizabeth","David"],"index":30636,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999360621,"difficulty":0.000639379}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim knows whether or not everyone's forehead is muddy. It is publicly announced that Kimberly'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":"Kimberly can now know that Jim can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jim","Kimberly"],"index":45111,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990153313,"difficulty":0.0009846687}
-{"premise":"There are two persons. Everyone is visible 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. 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 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":"William can now know whether Craig can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Craig","William"],"index":28651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991600513,"difficulty":0.0008399487}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luana does not know whether Luana'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 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Luana can now know whether Lizzie can know that Luana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lizzie","Luana","Kenneth"],"index":21575,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8651457429,"difficulty":0.1348542571}
-{"premise":"There are four persons. Everyone is visible 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 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) ] 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 2) ] 0","hypothesis":"Priscilla can now know that Patricia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Patricia","Priscilla","Timothy"],"index":17470,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989250302,"difficulty":0.0010749698}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Henry can now know that Stephanie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Stephanie","Betty","William"],"index":38184,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989429116,"difficulty":0.0010570884}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Wendy's card is shown to Todd. Todd's card is shown to Wendy. Wendy's card is shown to Wendy. Michael's card is shown to Wendy. Wendy'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:2,3,4 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 Agentb:2,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Todd can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roberta","Todd","Wendy","Michael"],"index":32859,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994143248,"difficulty":0.0005856752}
-{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Betty knows whether Betty's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Keith 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)) ] (Agentb 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":"Keith can now know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Betty","Keith"],"index":55134,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994458437,"difficulty":0.005541563}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sara 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 ] (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) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"Robert can now know that Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Joseph","Sara","James"],"index":5965,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976010919,"difficulty":0.0023989081}
-{"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 (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":"Deborah can now know whether Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Deborah"],"index":23522,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984361529,"difficulty":0.0015638471}
-{"premise":"There are four persons. Everyone is visible 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 Raelene's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Douglas can now know that Raelene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raelene","Justin","Antonio","Douglas"],"index":63095,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9685149193,"difficulty":0.0314850807}
-{"premise":"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 (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":"William can now know whether Latasha can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tasha","Latasha","William"],"index":14120,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9623618722,"difficulty":0.0376381278}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marylou 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 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":"Effie can now know whether David can know whether Effie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Effie","Marylou","David"],"index":40286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993784428,"difficulty":0.0006215572}
-{"premise":"There are four persons. Everyone is visible 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 Heather 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 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) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Rose can now know that Heather can know that Heather's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Andy","Brian","Heather"],"index":61569,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9904604554,"difficulty":0.0095395446}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Samuel knows whether Gustavo's forehead is muddy.","smcdel_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 whether (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) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gustavo can now know whether Samuel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gustavo","Samuel","Alicia"],"index":14261,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994028807,"difficulty":0.0005971193}
-{"premise":"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 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 3)","n_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":"Nichole can now know that Lazaro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Berenice","Nichole","Lazaro"],"index":34321,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980475903,"difficulty":0.0019524097}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Debra. Debra's card is shown to Rosa. Rosa's card is shown to Rosa. 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|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Rosa can now know that Debra can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Debra","Rosa"],"index":21113,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993891716,"difficulty":0.0006108284}
-{"premise":"There are 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)","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":"Oscar can now know that Roxanne can know that Roxanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roxanne","Helen","Betty","Oscar"],"index":8399,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982765913,"difficulty":0.0017234087}
-{"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 Robert. Robert's card is shown to Robert. Robert'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 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 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":"Mary can now know whether Robert can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Robert","Mary"],"index":18030,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5817809105,"difficulty":1.5817809105}
-{"premise":"There are four persons. Everyone is visible 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 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":"Jim can now know whether Jim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","Jim","Lindsay","Doug"],"index":41650,"s-l":"forehead_mirror-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 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":"Sergio can now know whether Stephen can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stephen","Sergio"],"index":15728,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994257689,"difficulty":0.0005742311}
-{"premise":"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 Joel 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 that 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":"Joel can now know that Albert can know that Joel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Albert","Joel"],"index":28057,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9806885719,"difficulty":0.0193114281}
-{"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 Frank is thirsty. It is publicly announced that Frank 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Wayne can now know whether Wayne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wayne","Andrew","Frank","Brian"],"index":9052,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9701393843,"difficulty":0.0298606157}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corina is not thirsty. It is publicly announced that Corina knows whether Corina is thirsty. It is publicly announced that Corina does not know whether Ruth 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 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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jacob can now know whether Ruth can know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corina","Ruth","Jacob"],"index":36721,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986201525,"difficulty":0.0013798475}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Vivian. Vivian's card is shown to Claire. 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 Vivian 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)) ] Agentb knows whether (Agenta knows whether 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":"Claire can now know whether Vivian can know whether Claire picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vivian","Claire"],"index":12231,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9967783093,"difficulty":0.0032216907}
-{"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. Sharon's card is shown to Robert. Robert's card is shown to Sharon. 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 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","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":"Sharon can now know whether Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Sharon"],"index":13291,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979819059,"difficulty":0.0020180941}
-{"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 Bryan. Frank's card is shown to Garth. Frank's card is shown to Frank. Frank'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:4 Agentb:3 Agentc: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:4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bryan","Garth","Frank","Barbara"],"index":15759,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993964434,"difficulty":0.0006035566}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jonathan does not know whether or not everyone is thirsty. It is publicly announced that Jonathan 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 (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know whether Jonathan can know that Daniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","Brittany","Wayne","Daniel"],"index":59175,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9780666828,"difficulty":0.0219333172}
-{"premise":"There are four persons. Everyone is visible 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 Geoffrey knows whether Geoffrey's forehead is muddy. It is publicly announced that Grant's forehead is muddy. It is publicly announced that Karla knows whether Grant's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (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":"Christopher can now know whether Grant can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Grant","Geoffrey","Karla","Christopher"],"index":46922,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994333386,"difficulty":0.0005666614}
-{"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. Scott's card is shown to Denise. Ray's card is shown to Denise. Rose's card is shown to Ray. Ray'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 1,2,3,4 LAW Top OBS Agenta:1,2,3 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:1,2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Denise can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Denise","Scott","Ray","Rose"],"index":13434,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
-{"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 Albert. Vicky's card is shown to Albert. Maxine's card is shown to Albert. Albert's card is shown to Vicky. Maxine's card is shown to Vicky. Albert's card is shown to Maxine. Maxine's card is shown to Maxine. It is publicly announced that someone picked a red card. It is publicly announced that Vicky knows whether or not nobody picked a red card. It is publicly announced that Albert knows whether Susan picked a red card. It is publicly announced that Vicky knows whether or not nobody picked a red card. It is publicly announced that Vicky picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 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:1,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Albert can now know whether Vicky can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Susan","Vicky","Maxine"],"index":12737,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9781746864,"difficulty":0.0218253136}
-{"premise":"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 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) ] [ ! (Agenta knows whether 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) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"James can now know that Russell can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Darlene","Brian","Russell"],"index":28691,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989350438,"difficulty":0.0010649562}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angela's card is shown to Sherry. Sherry's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Sherry does not know whether or not everyone picked a red card. It is publicly announced that Angela knows whether Angela 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 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)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sherry can now know that Angela can know that Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherry","Angela"],"index":60130,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5541439056,"difficulty":0.4458560944}
-{"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. David's card is shown to Susan. Susan'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 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:1,2 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:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"David can now know that Susan can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","David"],"index":51853,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990647435,"difficulty":0.0009352565}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Dora. Brian's card is shown to Dora. Dora'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:2,3 Agentb: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:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marjorie can now know whether Dora can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dora","Marjorie","Brian"],"index":48144,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992685914,"difficulty":0.0007314086}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lula's card is shown to Lula. Lula's card is shown to Blanca. Donna's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Lula knows whether or not nobody picked a red card. It is publicly announced that Lula does not know whether Donna 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 whether (Agentc knows that (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":"Blanca can now know whether Donna can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lula","Blanca","Donna"],"index":43257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994298816,"difficulty":0.0005701184}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candace knows whether Candace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Candace can now know that Candace's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Candace","Evelyn","Kerry"],"index":14649,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9594967961,"difficulty":1.9594967961}
-{"premise":"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 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":"Susan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Teresa","Raymond","Kenneth","Susan"],"index":54217,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989216328,"difficulty":0.0010783672}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chuck is 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 (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":"Kimberly can now know whether Edward can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Kimberly","Edward","Chuck"],"index":4307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993853569,"difficulty":0.0006146431}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexandra does not know whether Mark is thirsty. It is publicly announced that Mark knows whether someone is thirsty.","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 whether 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":"Alexandra can now know whether Alexandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Alexandra"],"index":7513,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9963266253,"difficulty":0.0036733747}
-{"premise":"There are three persons. Everyone is visible 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 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":"Maryann can now know whether Ann can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ann","Maryann","Katherine"],"index":67435,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993027449,"difficulty":0.0006972551}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larue's card is shown to Larue. Larue's card is shown to Roberta. It is publicly announced that someone picked a red card. It is publicly announced that Larue does not know whether Roberta picked a red card. It is publicly announced that Larue 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))) ] (Agenta knows that (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":"Larue can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Larue","Roberta"],"index":60735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994578958,"difficulty":0.0005421042}
-{"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. Joseph's card is shown to Robert. Joseph's card is shown to Joseph. 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:1,2 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:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph 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","Joseph","Janet"],"index":51953,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999062717,"difficulty":0.000937283}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sabra 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 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":"Sabra can now know whether Rafael can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sabra","Kim","Carol","Rafael"],"index":43489,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7188408971,"difficulty":0.2811591029}
-{"premise":"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's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy does not know whether Jeremy'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 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":"Margaret can now know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Margaret"],"index":23351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7241882086,"difficulty":0.2758117914}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clara 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 1) ] 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) ] 0","hypothesis":"Clara can now know whether Myra can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clara","Rebecca","Myra"],"index":39433,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993718266,"difficulty":0.0006281734}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roger does not know whether Francisco 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 Joanna is thirsty. It is publicly announced that Roger does not know whether Joanna is 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 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) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Roger can now know that Joanna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanna","Francisco","Roger","Pricilla"],"index":56462,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944406152,"difficulty":0.0055593848}
-{"premise":"There are four persons. Everyone is visible 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":"Karon can now know that Flora can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Flora","Karon","Annie","Yolanda"],"index":58529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992239475,"difficulty":0.0007760525}
-{"premise":"There are four persons. Everyone is visible 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'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 (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) ] [ ! ~(4) ] 0","hypothesis":"Lonnie can now know that Wanda can know that Lonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wanda","Denise","Dorothy","Lonnie"],"index":23172,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977299571,"difficulty":0.0022700429}
-{"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 Roger. Randall's card is shown to Randall. Roger'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 knows whether Roger picked a red card. It is publicly announced that Randall does not know whether Roger 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) ] (Agentc 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":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roger","Randall","Mary"],"index":11205,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994327426,"difficulty":0.0005672574}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lessie 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 3)","n_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":"Lessie can now know whether Carlota's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Lessie","Carlota"],"index":16859,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991946816,"difficulty":0.0008053184}
-{"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 Felisa. George's card is shown to Felisa. Felisa's card is shown to Kent. George's card is shown to George. Earnest's card is shown to George. Earnest's card is shown to Earnest. It is publicly announced that someone picked a red card. It is publicly announced that Earnest does not know whether Kent picked a red card. It is publicly announced that Felisa knows whether George picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Earnest can now know whether Felisa can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Felisa","Kent","George","Earnest"],"index":61670,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9577646852,"difficulty":1.9577646852}
-{"premise":"There are three 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 Mitchel. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Bruce knows whether or not nobody picked a red card. It is publicly announced that Bruce does not know whether Frank 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 that (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":"Frank can now know whether Bruce can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Mitchel","Frank"],"index":16877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9769206047,"difficulty":0.0230793953}
-{"premise":"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 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) ] [ ! ~(Agenta knows whether 1) ] Agenta 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) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donna can now know that Lillie can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Julie","Edward","Lillie"],"index":33864,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970914125,"difficulty":0.0029085875}
-{"premise":"There are four persons. Everyone is visible 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 Edwina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Cathy can now know whether Sheila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edwina","Linda","Sheila","Cathy"],"index":64427,"s-l":"forehead_mirror-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). Amber's card is shown to Sandra. Katherine's card is shown to Amber. Katherine's card is shown to Benjamin. It is publicly announced that someone picked a red card. It is publicly announced that Katherine knows whether or not nobody picked a red card. It is publicly announced that Amber 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 ] (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:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 2 ] 0","hypothesis":"Amber can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Amber","Katherine","Benjamin"],"index":37907,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990398288,"difficulty":0.0009601712}
-{"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 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":"Bridgette can now know whether Timothy can know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mollie","Timothy","Bridgette","Lori"],"index":66950,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991649389,"difficulty":0.0008350611}
-{"premise":"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 Jewell's forehead 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 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 2) ] 0","hypothesis":"Jewell can now know whether Steven can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herbert","Jewell","Steven"],"index":45910,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992911816,"difficulty":0.0007088184}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Silas's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Silas'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 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) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Cynthia can now know whether Haydee can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Silas","Haydee","Cynthia"],"index":66001,"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. 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 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 ] 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":"Shirley can now know whether Jeremy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Jo","Jeremy"],"index":33940,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993380904,"difficulty":0.0006619096}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ken knows whether Lonnie's forehead 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 (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 1) ] 0","hypothesis":"Matthew can now know that Lonnie can know whether Lonnie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lonnie","Matthew","Ken"],"index":62653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9701254964,"difficulty":0.0298745036}
-{"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. Lee's card is shown to Karen. Karen's card is shown to Rita. Rita's card is shown to Rita. Jaclyn's card is shown to Jaclyn. 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: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:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Rita","Lee","Jaclyn"],"index":6275,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989159107,"difficulty":0.0010840893}
-{"premise":"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) ] [ ! (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: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":"Melba can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","Melba","Daniel","Joshua"],"index":7687,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994231462,"difficulty":0.0005768538}
-{"premise":"There are three 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 Patricia does not know whether or not everyone is thirsty. It is publicly announced that Patricia does not know whether or not everyone 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) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&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) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Patricia can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bobby","Patricia","Leon"],"index":48477,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976014495,"difficulty":0.0023985505}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 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":"Bill can now know that John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bill","Emelda","John","Karla"],"index":15013,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8293312788,"difficulty":0.1706687212}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon does not know whether Patsy 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 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 1) ] [ ! (1&2) ] 0","hypothesis":"Sharon can now know whether Patsy can know that Sharon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patsy","Sharon"],"index":32958,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9821451902,"difficulty":0.0178548098}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Victor 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 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":"Victor can now know that Gordon can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gordon","Victor"],"index":8324,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Isabel 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Isabel can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","David","Ethel","Isabel"],"index":46149,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9952175617,"difficulty":0.0047824383}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Otha's card is shown to Otha. Jacqueline's card is shown to Lori. Ginger's card is shown to Lori. Otha's card is shown to Jacqueline. Otha's card is shown to Ginger. It is publicly announced that someone picked a red card. It is publicly announced that Ginger does not know whether Ginger picked a red card. It is publicly announced that Jacqueline 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 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":"Ginger can now know whether Jacqueline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Otha","Lori","Jacqueline","Ginger"],"index":47509,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9176466465,"difficulty":0.0823533535}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. 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: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 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":"Yvonne can now know that Carol can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","David","Yvonne","Gina"],"index":63332,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992762208,"difficulty":0.0007237792}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carole does not know whether or not everyone is thirsty. It is publicly announced that Carole 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maria can now know whether Bertha can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carole","Bertha","Maria"],"index":49295,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992087483,"difficulty":0.0007912517}
-{"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 Wade. Margaret's card is shown to Shirley. 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 Margaret knows whether Margaret picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta 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:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Wade can now know whether Margaret can know whether Shirley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Wade","Shirley"],"index":64607,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987549782,"difficulty":0.0012450218}
-{"premise":"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 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 (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":"Karen 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":["Kenneth","Shannon","Patricia","Karen"],"index":63002,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9868572354,"difficulty":0.0131427646}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Susan can now know whether Meredith can know whether Meredith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Heather","Meredith"],"index":29277,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993798733,"difficulty":0.0006201267}
-{"premise":"There are four persons. Everyone is visible 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'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 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":"Angelique can now know that Justina can know that Sean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angelique","Sean","Wendy","Justina"],"index":44703,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973191619,"difficulty":0.0026808381}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanja's card is shown to Christine. Christine's card is shown to Tanja. Rosa's card is shown to Tanja. Rosa's card is shown to Rosa. It is publicly announced that someone picked a red card. It is publicly announced that Rosa does not know whether Christine 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) ] Agentc knows whether (Agenta knows whether 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":"Rosa can now know whether Christine can know whether Rosa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christine","Tanja","Rosa"],"index":61803,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980408549,"difficulty":0.0019591451}
-{"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. Ashley's card is shown to Christopher. Alexander's card is shown to Alexander. Robert's card is shown to Alexander. Alexander's card is shown to Ashley. Ashley'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:1,3 Agentb:2,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 1)","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":"Robert can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Alexander","Ashley","Robert"],"index":58859,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5617179871,"difficulty":1.5617179871}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Matt 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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Wayne can now know that Matt can know whether Matt is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Wayne","Matt"],"index":15823,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984899759,"difficulty":0.0015100241}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby does not know whether or not everyone is thirsty. It is publicly announced that Carol does not know whether Cathryn 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 (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)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ruby can now know that Carol can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Cathryn","Carol"],"index":7137,"s-l":"internal-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 Harold'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 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) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Patty can now know whether Harold can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patty","Harold","Michael"],"index":9055,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9867292643,"difficulty":0.0132707357}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jamie's card is shown to Jamie. Jamie's card is shown to Jane. It is publicly announced that someone picked a red card. It is publicly announced that Jamie does not know whether Jane picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb 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:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Nora can now know that Jamie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nora","Jamie","Jane"],"index":7471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999047935,"difficulty":0.000952065}
-{"premise":"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 does not know whether Theresa's forehead is muddy. It is publicly announced that Theresa 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)) ] 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) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Theresa can now know whether Pearl can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pearl","Lonnie","Theresa"],"index":25278,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9878314137,"difficulty":0.0121685863}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Douglas can now know whether Grover can know whether Jerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Grover","Leah","Douglas"],"index":50871,"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 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)","n_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":"Annie can now know that Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Annie","Susie","David"],"index":41370,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9868817329,"difficulty":0.0131182671}
-{"premise":"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) ] [ ! ~(Agentb knows whether 2) ] (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":"Gary can now know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Dennis","Aaron","Brandon"],"index":41791,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912762642,"difficulty":0.0087237358}
-{"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. Carmen's card is shown to John. Michael's card is shown to John. Carmen's card is shown to Rick. Carmen's card is shown to Carmen. Carmen's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Rick 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 whether (Agentc knows that (1&2&3&4))","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":"John can now know whether Carmen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Rick","Carmen","Michael"],"index":3220,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9592522383,"difficulty":0.0407477617}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Cindy can now know whether Abel can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Cindy","Mark","Abel"],"index":56130,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992832541,"difficulty":0.0007167459}
-{"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 Gloria. James's card is shown to Gloria. Teresa's card is shown to Teresa. 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 Gloria 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 (Agenta knows whether 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":"James can now know whether Gloria can know whether James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Teresa","James"],"index":52426,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981437922,"difficulty":0.0018562078}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Xiomara's card is shown to Sharon. Richard's card is shown to Sharon. Sharon's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Xiomara does not know whether Kathy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Xiomara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Xiomara","Kathy","Sharon","Richard"],"index":51743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994235039,"difficulty":0.0005764961}
-{"premise":"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 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) ] [ ! (Agentc knows whether 1) ] 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 1) ] 0","hypothesis":"Jerry can now know whether Sandra can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Ruth","Sandra"],"index":29586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7922455668,"difficulty":0.2077544332}
-{"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 Charles. Charles's card is shown to Mildred. Mildred's card is shown to Mildred. Rita's card is shown to Mildred. William's card is shown to Mildred. Mildred's card is shown to Rita. 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:1,2,3,4 Agentc:2 Agentd: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:4 Agentb:1,2,3,4 Agentc:2 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":["Charles","Mildred","Rita","William"],"index":4511,"s-l":"explicit-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 Irene is not thirsty. It is publicly announced that 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) ] [ ! ~(3) ] [ ! 4 ] Agenta 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) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"Linda can now know whether Irene can know that Irene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Michael","Irene","Christy"],"index":13789,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956947565,"difficulty":0.0043052435}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Ronnie. Edward's card is shown to Ronnie. Ronnie's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Ronnie knows whether Ronnie picked a red card. It is publicly announced that Edward does not know whether or not everyone picked a red card. It is publicly announced that Edward does not know whether Edward 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 that (Agenta knows whether 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":"Edward can now know that Ronnie can know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronnie","Edward"],"index":6588,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8688269854,"difficulty":0.1311730146}
-{"premise":"There are four 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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 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) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Louis can now know whether Kevin can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Albert","Marie","Kevin","Louis"],"index":40533,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999479115,"difficulty":0.000520885}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nora does not know whether Kristen 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 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) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nora can now know that Quentin can know whether Quentin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kristen","Nora","Quentin"],"index":62448,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8363243937,"difficulty":1.8363243937}
-{"premise":"There are four persons. Everyone is visible 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":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wendy","Anthony","Lucy","John"],"index":62314,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989894032,"difficulty":0.0010105968}
-{"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 Kathleen 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))) ] 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|2))) ] 0","hypothesis":"Linda can now know that Kathleen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Kathleen"],"index":43936,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993816614,"difficulty":0.0006183386}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresia's card is shown to Carolyn. Carolyn'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 Agentb:2 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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Theresia can now know that Carolyn can know whether Julie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theresia","Carolyn","Julie"],"index":31570,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973345995,"difficulty":0.0026654005}
-{"premise":"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 Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Laura","Mary","Karen","Sandra"],"index":30627,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993593097,"difficulty":0.0006406903}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krystal 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":"Krystal can now know whether Phillip can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Krystal","Phillip","Christopher"],"index":44232,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Echo knows whether Echo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Echo can now know that Dolores can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","Dolores","Tamara","Echo"],"index":64390,"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. Each person draws a card, face unrevealed (red or black). John's card is shown to Roger. Russell's card is shown to Roger. Roger's card is shown to John. John's card is shown to John. Roger's card is shown to Russell. 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 Russell knows whether Russell 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 2)","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":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roger","John","Russell"],"index":61391,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9955436587,"difficulty":0.0044563413}
-{"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. Harry's card is shown to Twila. Harry's card is shown to Harry. Twila's card is shown to Matthew. 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 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)","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":"Twila can now know that Twila picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Twila","Harry","Matthew"],"index":62323,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9397266507,"difficulty":0.0602733493}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Issac does not know whether Issac's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Issac can now know whether Tiffany can know that Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Royce","Lisa","Tiffany","Issac"],"index":48567,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9908379912,"difficulty":1.9908379912}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlene knows whether Bennie's forehead is muddy. It is publicly announced that Carlene 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 whether (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) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Bennie can now know whether Carlene can know that Carlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bennie","Carlene","Julie"],"index":15251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993340373,"difficulty":0.0006659627}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herman knows whether Felix's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentd knows whether 1) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Herman can now know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Felix","Cara","Kenneth","Herman"],"index":53845,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994724393,"difficulty":0.0005275607}
-{"premise":"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) ] [ ! ~(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: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":"Christina can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Rey","Christina","James"],"index":10927,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9801415205,"difficulty":0.0198584795}
-{"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 Davida is thirsty. It is publicly announced that David does not know whether Donald 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Davida can now know that Caterina can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Caterina","Davida","David"],"index":4486,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9400128722,"difficulty":1.9400128722}
-{"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 Lauren. Virgil's card is shown to Theodore. Lauren's card is shown to Clara. Clara's card is shown to Clara. 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 whether 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":"Lauren can now know that Virgil can know whether Clara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lauren","Theodore","Virgil","Clara"],"index":7277,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6438952684,"difficulty":1.6438952684}
-{"premise":"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 Gayla'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) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gayla","Helen","Robert","George"],"index":37582,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990119934,"difficulty":0.0009880066}
-{"premise":"There are three persons. Everyone is visible 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 Joshua's forehead is muddy.","smcdel_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 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":"Catherine can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joshua","Roy","Catherine"],"index":46065,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999243021,"difficulty":0.000756979}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evan'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 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) ] [ ! ~(1) ] 0","hypothesis":"Evan can now know whether Samantha can know whether Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Evan","Samantha","Dorothy"],"index":40439,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994235039,"difficulty":0.0005764961}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Millie does not know whether Millie's forehead 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 3)","n_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":"Michele can now know that Angela can know that Millie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Michele","Millie"],"index":28859,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969453216,"difficulty":0.0030546784}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derek's card is shown to Derek. Ronald's card is shown to Derek. 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. It is publicly announced that Ronald 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)) ] (Agenta knows that (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":"Derek can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Derek","Ronald"],"index":38097,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968915582,"difficulty":0.0031084418}
-{"premise":"There are three persons. Everyone is visible 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)) ] 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":"Julie 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","Julie","Denise"],"index":6419,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978061318,"difficulty":0.0021938682}
-{"premise":"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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 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) ] [ ! 2 ] 0","hypothesis":"Lisette can now know whether John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lisette","John"],"index":34036,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989971519,"difficulty":0.0010028481}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell's forehead is not 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":"Russell can now know that Vincent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vincent","Russell"],"index":14427,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9978606105,"difficulty":1.9978606105}
-{"premise":"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) ] [ ! ~(3) ] (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) ] [ ! ~(3) ] 0","hypothesis":"Roberta can now know that Rubie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roberta","Rubie","Joseph","Alicia"],"index":64588,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976066351,"difficulty":0.0023933649}
-{"premise":"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 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) ] [ ! ~(Agenta knows whether 1) ] 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Christopher can now know that Howard can know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Howard","Brandon"],"index":63139,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999266088,"difficulty":0.000733912}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catharine'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 whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Catharine can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Catharine"],"index":45571,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994698167,"difficulty":0.0005301833}
-{"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. William's card is shown to Michael. William's card is shown to Kristina. 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 that 2)","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":"Michael can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Michael","Kristina"],"index":48718,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9878150225,"difficulty":0.0121849775}
-{"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 Mike. John's card is shown to John. Linda's card is shown to John. John'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:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","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":"John can now know whether Mike picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mike","Theodore","John","Linda"],"index":4466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982514977,"difficulty":0.0017485023}
-{"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. Carl's card is shown to Kenneth. Carl's card is shown to Carl. Michael's card is shown to Carl. Kenneth's card is shown to Michael. Carl's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael knows whether Carl 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 2)","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":"Carl can now know that Carl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Carl","Michael"],"index":35793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9639113545,"difficulty":0.0360886455}
-{"premise":"There are three persons. Everyone is visible 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 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":"Kraig can now know whether Kelly can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kraig","Christopher","Kelly"],"index":67007,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992915392,"difficulty":0.0007084608}
-{"premise":"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 (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":"Leroy can now know whether Matthew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leroy","Matthew","Donna"],"index":67506,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9724444151,"difficulty":0.0275555849}
-{"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 Tamar. John's card is shown to Tamar. Connie's card is shown to Connie. Tamar's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Tamar 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 (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":"Tamar can now know whether John can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tamar","Connie","John"],"index":50248,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9915573597,"difficulty":1.9915573597}
-{"premise":"There are three persons. Everyone is visible 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 not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan'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 (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":"Sharla 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":["Susan","Sharla","Margaret"],"index":7693,"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's forehead is muddy. It is publicly announced that Jesse'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 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":"Charles can now know that Jesse can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Wesley","Charles","Jesse"],"index":50783,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976673126,"difficulty":0.0023326874}
-{"premise":"There are two persons. Everyone is visible 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 Sue's forehead is muddy. It is publicly announced that Sue knows whether Jimmy'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 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jimmy can now know that Sue can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sue","Jimmy"],"index":5068,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992678761,"difficulty":0.0007321239}
-{"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 Robin. Mark's card is shown to Robin. Mark's card is shown to Melanie. Robin's card is shown to Mark. 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.","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)) ] (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:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Melanie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Robin","Melanie","Mark"],"index":24748,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9806975126,"difficulty":0.0193024874}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hans knows whether Hans's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Thomas can now know that Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janette","Hans","Rebecca","Thomas"],"index":31558,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998243928,"difficulty":0.001756072}
-{"premise":"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's forehead is muddy. It is publicly announced that Katherine's forehead is muddy. It is publicly announced that Luana 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)) ] Agenta knows that (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 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Willie can now know that Luana can know whether Jacob's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Katherine","Jacob","Luana"],"index":48378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999324441,"difficulty":0.000675559}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon does not know whether Michael 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 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":"Michael can now know that Sharon can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Sharon"],"index":28899,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994396567,"difficulty":0.0005603433}
-{"premise":"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 Esther'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 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) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Christina can now know whether Esther can know whether Esther's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Esther","Christina","Ethel"],"index":8007,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9930348396,"difficulty":0.0069651604}
-{"premise":"There are three persons. Everyone is visible 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 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 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Reginald can know whether Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","James","Reginald"],"index":47766,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993931055,"difficulty":0.0006068945}
-{"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 Kathleen is thirsty. It is publicly announced that Kathleen does not know whether Anthony is thirsty. It is publicly announced that Anthony is thirsty. It is publicly announced that Terri does not know whether Kathleen is thirsty.","smcdel_problem":"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 (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":"Shirley can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anthony","Kathleen","Terri","Shirley"],"index":58306,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994816184,"difficulty":0.0005183816}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarina knows whether or not nobody is thirsty. It is publicly announced that Sarina does not know whether Hortencia is thirsty. It is publicly announced that Pam does not know whether or not everyone is thirsty. It is publicly announced that Sarina 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)) ] Agentc knows whether (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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Pam can now know whether Hortencia can know that Sarina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hortencia","Sarina","Pam"],"index":56061,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9511682987,"difficulty":0.0488317013}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana does not know whether Christal is thirsty. It is publicly announced that Diana does not know whether or not everyone is thirsty. It is publicly announced that Diana does not know whether Christal is thirsty. It is publicly announced that Christal 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 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":"Christal can now know whether Diana can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Diana","Christal"],"index":60226,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999317646,"difficulty":0.000682354}
-{"premise":"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 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 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":"Mary can now know that Marian can know whether Marian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Marian","Mary"],"index":16909,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6765496135,"difficulty":1.6765496135}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Oscar's card is shown to Andrew. Mildred's card is shown to Oscar. Andrew's card is shown to Mildred. Oscar's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Oscar knows whether or not nobody picked a red card. It is publicly announced that Oscar does not know whether Andrew 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) ] (Agenta knows that 1)","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":"Andrew can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Oscar","Mildred"],"index":32272,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9891659617,"difficulty":0.0108340383}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natasha knows whether Natasha'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":"Robert can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Natasha"],"index":2593,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993593097,"difficulty":0.0006406903}
-{"premise":"There are 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":"Curtis can now know whether Steven can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Steven","Curtis","Ernest"],"index":25203,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991607666,"difficulty":0.0008392334}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Damon's card is shown to Terrance. Terrance's card is shown to Damon. Stacy'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:3 Agentb:2 Agentc: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:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Terrance can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacy","Terrance","Damon","Robert"],"index":29724,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993370175,"difficulty":0.0006629825}
-{"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. Josephine's card is shown to Stacy. Jonathan'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:1 Agentc: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 Agentb:1 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacy can now know whether Jonathan can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Josephine","Stacy","Jonathan","John"],"index":26293,"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 Dexter 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 (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":"Barbara can now know whether Ellyn can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dexter","Richard","Barbara","Ellyn"],"index":2188,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9744935632,"difficulty":0.0255064368}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Davis's card is shown to Sharon. Walter's card is shown to Sharon. Sharon's card is shown to Davis. Davis's card is shown to Davis. Sharon's card is shown to Donald. Walter's card is shown to Donald. Sharon'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:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 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:2,4 Agentb:1,2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Davis can now know whether Walter can know whether Davis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Davis","Donald","Walter"],"index":53670,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969735146,"difficulty":0.0030264854}
-{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that Harry knows whether Jaime's forehead is muddy.","smcdel_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 (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":"Harry can now know that Martha can know whether Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jaime","Harry","Martha"],"index":64854,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994748235,"difficulty":0.0005251765}
-{"premise":"There are three persons. Everyone is visible 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 Sally's forehead is muddy. It is publicly announced that Sally knows whether Susan's forehead is muddy. It is publicly announced that Frances'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 (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) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Frances can now know whether Susan can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Sally","Frances"],"index":42098,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994200468,"difficulty":0.0005799532}
-{"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 not thirsty. It is publicly announced that Amy is not thirsty. It is publicly announced that Irene does not know whether Anya is 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) ] 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) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Steven can now know that Amy can know that Anya is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anya","Irene","Steven","Amy"],"index":6281,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9875534773,"difficulty":0.0124465227}
-{"premise":"There are four persons. Everyone is visible 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 Travis'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&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":"Fred can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fred","Lucie","Paul","Travis"],"index":16317,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988425374,"difficulty":0.0011574626}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margret does not know whether or not everyone is thirsty. It is publicly announced that John knows whether John 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)) ] (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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Margret can now know whether Margret is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Margret","John","Erica","Agnes"],"index":40172,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984329343,"difficulty":0.0015670657}
-{"premise":"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 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) ] (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":"Sherry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Kristen","Jane"],"index":31193,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99899894,"difficulty":0.00100106}
-{"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 James. James's card is shown to Stephanie. Ilse's card is shown to Stephanie. Ilse's card is shown to Ilse. 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 Stephanie 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 whether (Agentc knows that 1)","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":"Janet can now know whether Stephanie can know that Janet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janet","James","Stephanie","Ilse"],"index":45950,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9699876904,"difficulty":1.9699876904}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emmett knows 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 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 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 (~(1|2|3))) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danelle","Elizabeth","Emmett"],"index":30091,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9624332786,"difficulty":0.0375667214}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 4 ] Agentc 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) ] [ ! 4 ] 0","hypothesis":"Scott can now know that Diane can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Robert","Scott","Diane"],"index":47957,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9909098744,"difficulty":0.0090901256}
-{"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 Tyler is thirsty. It is publicly announced that Gregory 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)) ] 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gregory can now know that Tyler can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tyler","Steven","Gregory"],"index":17115,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995037317,"difficulty":0.0004962683}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether William's forehead is muddy. It is publicly announced that Lloyd knows whether Lloyd's forehead 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 (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 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lloyd can now know that William can know whether Lloyd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Lloyd","Elizabeth"],"index":48642,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9074786305,"difficulty":0.0925213695}
-{"premise":"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.","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":"Carol can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Carol","Kimberly"],"index":64860,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998662591,"difficulty":0.001337409}
-{"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 Phyllis is thirsty. It is publicly announced that Guadalupe does not know whether Teresa 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) ] 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Phyllis can now know that Teresa can know whether Guadalupe is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Guadalupe","Phyllis","John","Teresa"],"index":17874,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954628348,"difficulty":0.0045371652}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas is not 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) ] [ ! ~(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) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"Douglas can now know that Monroe is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Monroe","Camilla","Douglas","Robert"],"index":22795,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963515997,"difficulty":0.0036484003}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather does not know whether Heather's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Brenda can now know that Sharon can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Brenda","Sharon","Heather"],"index":8979,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931069016,"difficulty":0.0068930984}
-{"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 Abigail. 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 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":"Mary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","Abigail"],"index":7732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas is thirsty. It is publicly announced that Thomas does not know whether Nelly 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 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":"Thomas can now know that Nelly can know whether Nelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Nelly"],"index":54255,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9637075663,"difficulty":0.0362924337}
-{"premise":"There are two persons. Everyone is visible 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 Javier's forehead is muddy. It is publicly announced that Javier'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)","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":"Javier can now know that Dorothy can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dorothy","Javier"],"index":3585,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9691898823,"difficulty":0.0308101177}
-{"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 Harry. Mary's card is shown to Harry. Harry's card is shown to Mary. Harry's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey does not know whether Jeffrey 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:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 1)","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":"Jeffrey can now know whether Harry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harry","Mary","Jeffrey"],"index":24227,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9137242436,"difficulty":0.0862757564}
-{"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 Joann. Joann's card is shown to Maria. Maria's card is shown to Maria. Maria'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:3 Agentb:1,2 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:3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Maria can now know whether Joann can know that Joann picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joann","Maria","Robert"],"index":36470,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6048618555,"difficulty":0.3951381445}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patty'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 (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) ] [ ! ~(2) ] 0","hypothesis":"Eric can now know that Patty can know that Patty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Patty","Terri","Ann"],"index":51983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958317876,"difficulty":0.0041682124}
-{"premise":"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's forehead is not muddy. 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 1,2,3,4 LAW 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 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":"Hannah can now know that Sean can know whether Hannah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Hannah","Morris","Sean"],"index":29718,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982126951,"difficulty":0.0017873049}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellen's card is shown to Ellen. Ellen's card is shown to Roy. Betty'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 Agentb: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:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know that Ellen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellen","Betty","Roy"],"index":43977,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956015348,"difficulty":0.0043984652}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Faye 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 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Marcus can now know whether Faye can know whether Carl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcus","Ellen","Carl","Faye"],"index":12832,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999378562,"difficulty":0.000621438}
-{"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 or not everyone is thirsty.","smcdel_problem":"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|2|3|4)))","n_announcements":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":"Mary can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","William","Raul","Sandra"],"index":44330,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990517497,"difficulty":0.0009482503}
-{"premise":"There are 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 (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":"James 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":["Daryl","James","Elsie","Fabian"],"index":3807,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989157915,"difficulty":0.0010842085}
-{"premise":"There are four persons. Everyone is visible 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 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":"Erica can now know that Bernard can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Connie","Billie","Erica","Bernard"],"index":23988,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990406632,"difficulty":0.0009593368}
-{"premise":"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 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) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Norma can now know that Jessica can know that Caterina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Norma","Caterina","Jessica"],"index":26647,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969627261,"difficulty":0.0030372739}
-{"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 Daniell. Stephen's card is shown to Daniell. Stephen's card is shown to Raymond. Daniell's card is shown to Stephen. Stephen's card is shown to Stephen. It is publicly announced that someone picked a red card. It is publicly announced that Daniell does not know whether Daniell picked a red card. It is publicly announced that Raymond does not know whether or not everyone picked a red card. It is publicly announced that Stephen picked a red card. It is publicly announced that Raymond 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 whether (Agenta knows whether 2)","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":"Stephen can now know whether Daniell can know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniell","Raymond","Stephen"],"index":54831,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985386133,"difficulty":0.0014613867}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Omega knows whether Omega 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 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":"Aaron can now know whether Omega can know that Aaron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Catherine","Aaron","Omega"],"index":32099,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9418872595,"difficulty":0.0581127405}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexander does not know whether Clarence is thirsty. It is publicly announced that Alexander does not know whether Clarence is thirsty. It is publicly announced that Alexander 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)) ] (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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ann can now know whether Rebecca is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ann","Clarence","Rebecca","Alexander"],"index":63347,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9820669889,"difficulty":0.0179330111}
-{"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 Robert knows whether Robert 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) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc 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) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Dallas can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dallas","Juanita","Robert"],"index":42744,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.903218627,"difficulty":0.096781373}
-{"premise":"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 James'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)","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":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Terry"],"index":60523,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6840852499,"difficulty":0.3159147501}
-{"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 Marjorie knows whether Marjorie is thirsty. It is publicly announced that Marjorie 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 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":"Marjorie can now know that Marjorie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melody","Ralph","Marjorie"],"index":62478,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.953954339,"difficulty":0.046045661}
-{"premise":"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 does not know whether Brian's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Harold can now know whether Karey can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Karey","Harold","Nell"],"index":22933,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
-{"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 Kenneth is not thirsty. It is publicly announced that Preston does not know whether Olga is 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) ] 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:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Daniel can now know that Preston can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Olga","Preston","Daniel","Kenneth"],"index":8956,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987772107,"difficulty":0.0012227893}
-{"premise":"There are four persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that 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 (~(1|2|3|4))) ] [ ! 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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Susan can now know that Beverly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lance","Beverly","Theresa","Susan"],"index":20114,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940595627,"difficulty":0.0059404373}
-{"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. David's card is shown to Charles. Daniel's card is shown to Charles. Daniel'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: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:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that David can know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","David","Daniel"],"index":2526,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979006052,"difficulty":0.0020993948}
-{"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 Glen. Maurice's card is shown to Annette. 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 or not everyone picked a red card. It is publicly announced that Annette does not know whether Glen 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)) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 1)","n_announcements":2,"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)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Glen can now know whether Maurice can know that Glen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glen","Annette","Maurice"],"index":21904,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.559333086,"difficulty":1.559333086}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eugene does not know whether Gregg 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":"Eugene can now know that Elizabeth can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","Gregg","Eugene"],"index":45934,"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'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)) ] 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":"George can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","William","George","Michael"],"index":65694,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5304114223,"difficulty":1.5304114223}
-{"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 Ruben 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)) ] (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) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruben","William","Howard","John"],"index":47088,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990502,"difficulty":0.0009498}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis does not know whether Lucia is thirsty. It is publicly announced that Lucia 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Louis can now know that Charles can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucia","Charles","Louis","Jeffery"],"index":23201,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971725345,"difficulty":0.0028274655}
-{"premise":"There are three persons. Everyone is visible 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 (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) ] [ ! 3 ] 0","hypothesis":"Gene can now know that Frances can know that Gene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","Frances","John"],"index":22603,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970126152,"difficulty":0.0029873848}
-{"premise":"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 Tammy'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 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] 0","hypothesis":"Walter can now know whether Tammy can know whether Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","Tammy"],"index":42787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9914035201,"difficulty":0.0085964799}
-{"premise":"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 Lewis's forehead 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":"Vincent can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremiah","Lewis","Vincent"],"index":23121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989441037,"difficulty":0.0010558963}
-{"premise":"There are four persons. Everyone is visible 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) ] (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":"Libby can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Allen","Clayton","Libby"],"index":59931,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993610978,"difficulty":0.0006389022}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Phillip. Stephanie'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 Phillip 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Phillip can now know whether Stephanie can know whether Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Phillip","Stephanie"],"index":46565,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979248047,"difficulty":0.0020751953}
-{"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 Jessica. Constance's card is shown to Jessica. Richard's card is shown to Richard. Constance's card is shown to Richard. Jessica's card is shown to Constance. Richard's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that Jessica 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) ] Agentb knows whether (Agentc knows whether 4)","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":"Richard can now know whether Constance can know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Richard","Constance","Daniel"],"index":52654,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982861876,"difficulty":0.0017138124}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Mark can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Robert","Mark","Raymond"],"index":44379,"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's forehead is muddy. It is publicly announced that Amada knows whether or not nobody's forehead is muddy. It is publicly announced that Clinton'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'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|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":"Eric can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Amada","Clinton","Jesse"],"index":48558,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989901185,"difficulty":0.0010098815}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann knows whether 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd 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: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":"Thomas can now know whether Ann can know whether Nicki is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tiffany","Ann","Nicki","Thomas"],"index":30219,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991544485,"difficulty":0.0008455515}
-{"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 Bob 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) ] 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) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Edward can now know that Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Bob","Robert","Thomas"],"index":35669,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999342978,"difficulty":0.000657022}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adriana 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 (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":"Michael can now know that Adriana can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Michael","Joe","Adriana"],"index":6515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999332726,"difficulty":0.000667274}
-{"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 Alan is thirsty.","smcdel_problem":"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 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":"Heather can now know that Destiny can know that Destiny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heather","Larry","Alan","Destiny"],"index":2649,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959704876,"difficulty":0.0040295124}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita 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 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) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Deborah can now know whether Donald can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Anita","Donald"],"index":26715,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994539618,"difficulty":0.0005460382}
-{"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 David. Peter's card is shown to David. Charles's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Peter picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card. It is publicly announced that Charles does not know whether David 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 (Agenta knows whether (1&2&3&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":"David can now know that Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","David","Richard","Peter"],"index":35657,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6399667859,"difficulty":1.6399667859}
-{"premise":"There are three 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 Vernon 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) ] [ ! ~(Agenta knows whether (1&2&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 (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Sandra can now know whether Eugene can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Sandra","Vernon"],"index":21795,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9935095906,"difficulty":0.0064904094}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Enriqueta does not know whether Walter is thirsty. It is publicly announced that Enriqueta does not know whether or not everyone is thirsty. It is publicly announced that Enriqueta does not know whether Nelson is thirsty. It is publicly announced that Walter 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (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 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Nelson can now know that Walter can know that Nelson is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nelson","Patricia","Walter","Enriqueta"],"index":61727,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8860610127,"difficulty":0.1139389873}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanisha 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Juan can now know whether Anthony can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Greg","Anthony","Tanisha","Juan"],"index":47301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9705462456,"difficulty":0.0294537544}
-{"premise":"There are three persons. Everyone is visible 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 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 3)","n_announcements":1,"pbcheck":"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":"Debra can now know that Birdie can know that Birdie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debra","Paul","Birdie"],"index":20625,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975190163,"difficulty":0.0024809837}
-{"premise":"There are three persons. Everyone is visible 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":"Dean can now know that David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dean","William","David"],"index":60782,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9961639643,"difficulty":0.0038360357}
-{"premise":"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 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 3)","n_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":"David can now know that Freddie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","David","Freddie"],"index":65953,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928190112,"difficulty":0.0071809888}
-{"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. Freda's card is shown to Freda. Richard's card is shown to Freda. Freda's card is shown to Richard. Freda's card is shown to Jesse. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether Freda picked a red card. It is publicly announced that Freda 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 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":"Jesse can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Freda","Richard","Jesse"],"index":57284,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994190931,"difficulty":0.0005809069}
-{"premise":"There are three persons. Everyone is visible 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'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 3)","n_announcements":1,"pbcheck":"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":"Sheila can now know that Jerry can know that Sheila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Lisa","Sheila"],"index":30272,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974634647,"difficulty":0.0025365353}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dena's card is shown to Patrick. Renee's card is shown to Renee. Dena's card is shown to Dena. 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 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc: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:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Patrick","Renee","Dena"],"index":26371,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974089265,"difficulty":0.0025910735}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gwendolyn's card is shown to Jon. Robert's card is shown to Robert. Gwendolyn's card is shown to Robert. Gwendolyn's card is shown to Gwendolyn. 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 (Agentb knows that 1)","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":"Gwendolyn can now know whether Robert can know that Jon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jon","Robert","Gwendolyn"],"index":22057,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9120473266,"difficulty":1.9120473266}
-{"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 Betty 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 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":"Brian can now know whether Bertha can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bertha","Brian","Betty"],"index":36653,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964959025,"difficulty":0.0035040975}
-{"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 Philip. Cherrie's card is shown to Philip. Anthony's card is shown to Lisa. Philip's card is shown to Cherrie. Cherrie'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:4 Agentc:1 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:2,3 Agentb:4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cherrie can now know whether Lisa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Philip","Lisa","Cherrie","Anthony"],"index":9696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9921938181,"difficulty":0.0078061819}
-{"premise":"There are 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 (~(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":"Wendy can now know that Jeannette can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeannette","John","Wendy","Jose"],"index":28591,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991906285,"difficulty":0.0008093715}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donn's card is shown to Donn. Donn's card is shown to Avis. Donn's card is shown to Frances. Frances's card is shown to Frances. Freddy's card is shown to Frances. Frances's card is shown to Freddy. 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 whether 1)","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":"Avis can now know whether Donn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donn","Avis","Frances","Freddy"],"index":52272,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5641435981,"difficulty":0.4358564019}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katie's card is shown to Jimmy. Jimmy's card is shown to Katie. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy does not know whether David 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 that (~(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":"Jimmy can now know whether David can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Jimmy","Katie"],"index":8988,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992142916,"difficulty":0.0007857084}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antoinette's card is shown to Antoinette. Antoinette's card is shown to Carl. Carl's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that Carl knows whether Carl 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 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":"Carl can now know that Antoinette picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Antoinette","Carl"],"index":10751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9341638088,"difficulty":0.0658361912}
-{"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 David. Ryan's card is shown to Stephen. David's card is shown to Stephen. Stephen's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Ryan knows whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Ryan can now know that David can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","David","Stephen","John"],"index":19877,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8748211861,"difficulty":0.1251788139}
-{"premise":"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 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":"Vivian can now know that Andrea can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emmanuel","Andrea","John","Vivian"],"index":41167,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753988981,"difficulty":0.0246011019}
-{"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 Frederick. Frederick's card is shown to Lisa. Jane's card is shown to David. Frederick's card is shown to Jane. Lisa'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:1 Agentc:4 Agentd:1,2,4 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:3 Agentb:1 Agentc:4 Agentd:1,2,4 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":["Frederick","Lisa","David","Jane"],"index":2462,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958429933,"difficulty":0.0041570067}
-{"premise":"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 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":"Lucretia can now know whether Kelly can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Kelly","Lucretia"],"index":5172,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992300272,"difficulty":0.0007699728}
-{"premise":"There are four persons. Everyone is visible 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 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 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|2|3|4))) ] 0","hypothesis":"Robin can now know whether Frances can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Robin","Terry","Arnold"],"index":53119,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999322176,"difficulty":0.000677824}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elisabeth does not know whether Elisabeth's forehead 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":"Terrence can now know that Amy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elisabeth","Terrence","Amy"],"index":49054,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989773035,"difficulty":0.0010226965}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall does not know whether Randall's forehead is muddy. It is publicly announced that Randall does not know whether Randall'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 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":"Randall can now know whether Randall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Randall"],"index":50095,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9897603393,"difficulty":0.0102396607}
-{"premise":"There are three persons. Everyone is visible 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 Patrick's forehead is muddy.","smcdel_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 (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 3) ] 0","hypothesis":"Jane can now know that Patrick can know whether Judith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Judith","Patrick"],"index":2469,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993533492,"difficulty":0.0006466508}
-{"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 Alexandria. Alma's card is shown to Alma. Alexandria's card is shown to Shakia. Shakia's card is shown to Shakia. It is publicly announced that someone picked a red card. It is publicly announced that Alma does not know whether Alexandria 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) ] Agentb knows whether (Agenta knows that 2)","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":"Alma can now know whether Alexandria can know that Alma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexandria","Alma","Shakia"],"index":54749,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8075041175,"difficulty":0.1924958825}
-{"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 Rebecca. Rebecca's card is shown to Jennifer. 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 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 that 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":"Jennifer can now know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rebecca","Jennifer"],"index":34484,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5692154765,"difficulty":0.4307845235}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether someone's forehead is muddy. It is publicly announced that Victoria knows whether Donald'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 (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 (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Victoria can know that Angie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Angie","Donald","Victoria"],"index":38052,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967204928,"difficulty":0.0032795072}
-{"premise":"There are four persons. Everyone is visible 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 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Joseph can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Elisha","Dawn","David"],"index":60086,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993643165,"difficulty":0.0006356835}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Genevieve's card is shown to Genevieve. Genevieve'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 Genevieve does not know whether Patricia 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 (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":"Patricia can now know that Genevieve can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Genevieve","Patricia"],"index":18793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989087582,"difficulty":0.0010912418}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raylene is thirsty. It is publicly announced that Raylene does not know whether Florence 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|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":"Raylene can now know that Florence can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Florence","Raylene"],"index":10363,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999497056,"difficulty":0.000502944}
-{"premise":"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 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carolyn can now know whether Carol can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Carolyn","Carol"],"index":23339,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7092048526,"difficulty":0.2907951474}
-{"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 or not everyone is thirsty. It is publicly announced that Mary 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) ] (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)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Anthony can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Barbara","Anthony"],"index":59685,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995098114,"difficulty":0.0004901886}
-{"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 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 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":"Juanita can now know that Juanita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Juanita","Evelyn","Morris"],"index":1059,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.963629961,"difficulty":0.036370039}
-{"premise":"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 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) ] [ ! (Agenta knows whether 2) ] (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 2) ] 0","hypothesis":"Steven can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Carrie","Steven","Robert"],"index":44835,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975300431,"difficulty":0.0024699569}
-{"premise":"There are three 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 Irene knows whether Mildred 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 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 3) ] 0","hypothesis":"Irene can now know whether Eric is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Irene","Eric","Mildred"],"index":57377,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978609681,"difficulty":0.0021390319}
-{"premise":"There are three persons. Everyone is visible 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 muddy.","smcdel_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 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":"Constance can now know whether Margaret can know whether Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Constance","Margaret","Stephen"],"index":23834,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994546771,"difficulty":0.0005453229}
-{"premise":"There are three persons. Everyone is visible 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 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 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 3) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","John","Barbara"],"index":44439,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982606769,"difficulty":0.0017393231}
-{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Ann knows whether Ann's forehead is muddy. It is publicly announced that Sharon 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 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":"Sharon can now know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ann","Bob","Sharon"],"index":52657,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963881969,"difficulty":0.0036118031}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma's forehead is muddy. It is publicly announced that Lillian knows whether someone's forehead is muddy. It is publicly announced that Norma 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 (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 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Norma can now know that Lillian can know that Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Gerry","Lillian"],"index":40505,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9815903306,"difficulty":0.0184096694}
-{"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. 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:2 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 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Christine"],"index":34442,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994559884,"difficulty":0.0005440116}
-{"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 someone is thirsty. It is publicly announced that Shelley does not know whether or not everyone is thirsty. It is publicly announced that Shelley 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 (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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jim can now know that Shelley can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelley","Lorinda","Jim"],"index":17772,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994736314,"difficulty":0.0005263686}
-{"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 Pamela. Pamela's card is shown to Denise. It is publicly announced that someone picked a red card. It is publicly announced that Andrea 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 whether 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":"Pamela can now know whether Denise picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrea","Pamela","Denise"],"index":48108,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9774466157,"difficulty":0.0225533843}
-{"premise":"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 Grace knows whether Merrill's forehead is muddy. It is publicly announced that Joanne 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)) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Pamela can now know that Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grace","Pamela","Merrill","Joanne"],"index":2108,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960307479,"difficulty":0.0039692521}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henrietta's card is shown to Ruth. Michael's card is shown to Ruth. Ruth's card is shown to Henrietta. Brenda's card is shown to Henrietta. Michael's card is shown to Henrietta. 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) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Henrietta can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Henrietta","Brenda","Michael"],"index":51522,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989602566,"difficulty":0.0010397434}
-{"premise":"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 Martin's forehead is muddy. It is publicly announced that Martin knows whether Ronald's forehead is muddy. It is publicly announced that Ronald'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 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) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Martin can now know whether Ronald can know that Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Ronald","James"],"index":18445,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8829094172,"difficulty":1.8829094172}
-{"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 Mary is thirsty. It is publicly announced that Val 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) ] [ ! ~(Agentd knows whether 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 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Mary can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Richard","Barbara","Val"],"index":47967,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9711179137,"difficulty":0.0288820863}
-{"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 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":"Juan can now know that Preston can know that Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emma","Preston","Juana","Juan"],"index":23068,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978172779,"difficulty":0.0021827221}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen 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 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":"Carmen can now know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmen","Maria","Lori"],"index":63283,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979452491,"difficulty":0.0020547509}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herman's card is shown to Herman. Gerald's card is shown to Herman. Timothy's card is shown to Herman. Timothy's card is shown to Gerald. Herman'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:1,2,3 Agentb:3 Agentc:1 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:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Gerald can now know that Timothy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Gerald","Timothy"],"index":53267,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993755221,"difficulty":0.0006244779}
-{"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 Clinton. Paul's card is shown to Paul. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Paul picked a red card. It is publicly announced that Paul does not know whether Rebecca 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 (Agenta knows whether 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":"Rebecca can now know whether Clinton can know whether Clinton picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clinton","Paul","Rebecca"],"index":16238,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7985431552,"difficulty":0.2014568448}
-{"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 Margaret is not thirsty. It is publicly announced that Margaret 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 whether (Agentb 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":"Brian can now know whether Margaret can know whether Brian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","Margaret"],"index":7750,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990547299,"difficulty":0.0009452701}
-{"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 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 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":"Teresa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teresa","Sue"],"index":38640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990686774,"difficulty":0.0009313226}
-{"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 Evelyn. Fred's card is shown to Evelyn. David's card is shown to David. Evelyn's card is shown to Fred. Fred's card is shown to Fred. Fred's card is shown to Francis. 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 whether 1)","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":"Evelyn can now know whether Evelyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","David","Fred","Francis"],"index":44301,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7078278661,"difficulty":1.7078278661}
-{"premise":"There are three persons. Everyone is visible 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 1,2,3 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 3)","n_announcements":1,"pbcheck":"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":"Christopher can now know that Timmy can know whether Timmy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Christopher","Timmy"],"index":51242,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993089437,"difficulty":0.0006910563}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Charles. Angela's card is shown to Charles. Charles's card is shown to Angela. Keith's card is shown to Angela. Angela'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:2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keith can now know whether Charles can know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Keith","Angela"],"index":63804,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989088774,"difficulty":0.0010911226}
-{"premise":"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 does not know whether Samuel's forehead is muddy. It is publicly announced that Samuel does not know whether Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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) ] 0","hypothesis":"Samuel can now know whether Sean's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Lillian","Sean","Karen"],"index":13820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999112308,"difficulty":0.000887692}
-{"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 Barbara. Forrest's card is shown to Adrienne. Barbara's card is shown to Forrest. 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)) ] (Agentb knows that 1)","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":"Adrienne can now know that Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Adrienne","Forrest"],"index":26957,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940689802,"difficulty":0.0059310198}
-{"premise":"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. It is publicly announced that Kate's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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 (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Kate can now know whether Daniel can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mabel","Jeffrey","Daniel","Kate"],"index":52204,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8916656971,"difficulty":0.1083343029}
-{"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 Mike. Mike's card is shown to Michael. Linda's card is shown to Michael. Michael'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:1,3 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:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mike can now know that Linda can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mike","Michael","Linda"],"index":7205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988960028,"difficulty":0.0011039972}
-{"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. Josue's card is shown to Josue. Tony's card is shown to Josue. Alex's card is shown to Tony. 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 that 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":"Alex can now know that Josue can know that Alex picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alex","Josue","Tony"],"index":21794,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960838556,"difficulty":0.0039161444}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Isabel's card is shown to Steven. Stephen's card is shown to Isabel. Angelina's card is shown to Angelina. Stephen's card is shown to Angelina. Angelina'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:4 Agentc:3,4 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:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Isabel","Angelina","Stephen"],"index":67039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994040728,"difficulty":0.0005959272}
-{"premise":"There are two persons. Everyone is visible to others. 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. It is publicly announced that Alan 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)","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":"Scott can now know whether Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alan","Scott"],"index":67677,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983452559,"difficulty":0.0016547441}
-{"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 Donnell is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mary is not thirsty. It is publicly announced that Donnell 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)) ] (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 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Donnell is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lloyd","Mary","Donnell","Kevin"],"index":7842,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9703753591,"difficulty":0.0296246409}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Meagan's forehead is not 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) ] [ ! ~(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) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janie","John","Claudia","Meagan"],"index":31798,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9771407843,"difficulty":0.0228592157}
-{"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 Richard. Leonard's card is shown to Julian. Richard's card is shown to Leonard. Lawrence'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:3 Agentc:1 Agentd: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:3 Agentb:3 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know that Julian can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Julian","Leonard","Lawrence"],"index":59639,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986822009,"difficulty":0.0013177991}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve does not know whether Barbara is thirsty. It is publicly announced that Steve does not know whether Sylvia 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 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 3) ] 0","hypothesis":"Barbara can now know that Steve can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Steve","Sylvia"],"index":18781,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9951123595,"difficulty":0.0048876405}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Kathleen can now know whether Gloria can know that Lynda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Lynda","Kathleen","Paul"],"index":54481,"s-l":"forehead_mirror-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 Jessica's forehead is not muddy. It is publicly announced that Renee 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 (~(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":"Renee can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Renee","Norbert"],"index":19512,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989116192,"difficulty":0.0010883808}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candace 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 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":"Jean can now know whether Candace can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jean","Candace"],"index":53037,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982940555,"difficulty":0.0017059445}
-{"premise":"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's forehead is muddy. It is publicly announced that Mark does not know whether Mark'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: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 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 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mark can now know that Ryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Ryan","Mark"],"index":32239,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921326041,"difficulty":0.0078673959}
-{"premise":"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) ] [ ! (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":"Grace can now know that Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Ronald","Grace","Geneva"],"index":36140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979422688,"difficulty":0.0020577312}
-{"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 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Karen can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","James","Violet","Pedro"],"index":16802,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973606467,"difficulty":0.0026393533}
-{"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 Phyllis. Phyllis's card is shown to Phyllis. Cathy's card is shown to Phyllis. Phyllis'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 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Phyllis can now know that Cathy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Derek","Phyllis","Cathy"],"index":40142,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.98662287,"difficulty":0.01337713}
-{"premise":"There are four persons. Everyone is visible 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 Theodore 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) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 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) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Theodore can now know that Loyd can know that Theodore's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Loyd","Richard","Barbara","Theodore"],"index":64874,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955984354,"difficulty":0.0044015646}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renna does not know whether or not everyone'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: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 ] (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&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Kelly can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephane","Renna","Todd","Kelly"],"index":65079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988834262,"difficulty":0.0011165738}
-{"premise":"There are two 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. It is publicly announced that Bradley does not know whether Bradley's forehead is muddy. It is publicly announced that Antonia's forehead is muddy. It is publicly announced that Antonia knows whether Bradley'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 that 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":"Bradley can now know that Antonia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bradley","Antonia"],"index":13870,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5288889408,"difficulty":0.4711110592}
-{"premise":"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 Bernice's forehead is muddy. It is publicly announced that Helene 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) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 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) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Bernice can now know whether Bernice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Christopher","Bernice","Helene"],"index":50575,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9858152866,"difficulty":0.0141847134}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelley 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 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: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":"Karen can now know whether Shelley can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Shelley","Thomas","Karen"],"index":44255,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7272988558,"difficulty":0.2727011442}
-{"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 Brett. Brett's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Ashley picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb: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:1 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Ashley can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ashley","Brett","Matthew","Leonard"],"index":16916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990505576,"difficulty":0.0009494424}
-{"premise":"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 Darcy's forehead is muddy. It is publicly announced that Darcy does not know whether Darcy's forehead is muddy. It is publicly announced that Darcy does not know whether Darcy's forehead is muddy. It is publicly announced that Darcy knows whether David'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":"David can now know that Darcy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Darcy"],"index":45386,"s-l":"forehead-0","deberta_pred":0,"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 Jan 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 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":"Jan can now know that Tammy can know whether Tammy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jan","Tammy"],"index":14453,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9988535643,"difficulty":0.0011464357}
-{"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 Betty. Mary's card is shown to Betty. Kenneth's card is shown to Kenneth. Robert's card is shown to Kenneth. Kenneth'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:2,4 Agentb:2,3 Agentc:2 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:2,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Betty can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Kenneth","Robert","Mary"],"index":20394,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993824959,"difficulty":0.0006175041}
-{"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 Mark 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 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) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Terry can now know whether Donald can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Donald","Terry"],"index":35083,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9920275807,"difficulty":0.0079724193}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tamara is 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 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":"Marc can now know whether Tamara can know that Marc is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Tamara","Marc","Jennifer"],"index":7922,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9833221436,"difficulty":0.0166778564}
-{"premise":"There are three persons. Everyone is visible 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 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 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 Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Edward","Rufus"],"index":33788,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983491898,"difficulty":0.0016508102}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Curtis does not know whether Kathleen is thirsty.","smcdel_problem":"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 (1|2|3|4))","n_announcements":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":"Steve can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Steve","Roy","Curtis"],"index":47789,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994422793,"difficulty":0.0005577207}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonio does not know whether Michelle is thirsty. It is publicly announced that Dawn does not know whether Antonio is thirsty. It is publicly announced that Antonio 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 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":"Dawn can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dawn","Antonio","Michelle","Lois"],"index":59380,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995045662,"difficulty":0.0004954338}
-{"premise":"There are four persons. Everyone is visible 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 Jerome knows whether Theresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"George can now know that Frank can know whether Theresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","George","Theresa","Jerome"],"index":19739,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999332726,"difficulty":0.000667274}
-{"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 Jason. Dana's card is shown to Dana. Dana'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:2 Agentb: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:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jason can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Dana","Raymond"],"index":55081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998985827,"difficulty":0.001014173}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clarence's card is shown to Clarence. Tameka's card is shown to Clarence. Sharon's card is shown to Sharon. Clarence's card is shown to Tameka. 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 (Agenta knows that (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":"Tameka can now know whether Clarence can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clarence","Sharon","Tameka"],"index":58464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994046688,"difficulty":0.0005953312}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve knows whether Travis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Travis","Steve","Jennifer","John"],"index":19990,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987063408,"difficulty":0.0012936592}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miquel 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 whether (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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Steven can now know whether Richard can know that Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Steven","Miquel"],"index":63620,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9554371238,"difficulty":0.0445628762}
-{"premise":"There are two persons. Everyone is visible 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 Tim'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&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":"Tim can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Tim"],"index":59643,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9927114248,"difficulty":0.0072885752}
-{"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 Andrea is thirsty. It is publicly announced that Jacqueline 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 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) ] [ ! ~(2) ] 0","hypothesis":"Raymond can now know whether Jacqueline can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Jacqueline","Andrea","Raymond"],"index":3892,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9916496277,"difficulty":0.0083503723}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Glenn does not know whether Lori 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":"Lindsey can now know that Lori can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Glenn","Lori","Lindsey"],"index":57259,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989414811,"difficulty":0.0010585189}
-{"premise":"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 does not know whether Hattie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Hattie can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillie","Alan","Linda","Hattie"],"index":65618,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971277118,"difficulty":0.0028722882}
-{"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 (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":"Curtis can now know that Nancy can know whether Horace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Curtis","Horace"],"index":2635,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9929002523,"difficulty":0.0070997477}
-{"premise":"There are two persons. Everyone is visible 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 Lillie's forehead is muddy. It is publicly announced that Lillie'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 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":"Emily can now know that Lillie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emily","Lillie"],"index":44028,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993492961,"difficulty":0.0006507039}
-{"premise":"There are two 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. It is publicly announced that Carey knows whether or not nobody's forehead is muddy. It is publicly announced that Ed does not know whether Ed's forehead is muddy. It is publicly announced that Carey 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 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)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Carey can now know whether Ed's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ed","Carey"],"index":67115,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979400039,"difficulty":0.0020599961}
-{"premise":"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. It is publicly announced that Beverly'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) ] 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 (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"Beverly can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Robert","Beverly"],"index":42586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990072846,"difficulty":0.0009927154}
-{"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. Jay's card is shown to Sandra. Jay's card is shown to Brock. Sandra's card is shown to Apryl. Brock's card is shown to Jay. Jay's card is shown to Jay. It is publicly announced that someone picked a red card. It is publicly announced that Brock does not know whether Sandra 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":"Brock can now know whether Apryl can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","Brock","Apryl","Jay"],"index":11031,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994109869,"difficulty":0.0005890131}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ellen's card is shown to Ellen. William's card is shown to Ellen. Martha'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 Martha knows whether Ellen 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) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ellen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ellen","Martha","William"],"index":26574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989848733,"difficulty":0.0010151267}
-{"premise":"There are three persons. Everyone is visible 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":"Alan can now know that Hubert can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bruce","Alan","Hubert"],"index":2380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9935796261,"difficulty":0.0064203739}
-{"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 Glenn 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Glenn can now know whether Joann can know whether Joann is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joann","Glenn"],"index":27881,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987786412,"difficulty":0.0012213588}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mitchell does not know whether Mitchell's forehead is muddy. It is publicly announced that Lisa 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|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":"Mitchell can now know that Lisa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mitchell","Lisa"],"index":40718,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994834661,"difficulty":0.0005165339}
-{"premise":"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 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) ] [ ! (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: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":"Earl can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Earl","Marylee","Tiffany"],"index":6624,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9085158706,"difficulty":1.9085158706}
-{"premise":"There are four persons. Everyone is visible 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) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! (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":["William","Jessica","Rosemary","Bonita"],"index":47124,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9986553192,"difficulty":0.0013446808}
-{"premise":"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.","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 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":"Richard can now know that Beth can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Eric","Beth"],"index":36065,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955848455,"difficulty":0.0044151545}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Inez can now know whether Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brooke","Donald","Inez","Kimberly"],"index":32545,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994357228,"difficulty":0.0005642772}
-{"premise":"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":"Dorothy can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Mona","Dorothy"],"index":18516,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9642881751,"difficulty":0.0357118249}
-{"premise":"There are three persons. Everyone is visible 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 Richard 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":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Richard","Roberta"],"index":7328,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989370704,"difficulty":0.0010629296}
-{"premise":"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|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":"Eric can now know that Lucy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Lucy","Stephen"],"index":65630,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99941957,"difficulty":0.00058043}
-{"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 Steven. Steven's card is shown to Larry. Steven's card is shown to Sharon. Larry'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 Larry 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 that (Agentb 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sharon can now know that Larry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Larry","Sharon"],"index":66377,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994266033,"difficulty":0.0005733967}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rachel does not know whether Patricia is thirsty. It is publicly announced that Rachel does not know whether Patricia 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)","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":"Patricia can now know that Rachel can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Patricia","Rachel"],"index":27854,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.928286314,"difficulty":0.071713686}
-{"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 Daniel is thirsty. It is publicly announced that Daniel 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) ] 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Vickie can now know whether Edward can know whether Erick is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erick","Vickie","Daniel","Edward"],"index":19915,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992857575,"difficulty":0.0007142425}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melanie does not know whether or not everyone is thirsty. It is publicly announced that Michael knows whether Michael is thirsty. It is publicly announced that Melanie 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 (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&2&3)) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lee can now know whether Michael can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Melanie","Lee"],"index":66684,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9825981259,"difficulty":1.9825981259}
-{"premise":"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 does not know whether Geneva's forehead is muddy. It is publicly announced that Geneva does not know whether Geneva'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":"Mildred can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Geneva","Mildred"],"index":5112,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989460111,"difficulty":0.0010539889}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reuben knows whether Reuben'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) ] (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 2) ] [ ! (1&2&3) ] 0","hypothesis":"John can now know that Reuben's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Reuben","Tina"],"index":17728,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.997635603,"difficulty":0.002364397}
-{"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 Fredricka is thirsty. It is publicly announced that Nancy does not know whether Edwin is thirsty.","smcdel_problem":"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) ] Agentc 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) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Fredricka can now know that Charles can know that Edwin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Charles","Fredricka","Edwin"],"index":67400,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979974627,"difficulty":0.0020025373}
-{"premise":"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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Cassandra'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 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))) ] Agenta knows that (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Donald can now know that Donna can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Donna","Cassandra"],"index":13024,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989008904,"difficulty":0.0010991096}
-{"premise":"There are three persons. Everyone is visible 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'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 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":"Norbert can now know whether George can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Della","George","Norbert"],"index":64419,"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 is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Athena 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] Agenta 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Athena can now know whether Derek can know whether Mae is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Athena","Pamela","Derek","Mae"],"index":39579,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999188602,"difficulty":0.000811398}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erica 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 that (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":"Erica can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erica","Roy"],"index":37165,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982391596,"difficulty":0.0017608404}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Roberta can now know that Sherry can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roberta","Daniel","Sherry"],"index":17498,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976562262,"difficulty":0.0023437738}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Milissa 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))","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":"Larue can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wendy","Larue","Milissa"],"index":46343,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9339268208,"difficulty":1.9339268208}
-{"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. Charlene's card is shown to Charlene. John's card is shown to Charlene. Charlene's card is shown to Peter. Peter'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:2,4 Agentc:2 Agentd: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 Agentb:2,4 Agentc:2 Agentd:3,4 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":["Nicole","Charlene","Peter","John"],"index":50544,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993025064,"difficulty":0.0006974936}
-{"premise":"There are three persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Kelvin'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|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":"Philip can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Philip","Leanora","Kelvin"],"index":57169,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994094372,"difficulty":0.0005905628}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nikki's card is shown to Walter. Nikki's card is shown to Nikki. Christine's card is shown to Nikki. Nikki's card is shown to Christine. 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 1)","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":"Walter can now know whether Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Walter","Nikki","Christine"],"index":24802,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9614754319,"difficulty":0.0385245681}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josephine 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 (~(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 that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Doris","Mamie","Josephine"],"index":58206,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988192916,"difficulty":0.0011807084}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! ~(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:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Deborah can now know whether Laura can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Scott","Laura","George"],"index":57855,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993339181,"difficulty":0.0006660819}
-{"premise":"There are three persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 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 Maya's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Maya","Douglas","Robert"],"index":14569,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9897722602,"difficulty":0.0102277398}
-{"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 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":"Frank can now know whether Nancy can know that Corinne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Nancy","Corinne","Ruth"],"index":55722,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9938474298,"difficulty":0.0061525702}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stella 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Jeffrey can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tracy","Stella","Jeffrey","Ursula"],"index":24866,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
-{"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 David does not know whether Trevor is thirsty. It is publicly announced that Trevor 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Robert can now know whether David can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","David","Winnifred","Trevor"],"index":13602,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993656278,"difficulty":0.0006343722}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoine does not know whether or not everyone's forehead is muddy. It is publicly announced that Antoine 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))) ] (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)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Antoine can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Malcolm","Jim","Antoine","John"],"index":10556,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5861070752,"difficulty":1.5861070752}
-{"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 Gordon. Gordon's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Gordon knows whether someone picked a red card. It is publicly announced that Edward does not know whether or not everyone picked a red card. It is publicly announced that Gordon 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|2)))","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":"Edward can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gordon","Edward"],"index":57329,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988453388,"difficulty":0.0011546612}
-{"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 Kari. Linda's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Kari knows whether Kari 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 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":"Kari can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kari","Linda"],"index":18479,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994583726,"difficulty":0.0005416274}
-{"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 George 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) ] [ ! (~(1&2&3)) ] [ ! ~(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) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Matthew can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","George","Carol"],"index":49040,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960629344,"difficulty":0.0039370656}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! 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) ] [ ! 1 ] 0","hypothesis":"Holly can now know that Alvin can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Holly","Alvin"],"index":13128,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993411899,"difficulty":0.0006588101}
-{"premise":"There are two persons. Everyone is visible 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'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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Francis can now know whether Richard can know that Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Francis"],"index":52418,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994537234,"difficulty":0.0005462766}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Denice does not know whether Doris is thirsty. It is publicly announced that Stella does not know whether Doris is thirsty. It is publicly announced that Denice knows whether Denice 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) ] (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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Denice can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stella","Doris","Denice"],"index":18613,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990467429,"difficulty":0.0009532571}
-{"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 Kevin 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)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"Kevin can now know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Julia"],"index":22010,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984081388,"difficulty":0.0015918612}
-{"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 Gayle is thirsty. It is publicly announced that James 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 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":"Gayle can now know that Jessica can know that Jessica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gayle","James","Jessica"],"index":16089,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9849768877,"difficulty":0.0150231123}
-{"premise":"There are 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 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":"Lewis can now know that Lawrence can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lewis","Goldie","Lawrence","Amanda"],"index":42099,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991563559,"difficulty":0.0008436441}
-{"premise":"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 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 (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|2|3|4)) ] 0","hypothesis":"Angelica can now know whether Janet can know that Tracie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angelica","Kenneth","Janet","Tracie"],"index":43825,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9526171088,"difficulty":0.0473828912}
-{"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 Stephanie. Stephanie's card is shown to Thomas. Thomas's card is shown to Thomas. Thomas's card is shown to Edna. Edna's card is shown to Edna. 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) ] Agenta knows whether (Agentc knows whether 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":"Carol can now know whether Thomas can know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Stephanie","Thomas","Edna"],"index":60153,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982510209,"difficulty":0.0017489791}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marceline does not know whether or not everyone is thirsty. It is publicly announced that Iris knows whether Marceline is thirsty. It is publicly announced that Iris 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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] Agentc 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&2&3&4)) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Iris can now know that Lillie can know whether Marceline is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","Marceline","Iris","Lillie"],"index":10243,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5636492968,"difficulty":1.5636492968}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricky does not know whether 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) ] [ ! ~(Agentb knows whether 4) ] Agentd 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 4) ] 0","hypothesis":"Patrick can now know whether Tiffany can know that Tiffany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Johnny","Ricky","Tiffany","Patrick"],"index":3697,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9916674495,"difficulty":0.0083325505}
-{"premise":"There are four persons. Everyone is visible 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 Roy's forehead is muddy. It is publicly announced that Marjorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Marjorie can now know that Roy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kimberley","Marjorie","Roy","Barbara"],"index":22692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9007482529,"difficulty":0.0992517471}
-{"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 Jennifer. Deanna's card is shown to Deanna. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether Deanna picked a red card.","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":"Deanna can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jennifer","Deanna"],"index":54793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
-{"premise":"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) ] [ ! (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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Shelley can now know that John can know whether Shelley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["April","Shelley","John"],"index":41294,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9383623004,"difficulty":0.0616376996}
-{"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 Mozell is thirsty. It is publicly announced that Dorothy does not know whether Monica is thirsty.","smcdel_problem":"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 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":"Monica can now know that Hilary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mozell","Hilary","Monica","Dorothy"],"index":11783,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983614087,"difficulty":0.0016385913}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone 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) ] [ ! ~(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) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know that Jerri can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jerri","Phyllis","Robert"],"index":49051,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994981289,"difficulty":0.0005018711}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Wilma 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) ] [ ! (Agentd knows whether 1) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Linda can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Freddie","Kimberly","Linda","Wilma"],"index":34011,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991368651,"difficulty":0.0008631349}
-{"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 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&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":"Maria can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesse","Maria","Sarah"],"index":47761,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9363729954,"difficulty":1.9363729954}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Elena knows whether Michael'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) ] 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 (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Michael can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Richard","Michael","Elena"],"index":40227,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9871270657,"difficulty":0.0128729343}
-{"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 Mary is thirsty. It is publicly announced that Mary does not know whether Marlene 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 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) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mary can now know that Marlene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marlene","Michael","Mary"],"index":43245,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996778667,"difficulty":0.003221333}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tommie does not know whether Minerva 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 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":"Minerva can now know whether Tommie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tommie","Minerva","Lucille"],"index":24486,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993446469,"difficulty":0.0006553531}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverley does not know whether Beverley'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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Beverley can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverley","Margaret","Andrew","Richard"],"index":27254,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8585059047,"difficulty":0.1414940953}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve does not know whether Steve's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Timothy can now know whether Charles can know whether Steve's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","William","Steve","Timothy"],"index":30017,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991735816,"difficulty":0.0008264184}
-{"premise":"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's forehead is muddy. It is publicly announced that Martin'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) ] Agenta 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) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"June can now know whether Martin can know whether Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["June","Scott","Martin","Stephine"],"index":23223,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9919576645,"difficulty":0.0080423355}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mari'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 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) ] [ ! ~(1) ] 0","hypothesis":"Mari can now know whether Anthony can know that Mari's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mari","Anthony","Christopher"],"index":46667,"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 Janice does not know whether Megan is thirsty.","smcdel_problem":"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)","n_announcements":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":"Michael can now know whether Janice is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheri","Michael","Megan","Janice"],"index":36159,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9815911055,"difficulty":0.0184088945}
-{"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. James's card is shown to Patricia. Patricia's card is shown to Jimmy. Chris's card is shown to Jimmy. Chris's card is shown to Chris. It is publicly announced that someone picked a red card. It is publicly announced that Jimmy does not know whether Jimmy 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 whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Jimmy","James","Chris"],"index":48845,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9807588458,"difficulty":0.0192411542}
-{"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 Jessica. Doris's card is shown to Jessica. Charlotte's card is shown to Charlotte. Jessica's card is shown to Doris. Charlotte's card is shown to Doris. Doris'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:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether 1)","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":"Doris can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jessica","Charlotte","Doris"],"index":23732,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7263852954,"difficulty":1.7263852954}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne does not know whether Alfred is thirsty. It is publicly announced that Andrew does not know whether Yvonne 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 (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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Alfred can now know whether Yvonne can know whether Yvonne is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfred","Andrew","Yvonne"],"index":34387,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985616803,"difficulty":0.0014383197}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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":"Lucille can now know that Bessie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Bessie","Lucille","Beatrice"],"index":67438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937931299,"difficulty":0.0062068701}
-{"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. 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) ] [ ! (Agentc knows whether 3) ] [ ! 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) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] 0","hypothesis":"Daniel can now know that Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sonny","Andrew","Daniel"],"index":2272,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9325891733,"difficulty":0.0674108267}
-{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Bonnie knows whether someone's forehead is muddy. It is publicly announced that Frank'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 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) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Frank can now know that Bonnie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Frank","Bonnie"],"index":9274,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986436963,"difficulty":0.0013563037}
-{"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 Paul. Paul's card is shown to Virginia. 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 LAW Top OBS Agenta:1 Agentb:1 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 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Paul can now know that Virginia can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Virginia"],"index":39854,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9745355248,"difficulty":1.9745355248}
-{"premise":"There are two persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that Clinton knows whether Warren's forehead is muddy. It is publicly announced that Clinton 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 (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":"Clinton can now know that Warren can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Clinton","Warren"],"index":227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988678694,"difficulty":0.0011321306}
-{"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 Alan knows whether Alan is thirsty. It is publicly announced that Alan 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 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":"Mattie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mattie","Alice","Alan"],"index":29792,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993799925,"difficulty":0.0006200075}
-{"premise":"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":"Ryan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Michael","Ryan","Napoleon"],"index":45424,"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 Alejandro does not know whether Alejandro's forehead is muddy. It is publicly announced that Alejandro 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))) ] Agentc 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":"Don can now know whether Amy can know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alejandro","Shawn","Don","Amy"],"index":42480,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9451264739,"difficulty":0.0548735261}
-{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(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) ] [ ! ~(1) ] 0","hypothesis":"Terry can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Thomas","Terry"],"index":38512,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9980575442,"difficulty":1.9980575442}
-{"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. Alphonso's card is shown to Vera. Vera'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 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:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eric can now know whether Vera can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vera","Eric","Alphonso"],"index":50714,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8297035098,"difficulty":0.1702964902}
-{"premise":"There are two persons. Everyone is visible 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 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 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":"Harold can now know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Harold","Barbara"],"index":2917,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981526732,"difficulty":0.0018473268}
-{"premise":"There are three persons. Everyone is visible 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 3)","n_announcements":1,"pbcheck":"VARS 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 whether Brian can know whether Tiffany's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Brian","Tiffany"],"index":6189,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993994236,"difficulty":0.0006005764}
-{"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. Herbert's card is shown to Jennifer. Ellen's card is shown to Jennifer. Jennifer's card is shown to Ellen. 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 (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":"Herbert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Herbert","Ellen"],"index":19161,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! ~(3) ] (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":"Betty can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Viola","Robert","Jim"],"index":47427,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9931580424,"difficulty":0.0068419576}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ariel's card is shown to Ariel. Valerie's card is shown to Ariel. Valerie's card is shown to Jessica. Ariel's card is shown to Valerie. Ariel'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 Jessica picked a red card. It is publicly announced that Gary does not know whether Gary picked a red card. It is publicly announced that Jessica does not know whether Gary 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) ] Agentd knows whether (Agentb knows that 2)","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":"Gary can now know whether Jessica can know that Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ariel","Jessica","Valerie","Gary"],"index":971,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7542353272,"difficulty":0.2457646728}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether or not nobody's forehead is muddy. It is publicly announced that Norma's forehead is muddy. It is publicly announced that Elbert'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 (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":"Elbert can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pedro","Norma","Elbert","Christopher"],"index":61051,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987712502,"difficulty":0.0012287498}
-{"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.","smcdel_problem":"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&2&3&4))","n_announcements":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":"Wilmer can now know whether Michael can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Wilmer","Matthew","Michael"],"index":23631,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.996121943,"difficulty":0.003878057}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather 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 (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":"Roxanne can now know that Steve can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steve","Roxanne","Heather"],"index":56027,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993713498,"difficulty":0.0006286502}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremiah knows whether Sara's forehead is muddy. It is publicly announced that Sara knows whether someone's forehead is muddy. It is publicly announced that Sara's forehead is muddy. It is publicly announced that Jeremiah 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 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) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jeremiah can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sara","Mary","Jeremiah"],"index":61699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9289800525,"difficulty":0.0710199475}
-{"premise":"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.","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 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":"Joshua can now know that Aaron can know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Ruth","Aaron"],"index":33917,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975681901,"difficulty":0.0024318099}
-{"premise":"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 Alexander knows whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth does not know 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 (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agenta 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Annie can now know that Doris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Alexander","Doris","Elizabeth"],"index":31171,"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 is thirsty. It is publicly announced that Lincoln does not know whether Jesse 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) ] [ ! ~(Agenta knows whether 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"James can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lincoln","James","Jesse"],"index":211,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9853762984,"difficulty":0.0146237016}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daphne's card is shown to Christopher. Christopher's card is shown to Cornelius. Christopher's card is shown to Daphne. 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) ] (Agenta knows whether 1)","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":"Christopher can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Cornelius","Daphne","Manuel"],"index":46928,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9384733438,"difficulty":1.9384733438}
-{"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)","n_announcements":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":"Justin can now know that Justin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justin","Cindy","Lloyd","Richard"],"index":65588,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9385725856,"difficulty":0.0614274144}
-{"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) ] [ ! (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":"Margaret can now know whether Joseph can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Kent","Joseph"],"index":61423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9911772013,"difficulty":0.0088227987}
-{"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 Edward. Alice's card is shown to Nona. Edward's card is shown to Alice. Nona'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 Nona picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb: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 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Edward can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edward","Nona","Alice"],"index":40067,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990413785,"difficulty":0.0009586215}
-{"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 (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":"Eduardo can now know that Agnes can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Spring","Eduardo","Agnes","Robert"],"index":32092,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991936088,"difficulty":0.0008063912}
-{"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 Susie is thirsty. It is publicly announced that Susie 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)) ] (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 (1|2|3|4)) ] 0","hypothesis":"Martha can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Frederick","Susie","Anna"],"index":31165,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993852377,"difficulty":0.0006147623}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evan's forehead is muddy.","smcdel_problem":"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 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":"Joy can now know that Ralph can know that Ralph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evan","Ralph","Joy"],"index":18700,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952347875,"difficulty":0.0047652125}
-{"premise":"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 knows 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 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":"Richard can now know that Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Jeanne","Richard","Tina"],"index":23226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969272017,"difficulty":0.0030727983}
-{"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 Anthony. Lydia's card is shown to Maurice. Anthony's card is shown to Maurice. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Lydia does not know whether Lydia picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card. It is publicly announced that Anthony does not know whether Maurice picked a red card. It is publicly announced that Anthony 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] (Agentb knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Anthony can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lydia","Anthony","Maurice","Mildred"],"index":33178,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994613528,"difficulty":0.0005386472}
-{"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 Jessie. Agnes's card is shown to Charles. Charles's card is shown to Agnes. 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) ] Agentb knows that (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charles can now know that Agnes can know whether Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessie","Charles","Agnes"],"index":51194,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9965862036,"difficulty":0.0034137964}
-{"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 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":"Janet can now know that Jenna can know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jenna","Janet","John","Patrick"],"index":16580,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969047904,"difficulty":0.0030952096}
-{"premise":"There are two persons. Everyone is visible 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 Dorothy knows whether Dorothy'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 (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) ] 0","hypothesis":"Micheal can now know whether Dorothy can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Micheal"],"index":48395,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992252588,"difficulty":0.0007747412}
-{"premise":"There are three persons. Everyone is visible 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 Jamie's forehead is muddy. It is publicly announced that Harold knows whether or not nobody's forehead is muddy. It is publicly announced that Jamie knows whether 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) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] (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) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Donna can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Harold","Jamie"],"index":28422,"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. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to John. Thomas's card is shown to Elizabeth. Tammy's card is shown to Elizabeth. Elizabeth's card is shown to Thomas. Tammy'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:2 Agentb:3,4 Agentc:2 Agentd: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:2 Agentb:3,4 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Elizabeth can know whether Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Elizabeth","Thomas","Tammy"],"index":59208,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9274653792,"difficulty":1.9274653792}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW 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":"Valda can now know that Valda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vivian","Carol","Kareem","Valda"],"index":43223,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9619244337,"difficulty":0.0380755663}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret 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 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":"Bret can now know that Juan can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debora","Bret","Juan"],"index":3124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993047714,"difficulty":0.0006952286}
-{"premise":"There are two persons. Everyone is visible 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 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)","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":"Heidi can now know that Kent's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kent","Heidi"],"index":58775,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978183508,"difficulty":0.0021816492}
-{"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) ] [ ! ~(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":"Carol can now know whether Stanley can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Stanley","Carol"],"index":36099,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9807059765,"difficulty":0.0192940235}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (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":"Peter can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Peter","Juan"],"index":6748,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990936518,"difficulty":0.0009063482}
-{"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 Lisa is thirsty. It is publicly announced that Lisa does not know whether or not everyone is thirsty. It is publicly announced that Lisa does not know whether Larry is thirsty. It is publicly announced that Lisa 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lisa can now know whether Larry can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mildred","Lisa","Larry"],"index":52407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8923855424,"difficulty":0.1076144576}
-{"premise":"There are three persons. Everyone is visible 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 Duane's forehead is muddy.","smcdel_problem":"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 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":"Leslie can now know that Samuel can know whether Samuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Samuel","Leslie","Duane"],"index":28440,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993076324,"difficulty":0.0006923676}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Andrew can now know whether Ross can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ross","Richard","Andrew"],"index":32159,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992232323,"difficulty":0.0007767677}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeanne's card is shown to Norma. Patricia's card is shown to Patricia. Norma's card is shown to Carmen. Norma's card is shown to Jeanne. Patricia's card is shown to Jeanne. 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 2)","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":"Norma can now know that Carmen can know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norma","Patricia","Carmen","Jeanne"],"index":7881,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982995391,"difficulty":0.0017004609}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany knows whether someone's forehead is muddy. It is publicly announced that Robert knows whether Tiffany's forehead 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 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":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Robert","Tiffany"],"index":17262,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9331991076,"difficulty":0.0668008924}
-{"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 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 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":"Ruben can now know whether Brandon can know whether Ruben is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandon","Lawrence","Harold","Ruben"],"index":48396,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990861416,"difficulty":0.0009138584}
-{"premise":"There are 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 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":"Samantha can now know that Leslie can know that Samantha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leslie","Samantha","Sandra"],"index":32819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985211492,"difficulty":0.0014788508}
-{"premise":"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))) ] 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 (~(1|2|3))) ] 0","hypothesis":"John can now know that Carolyn can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Mitchell","Carolyn"],"index":57928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958288074,"difficulty":0.0041711926}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Leo can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Robert","Leo","Eugenia"],"index":21100,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994568229,"difficulty":0.0005431771}
-{"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 John. Amanda's card is shown to William. John's card is shown to Michael. Amanda's card is shown to Michael. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 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 Agentb:4 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"John can now know that William can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","William","Michael","Amanda"],"index":58868,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990417361,"difficulty":0.0009582639}
-{"premise":"There are four persons. Everyone is visible 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 Darlene's forehead is muddy. It is publicly announced that Marie 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) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] (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) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Betty can now know whether Darlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jo","Betty","Darlene","Marie"],"index":61875,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994363189,"difficulty":0.0005636811}
-{"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. Jennifer's card is shown to Fred. Kyle's card is shown to Jessica. 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 does not know whether Kyle picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kyle can now know that Fred can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Fred","Kyle","Jessica"],"index":50885,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935469031,"difficulty":0.0064530969}
-{"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 Angela 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) ] [ ! ~(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) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Ricky can now know whether Angela can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edna","Ricky","Harold","Angela"],"index":14354,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9962149262,"difficulty":0.0037850738}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lucy's card is shown to Lucy. Larry's card is shown to Lucy. Carolyn's card is shown to Lucy. Carolyn's card is shown to Larry. Larry's card is shown to Carolyn. It is publicly announced that someone 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 Carolyn does not know whether Carolyn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 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:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Larry can now know whether Carolyn can know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucy","Larry","Carolyn"],"index":47483,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9954081178,"difficulty":0.0045918822}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Bonnie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bonnie","Lawrence","Neil","Michael"],"index":40212,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993348718,"difficulty":0.0006651282}
-{"premise":"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 Gerri's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 ] (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|2|3|4) ] [ ! 1 ] 0","hypothesis":"Krista can now know whether Gerri's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerri","Floyd","Stuart","Krista"],"index":60860,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989776611,"difficulty":0.0010223389}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Royce's card is shown to Alice. Alice's card is shown to James. Alice's card is shown to Royce. James's card is shown to Royce. Royce'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 Alice 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) ] (Agenta 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":"Alice can now know that Jonathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alice","James","Royce","Jonathan"],"index":13021,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973145127,"difficulty":0.0026854873}
-{"premise":"There are 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 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":"Thora can now know whether Anthony can know whether Kerri's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kerri","Anthony","Thora"],"index":57416,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993959665,"difficulty":0.0006040335}
-{"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 Trevor. Priscilla's card is shown to Priscilla. 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":"Suzanne can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Suzanne","Trevor","Priscilla","Herb"],"index":45938,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989756346,"difficulty":0.0010243654}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradford knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Holly knows whether Angel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Angel can now know whether Holly can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Holly","Dwight","Bradford","Angel"],"index":63406,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991832376,"difficulty":0.0008167624}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phyllis's card is shown to Phyllis. Sarah's card is shown to Ruth. Sarah's card is shown to David. Phyllis's card is shown to Sarah. Sarah'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:4 Agentd: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 Agentb:4 Agentc:4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phyllis","Ruth","David","Sarah"],"index":8645,"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). Kent's card is shown to Kent. Jay's card is shown to Kent. Myrtle's card is shown to Kent. Jay's card is shown to Williams. Myrtle's card is shown to Williams. Williams's card is shown to Jay. Kent's card is shown to Myrtle. Myrtle's card is shown to Myrtle. It is publicly announced that someone picked a red card. It is publicly announced that Jay does not know whether Jay picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3,4 Agentc:2 Agentd:1,4 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:1,3,4 Agentb:3,4 Agentc:2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jay can now know whether Williams picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kent","Williams","Jay","Myrtle"],"index":42443,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9428710938,"difficulty":1.9428710938}
-{"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 Beverly is thirsty. It is publicly announced that Beverly does not know whether Ina is thirsty. It is publicly announced that Ina 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) ] 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:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Ina can now know whether Patricia can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Patricia","Ina","Beverly"],"index":3483,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994046688,"difficulty":0.0005953312}
-{"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 Micheal. Micheal's card is shown to Carlos. Mona'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: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":"Mona can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Micheal","Mona","Carlos"],"index":30081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989852309,"difficulty":0.0010147691}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stanley's card is shown to Jill. Jill's card is shown to Stanley. 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 (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":"Jill can now know whether Stanley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jill","Stanley"],"index":31334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8844514489,"difficulty":0.1155485511}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (~(1&2&3)) ] [ ! 1 ] (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":"Jackie can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Jackie","Barrett"],"index":65027,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992402792,"difficulty":0.0007597208}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacie knows whether 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 Stacie 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&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":"Louis can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Louis","Stacie"],"index":28580,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.557918787,"difficulty":1.557918787}
-{"premise":"There are three persons. Everyone is visible 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 Robert knows whether Robert's forehead is muddy. It is publicly announced that Joyce 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 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":"Joyce can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Timothy","Joyce"],"index":33970,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9904120564,"difficulty":0.0095879436}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Raymond can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Fred","Linda","Raymond"],"index":46522,"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'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 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":"Timothy can now know whether Edith can know that Edith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arnold","Edith","Timothy"],"index":59853,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995443821,"difficulty":0.004556179}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Thomas can now know that Kevin can know that Jacqueline's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Jacqueline","Kevin"],"index":3110,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974681139,"difficulty":0.0025318861}
-{"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 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":"Robert can now know whether Kimberly can know that Melvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Kimberly","Melvin","Robert"],"index":47597,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9947811961,"difficulty":0.0052188039}
-{"premise":"There are three persons. Everyone is visible 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 Mark 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 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":"William can now know whether Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Terry","Mark"],"index":8797,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994370341,"difficulty":0.0005629659}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erica knows 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 4) ] Agentd 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) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mildred can now know whether Michael can know that Gina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erica","Gina","Michael","Mildred"],"index":9356,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9727368355,"difficulty":0.0272631645}
-{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Frank knows whether Frank'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":"Xavier can now know that Frank can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Frank","Xavier"],"index":6943,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989088774,"difficulty":0.0010911226}
-{"premise":"There are three persons. Everyone is visible 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 Heather's forehead is muddy.","smcdel_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 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":"Morgan can now know that Heather can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hannah","Morgan","Heather"],"index":17040,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999380827,"difficulty":0.000619173}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether 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 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 that (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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"William can now know that Eugene can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Lorraine","Eugene"],"index":52136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8263214827,"difficulty":0.1736785173}
-{"premise":"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. It is publicly announced that Irene'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)","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":"Victor can now know that Victor's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Enrique","Christina","Irene"],"index":19059,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976297617,"difficulty":0.0023702383}
-{"premise":"There are four persons. Everyone is visible 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 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Brett can now know that Sylvia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brett","Natalie","Jose","Sylvia"],"index":43062,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9929192662,"difficulty":0.0070807338}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carlton does not know whether or not everyone is thirsty. It is publicly announced that Carlton does not know whether Maureen 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 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":"Joseph can now know that Maureen can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carlton","Maureen","Joseph"],"index":54572,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9118512273,"difficulty":0.0881487727}
-{"premise":"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 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 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":"Margaret can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Pamela"],"index":15947,"s-l":"forehead-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 Maegan 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 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":"Jeffrey can now know that Deloris can know that Deloris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Deloris","Maegan"],"index":33733,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959449172,"difficulty":0.0040550828}
-{"premise":"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 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":"Barbara can now know that Mary can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Barbara","Janna","Shawn"],"index":43455,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945947528,"difficulty":0.0054052472}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cody knows whether Ami's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Cody knows whether Cody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] Agenta 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) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Cody can now know that Robert can know that Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cody","Lauren","Ami","Robert"],"index":6274,"s-l":"forehead-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 Mary does not know whether Mary'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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know whether Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Jennifer"],"index":5925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9793014526,"difficulty":0.0206985474}
-{"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 Eric is thirsty. It is publicly announced that Laurel 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 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":"Laurel can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alfonso","Eric","Ruth","Laurel"],"index":22598,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985099435,"difficulty":0.0014900565}
-{"premise":"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 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 (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":"Barbara can now know whether Kimberly can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Kimberly","Yesenia","John"],"index":41085,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6892459989,"difficulty":0.3107540011}
-{"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 Laura 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 (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":"Eva can now know that Omar can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eva","Laura","John","Omar"],"index":20233,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994589686,"difficulty":0.0005410314}
-{"premise":"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 (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":"Maria can now know that Betty can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Joanne","John","Betty"],"index":40854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988725781,"difficulty":0.0011274219}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nu's card is shown to Alton. Nu's card is shown to Christopher. 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 whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know whether Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alton","Christopher","Nu"],"index":7035,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6747925878,"difficulty":0.3252074122}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Reba 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 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":"Reba can now know whether Reba is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Rickie","Reba"],"index":21643,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9935137033,"difficulty":0.0064862967}
-{"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 Mary. Mary's card is shown to Emma. Walter's card is shown to Emma. 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 (Agenta 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":"Emma can now know whether Mary can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Emma","Lauri","Walter"],"index":10010,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9899142981,"difficulty":0.0100857019}
-{"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 Mike is thirsty. It is publicly announced that Sabrina knows whether someone is thirsty. 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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mike can now know that Sabrina is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Mike","Charles","Sabrina"],"index":47693,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9279511571,"difficulty":0.0720488429}
-{"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 Eva is thirsty. It is publicly announced that Nita does not know whether Eva 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 whether 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":"Eva can now know whether Nita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Eva","Nita"],"index":30521,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9835786819,"difficulty":1.9835786819}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karen 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 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Karen can now know whether Sandra can know whether Karen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Karen","Sandra"],"index":10328,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987667799,"difficulty":0.0012332201}
-{"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 Jerome. Jerome's card is shown to Stacey. Stacey's card is shown to Stacey. Alice's card is shown to Stacey. Stacey's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Alice knows whether Stacey 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) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alice can now know that Stacey can know that Stacey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerome","Stacey","Alice"],"index":29639,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9144585133,"difficulty":0.0855414867}
-{"premise":"There are three persons. Everyone is visible 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 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&2&3))","n_announcements":1,"pbcheck":"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":"Mary can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","David","Sarah"],"index":33777,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989722967,"difficulty":0.0010277033}
-{"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 Ron. Ron's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 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 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Ron can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Ron","John","David"],"index":2763,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9888021946,"difficulty":0.0111978054}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"Jeannie can now know whether Donald can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Gus","Bart","Jeannie"],"index":42086,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994379878,"difficulty":0.0005620122}
-{"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 Michael. Jessica's card is shown to Linda. Linda's card is shown to Linda. Linda's card is shown to Barbra. 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 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":"Linda can now know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Jessica","Linda","Barbra"],"index":40169,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7628654838,"difficulty":1.7628654838}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jack's card is shown to Jack. Paul's card is shown to Jack. Jack's card is shown to David. Jack'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 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 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:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jack can now know whether Paul can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","David","Paul"],"index":61597,"s-l":"explicit-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 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&2&3&4))","n_announcements":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 that James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Autumn","James","Marian"],"index":11118,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9926261306,"difficulty":0.0073738694}
-{"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) ] [ ! ~(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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Carlos can now know that Dorothy can know that Carol is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carlos","Dorothy","Gerald","Carol"],"index":47733,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.945561111,"difficulty":0.054438889}
-{"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 Esther. Marie's card is shown to John. Esther's card is shown to Marie. John's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie 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 (Agentc knows that (1&2&3))","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":"Esther can now know whether Marie can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Esther","John","Marie"],"index":37751,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9932761192,"difficulty":1.9932761192}
-{"premise":"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. It is publicly announced that Luke does not know whether Luke's forehead is muddy. It is publicly announced that Dorothy 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))) ] Agentb 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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that Dorothy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luke","James","Dorothy","Mark"],"index":47545,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990531802,"difficulty":0.0009468198}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarence 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 (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":"Clarence can now know that Charles can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clarence","Robert","Charles"],"index":9990,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983475208,"difficulty":0.0016524792}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille is thirsty. It is publicly announced that Ashley does not know whether Barbara is thirsty. It is publicly announced that Lucille knows whether Lucille is thirsty. It is publicly announced that Ashley 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)","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":"Ashley can now know that Ashley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ashley","Barbara","Lucille"],"index":1871,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5116080046,"difficulty":0.4883919954}
-{"premise":"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 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":"Robert can now know that Quinn can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronnie","Maurice","Robert","Quinn"],"index":38405,"s-l":"forehead-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 Ann knows whether or not nobody is thirsty. It is publicly announced that Ann does not know whether Bernard is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty. It is publicly announced that Ann 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)) ] Agentc 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|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that Bernard can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernard","Ann","Richard"],"index":53288,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8017603755,"difficulty":0.1982396245}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lee knows whether Arthur is thirsty. It is publicly announced that Arthur is thirsty. It is publicly announced that Arthur 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))) ] 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 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Arthur can now know that Lee can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lee","Arthur"],"index":52203,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984153509,"difficulty":0.0015846491}
-{"premise":"There are four persons. Everyone is visible 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 Tom's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Margarito 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":["Tom","Jennifer","Angela","Margarito"],"index":26722,"s-l":"forehead_mirror-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 is thirsty. It is publicly announced that Connie does not know whether or not everyone is thirsty. It is publicly announced that Diane 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 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":"Connie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diane","Connie","Gary"],"index":59381,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990850687,"difficulty":0.0009149313}
-{"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 Marietta 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta 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 2) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Sylvia can now know whether Rosella can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","Marietta","Rosella","Sylvia"],"index":63511,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9857738018,"difficulty":0.0142261982}
-{"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. Ruthie's card is shown to Mark. Andrew's card is shown to Mark. Ruthie's card is shown to Ruthie. Andrew's card is shown to Ruthie. Ruthie's card is shown to Jessica. Mark's card is shown to Andrew. Ruthie'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:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruthie can now know that Andrew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Ruthie","Jessica","Andrew"],"index":25384,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978510141,"difficulty":0.0021489859}
-{"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. Raymond's card is shown to Leah. Brittney's card is shown to Leah. Raymond'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:1,2,3 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:1,2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leah can now know that Raymond can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leah","Raymond","Brittney"],"index":42220,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kayla does not know whether Gregoria is thirsty. It is publicly announced that Carter does not know whether Jimmy is thirsty. It is publicly announced that Kayla does not know whether Carter is thirsty.","smcdel_problem":"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) ] 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 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":"Jimmy can now know that Carter can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carter","Jimmy","Gregoria","Kayla"],"index":40939,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990764856,"difficulty":0.0009235144}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine 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 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) ] [ ! ~(1) ] 0","hypothesis":"Catherine can now know that Edward can know whether Denise is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Danielle","Denise","Edward"],"index":19344,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972726703,"difficulty":0.0027273297}
-{"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 Patricia is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 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) ] 0","hypothesis":"Patricia can now know whether Shane can know that Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Patricia","Shane"],"index":4735,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.925763011,"difficulty":1.925763011}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patti does not know whether Gerald is thirsty. It is publicly announced that Gerald 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 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":"Gerald can now know that Don is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Augusta","Don","Gerald","Patti"],"index":20694,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984148741,"difficulty":0.0015851259}
-{"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 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":"Frankie can now know whether Joseph can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Joseph","Frankie"],"index":17768,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957343936,"difficulty":0.0042656064}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annie is thirsty. It is publicly announced that Annie does not know whether Dori is thirsty. It is publicly announced that Regina does not know whether Dori is 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 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) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Arthur can now know whether Dori is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Regina","Arthur","Dori","Annie"],"index":6907,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9715482593,"difficulty":0.0284517407}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerrie does not know whether Kerrie's forehead is muddy. It is publicly announced that Jesus knows whether Kerrie's forehead is muddy. It is publicly announced that Jesus does not know whether Jesus's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Deborah can now know that Kerrie can know whether Kerrie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Thomas","Jesus","Kerrie"],"index":53063,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7174072266,"difficulty":1.7174072266}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Justin. Justin's card is shown to Bryan. Bryan's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Justin 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 that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Justin can now know that Bryan can know that Justin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Justin","Bryan"],"index":61143,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.907800436,"difficulty":0.092199564}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gladys does not know whether Sherry 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)) ] (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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sherry can now know whether Sherry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sherry","Lisa","Gladys","Nicholas"],"index":40277,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980555773,"difficulty":0.0019444227}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Linda can now know whether Albert can know that Richard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gail","Albert","Richard","Linda"],"index":57336,"s-l":"forehead_mirror-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. It is publicly announced that Andre knows whether Joaquina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Joaquina can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Liliana","Andre","Joaquina"],"index":21388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990066886,"difficulty":0.0009933114}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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 (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":"Jack can now know whether Sierra can know that Jack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sierra","Deborah","Jack"],"index":31112,"s-l":"forehead_mirror-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's forehead is muddy. It is publicly announced that Karen knows whether Karen'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 (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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Shannon can now know that Karen can know that Joy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Joy","Karen","Shannon"],"index":46838,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992723763,"difficulty":0.007276237}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina knows 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 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Regina can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edmund","Flossie","Regina","Ronald"],"index":25247,"s-l":"forehead-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 Shirley's forehead is muddy. It is publicly announced that Shirley knows whether or not nobody's forehead is muddy. It is publicly announced that Numbers does not know whether Numbers's forehead 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 (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 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Shirley can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Numbers","Richard","Shirley"],"index":49041,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990255833,"difficulty":0.0009744167}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentd 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:1,2,3,4 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":"Adrienne can now know whether Elizabeth can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Adrienne","Lisa","Francis"],"index":13222,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993638396,"difficulty":0.0006361604}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Craig can now know that Amy can know that Craig's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amy","Craig","Michael","Rosemarie"],"index":57269,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983353019,"difficulty":0.0016646981}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Arnold. Dwight's card is shown to Arnold. Omar's card is shown to Arnold. Edwin's card is shown to Dwight. Arnold's card is shown to Omar. Arnold's card is shown to Edwin. Dwight's card is shown to Edwin. Omar's card is shown to Edwin. Edwin's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Dwight does not know whether Omar 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) ] Agenta knows whether (Agentb knows that 3)","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":"Arnold can now know whether Dwight can know that Omar picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arnold","Dwight","Omar","Edwin"],"index":24903,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.954169631,"difficulty":0.045830369}
-{"premise":"There are four persons. Everyone is visible 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":"Mark can now know whether Harold can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Michael","Mark","Charles"],"index":5809,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999330163,"difficulty":0.000669837}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jerome's card is shown to Jerome. Steve's card is shown to Jerome. Jerome's card is shown to Christa. Barbara'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:2,4 Agentb:2 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:2,4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Jerome","Christa","Steve"],"index":3242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989666939,"difficulty":0.0010333061}
-{"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 Karen is thirsty. It is publicly announced that Mark does not know whether or not everyone is thirsty. It is publicly announced that Mark does not know whether Karen is thirsty. It is publicly announced that Karen 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 (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":"Candace can now know that Karen can know that Karen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Candace","Karen","Jose","Mark"],"index":23754,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7396417856,"difficulty":1.7396417856}
-{"premise":"There are four persons. Everyone is visible 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 not muddy. It is publicly announced that Kevin's forehead is not 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) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentd 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":"Andrew can now know whether Cody can know whether Steve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steve","Kevin","Cody","Andrew"],"index":35095,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994531274,"difficulty":0.0005468726}
-{"premise":"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 Gary'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 (~(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":"Gary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Don","Gary"],"index":16577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989649057,"difficulty":0.0010350943}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allan's card is shown to Daniel. Daniel's card is shown to Jefferson. Jefferson's card is shown to Allan. 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) ] Agentc 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":"Allan can now know that Jefferson can know whether Jefferson picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Jefferson","Allan"],"index":4294,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8645808697,"difficulty":0.1354191303}
-{"premise":"There are 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)","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":"Erwin can now know that Michelle can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Michelle","John","Erwin"],"index":25861,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993575215,"difficulty":0.0006424785}
-{"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) ] 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 1) ] 0","hypothesis":"Alisha can now know that Trisha can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janice","Trisha","Kelley","Alisha"],"index":22755,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988778234,"difficulty":0.0011221766}
-{"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 Tracy. Tracy's card is shown to Jose. Faith's card is shown to Jose. Tracy's card is shown to Faith. Jose's card is shown to Faith. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether Francis 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) ] (Agenta knows that 4)","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":"Tracy can now know that Faith picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Jose","Francis","Faith"],"index":16950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948878884,"difficulty":0.0051121116}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Violet 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)) ] 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":"Bobby can now know that Violet can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","Robert","Violet"],"index":23818,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994457364,"difficulty":0.0005542636}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 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":"Michael can now know whether Gary can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gary","Mary","Charles","Michael"],"index":16095,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994210005,"difficulty":0.0005789995}
-{"premise":"There are two persons. Everyone is visible 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 Tracy'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":"Tracy 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":["Tracy","James"],"index":34752,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989575148,"difficulty":0.0010424852}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Riley does not know whether Jennifer is thirsty. It is publicly announced that Christopher does not know whether Jennifer is thirsty. It is publicly announced that Riley 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) ] (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) ] [ ! ~(1) ] 0","hypothesis":"Riley can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Riley","James","Christopher","Jennifer"],"index":11011,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998496294,"difficulty":0.001503706}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stuart 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 (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&2)) ] 0","hypothesis":"Stuart can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stuart","Mary"],"index":58185,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947192669,"difficulty":0.0052807331}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nelson 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 (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":"Xenia can now know that Nelson can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dana","Ben","Xenia","Nelson"],"index":4781,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994801879,"difficulty":0.0005198121}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Magda does not know whether Karima is thirsty. It is publicly announced that Jerry does not know whether Magda is thirsty. It is publicly announced that Karima 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 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(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 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Karima can now know that Jerry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Magda","Jerry","Karima"],"index":36177,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9945662022,"difficulty":0.0054337978}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cristin is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Cristin does not know whether Raymond 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|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) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Lonnie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lonnie","Cristin","Raymond"],"index":40946,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990215302,"difficulty":0.0009784698}
-{"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 Gregory. Eric's card is shown to Gregory. Andrea's card is shown to Andrea. Gregory's card is shown to Eric. 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 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":"Andrea can now know that Eric can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gregory","Andrea","Eric"],"index":57753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989418387,"difficulty":0.0010581613}
-{"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 Charles is thirsty. It is publicly announced that Annette 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)) ] (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) ] [ ! ~(Agentd knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Charles can now know whether Annette is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Annette","Cesar","Danielle"],"index":1979,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918676019,"difficulty":0.0081323981}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! 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":"Christy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Derek","Meghan","Christy"],"index":21525,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988345504,"difficulty":0.0011654496}
-{"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. Bridget's card is shown to Bridget. James's card is shown to Bridget. Jeffrey'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:1 Agentb:2,3 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:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jeffrey can now know that Bridget can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Bridget","James"],"index":17599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990547299,"difficulty":0.0009452701}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecilia 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) ] [ ! (Agentb knows whether 3) ] (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":"Cecilia can now know whether Cecilia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Cecilia","Alexander","Kenneth"],"index":4165,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891521931,"difficulty":0.0108478069}
-{"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. Alicia's card is shown to Judy. John's card is shown to Alicia. John's card is shown to John. 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:1,2 Agentb:3 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:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alicia can now know whether Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judy","Alicia","John","Eugene"],"index":15879,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9254385233,"difficulty":0.0745614767}
-{"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)","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":"Laura can now know that Gerald can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Laura","Gerald"],"index":21586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960889816,"difficulty":0.0039110184}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 (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":"Alejandro can now know whether William can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alejandro","Carol","Terry","William"],"index":27874,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993330836,"difficulty":0.0006669164}
-{"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)","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":"Guadalupe can now know that Lyn can know that Katelynn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Katelynn","Lyn","Guadalupe"],"index":65726,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943686128,"difficulty":0.0056313872}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Louis does not know whether Alex is thirsty. It is publicly announced that Louis 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 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":"Alex can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louis","Alex"],"index":42158,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994950294,"difficulty":0.0005049706}
-{"premise":"There are 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 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":"Adam can now know that Donald can know whether Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Victor","Adam","Fredericka"],"index":60686,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992434978,"difficulty":0.0007565022}
-{"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 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 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":"Robert can now know whether Earl can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Earl","Robert"],"index":63924,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9503433704,"difficulty":0.0496566296}
-{"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 Michelle. Michelle's card is shown to Edna. It is publicly announced that someone picked a red card. It is publicly announced that Janice picked a black card. It is publicly announced that Janice picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(1) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(1) ] 0","hypothesis":"Michelle can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Michelle","Edna","Kenneth"],"index":59458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985086322,"difficulty":0.0014913678}
-{"premise":"There are 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":"Sue can now know that Carmen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sue","Carmen","Timothy"],"index":24123,"s-l":"forehead_mirror-0","deberta_pred":0,"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 Donald knows whether Rita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 3) ] 0","hypothesis":"Donald can now know that Henry can know that Rita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Donald","Rita","Kristen"],"index":33221,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977782369,"difficulty":0.0022217631}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Jimmie knows whether someone's forehead is muddy. It is publicly announced that Peter knows whether Jimmie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Peter can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Peter","Natalia","Ada","Jimmie"],"index":18966,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993582368,"difficulty":0.0006417632}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle'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 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":"Michelle can now know that Denise can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michelle","Denise"],"index":63652,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5852844715,"difficulty":1.5852844715}
-{"premise":"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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Joseph can now know that Jarrett can know that Regina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Jarrett","Evelyn","Regina"],"index":31449,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968675971,"difficulty":0.0031324029}
-{"premise":"There are three persons. Everyone is visible 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 Cheryl's forehead is muddy.","smcdel_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 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":"John can now know that Cheryl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dale","Cheryl","John"],"index":21457,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942706823,"difficulty":0.0057293177}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Charles 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)) ] [ ! (Agentc knows whether 2) ] (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)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Geraldine can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geraldine","Justin","Charles","Julia"],"index":34047,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998233676,"difficulty":0.001766324}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fermin knows whether someone is thirsty. It is publicly announced that Marie knows whether Marie 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":"Marie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marie","Fermin"],"index":27611,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994478822,"difficulty":0.0005521178}
-{"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 Rosemary. Stephanie's card is shown to Ray. Patricia's card is shown to Stephanie. Ray's card is shown to Stephanie. 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 that (Agentc knows that 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":"Rosemary can now know that Ray can know that Rosemary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Rosemary","Ray","Stephanie"],"index":22731,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981939197,"difficulty":0.0018060803}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvette 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) ] [ ! ~(Agentc knows whether (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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Yvette can now know that Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Allan","Christopher","Yvette"],"index":3441,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9580766559,"difficulty":1.9580766559}
-{"premise":"There are 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":"Edward 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":["Edward","Richard","Jonathan","Annie"],"index":14393,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988656044,"difficulty":0.0011343956}
-{"premise":"There are three persons. Everyone is visible 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 Bobby's forehead is muddy.","smcdel_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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Norma can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bobby","Norma","Eileen"],"index":28248,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990764856,"difficulty":0.0009235144}
-{"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 William. William's card is shown to Sarah. Sarah's card is shown to Sarah. 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 whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Sarah","Janette"],"index":52171,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7634845376,"difficulty":0.2365154624}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauletta's card is shown to Pauletta. Pauletta's card is shown to Kimberly. Kimberly's card is shown to Kimberly. It is publicly announced that someone picked a red card. It is publicly announced that Pauletta knows whether Pauletta picked a red card. It is publicly announced that Pauletta does not know whether Kimberly 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) ] Agenta knows that (Agentb 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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Pauletta can now know that Kimberly can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Pauletta","Kimberly"],"index":5387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
-{"premise":"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 knows whether 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) ] [ ! (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":"Kathryn can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Kathryn"],"index":48070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988889098,"difficulty":0.0011110902}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Celia's card is shown to Celia. Celia's card is shown to Herbert. Luann's card is shown to Herbert. Herbert's card is shown to Luann. It is publicly announced that someone picked a red card. It is publicly announced that Herbert 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)) ] (Agenta knows whether 2)","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":"Celia can now know whether Herbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Celia","Herbert","Luann"],"index":33150,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.867991209,"difficulty":1.867991209}
-{"premise":"There are four persons. Everyone is visible 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'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 (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) ] [ ! ~(2) ] 0","hypothesis":"Velma can now know that Richard can know whether Velma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Velma","Bobby","Dwayne"],"index":17202,"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 is thirsty. It is publicly announced that Richard does not know whether Philip is thirsty. It is publicly announced that Richard 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Juan can now know that Juan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Philip","Richard","Anthony"],"index":53123,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942985177,"difficulty":0.0057014823}
-{"premise":"There are four 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 1,2,3,4 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 (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":"Concetta can now know that Robert can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Concetta","Robert","Richard","Jim"],"index":19861,"s-l":"forehead-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 is thirsty. It is publicly announced that Melanie knows whether someone is thirsty. It is publicly announced that Christopher knows whether or not nobody is thirsty. It is publicly announced that Aurelia knows whether Aurelia is thirsty. It is publicly announced that Christopher 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 (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Aurelia can now know that Melanie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melanie","Aurelia","Christopher","Jason"],"index":19383,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.993899107,"difficulty":0.006100893}
-{"premise":"There are four persons. Everyone is visible 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 Tanya's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 ] (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)) ] [ ! 1 ] 0","hypothesis":"Jeffrey can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tanya","Kelly","Jeffrey","Ulysses"],"index":46434,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989309907,"difficulty":0.0010690093}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margarito 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 (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":"Margarito can now know that Deborah can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mia","Margarito","Martha","Deborah"],"index":18475,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993698001,"difficulty":0.0006301999}
-{"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. Martin's card is shown to Charles. Frankie'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 Martin picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Frankie can now know that Frankie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Martin","Frankie","Charles"],"index":23227,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.957262516,"difficulty":0.042737484}
-{"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 Miguel is thirsty. It is publicly announced that Gregory 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 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 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Christine can now know that Gregory can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christine","Rick","Miguel","Gregory"],"index":16407,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993997812,"difficulty":0.0006002188}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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":"Heather can now know that Heather's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Carlos","Heather"],"index":67358,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979549646,"difficulty":0.0020450354}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lydia's card is shown to Lydia. Lydia's card is shown to Gloria. Gloria's card is shown to Gloria. Lydia's card is shown to Lamar. Gloria's card is shown to Lamar. Lamar'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 Agentb:1,2 Agentc:1,2 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:1 Agentb:1,2 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lydia can now know that Lamar picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lydia","Gloria","Lamar","Carol"],"index":35353,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970549345,"difficulty":0.0029450655}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffery is thirsty. It is publicly announced that Frederick does not know whether Anthony is thirsty. It is publicly announced that Frederick 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) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentd knows whether (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 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jeffery can now know whether Frederick can know whether Frederick is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frederick","James","Anthony","Jeffery"],"index":16738,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987444878,"difficulty":0.0012555122}
-{"premise":"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'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":"Karen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sean","Ruby","David","Karen"],"index":58622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989908338,"difficulty":0.0010091662}
-{"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. Jeremy's card is shown to Victor. Abigail'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:1,2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Jeremy","Abigail","Nina"],"index":16914,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977900982,"difficulty":0.0022099018}
-{"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 Ruth. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card. It is publicly announced that Ruth 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 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":"Ruth can now know that David can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Ruth"],"index":10061,"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'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) ] [ ! ~(Agentc 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Keith can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","John","Keith"],"index":46005,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992640615,"difficulty":0.0007359385}
-{"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 (~(1|2|3|4)))","n_announcements":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":"Jack can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dianne","Anthony","Jack","John"],"index":47274,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988892674,"difficulty":0.0011107326}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc knows whether 1) ] (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":"Frank can now know that Nicholas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Nellie","Nicholas"],"index":54107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983505011,"difficulty":0.0016494989}
-{"premise":"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 William'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":"Patricia can now know that William can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","William"],"index":51679,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5314003825,"difficulty":1.5314003825}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jere knows whether Michael's forehead is muddy. It is publicly announced that Jere 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 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 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) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patrick can now know whether Jere can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Patrick","Jere"],"index":7764,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994658828,"difficulty":0.0005341172}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph does not know whether Ray is thirsty. It is publicly announced that Joseph 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 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) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Joseph can now know whether Ray can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ray","Joseph"],"index":13443,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9917776585,"difficulty":1.9917776585}
-{"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 (~(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":"Susan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Lawrence","Deanna","Arnold"],"index":55260,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984462857,"difficulty":0.0015537143}
-{"premise":"There are four persons. Everyone is visible 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 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":"Rose can now know that Karen can know that Isabelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Isabelle","James","Karen","Rose"],"index":62328,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9896060228,"difficulty":0.0103939772}
-{"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 or not everyone is thirsty.","smcdel_problem":"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 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":"Nancy can now know that Erasmo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Erasmo","Cindy","Richard"],"index":52299,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8752478361,"difficulty":0.1247521639}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fiona's card is shown to Joyce. Marcus's card is shown to Joyce. Chester's card is shown to Fiona. Marcus'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:3,4 Agentb:2 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:3,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Chester can now know whether Joyce can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Chester","Fiona","Marcus"],"index":16890,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994035959,"difficulty":0.0005964041}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maureen does not know 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: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 (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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Maureen can now know that Joseph can know whether Maureen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Eddie","Maureen","Joseph"],"index":40406,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.949339509,"difficulty":0.050660491}
-{"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 Samuel. Vanesa's card is shown to Inez. Inez's card is shown to Inez. 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:1,3 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 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Vanesa can now know whether Samuel can know that Inez picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vanesa","Samuel","Inez"],"index":8329,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9166252613,"difficulty":1.9166252613}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! 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) ] [ ! 3 ] 0","hypothesis":"Judith can now know whether Mary can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judith","Connie","Mary"],"index":28264,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993259907,"difficulty":0.0006740093}
-{"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 Josephine is thirsty.","smcdel_problem":"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 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":"Benjamin can now know that Deborah can know whether Josephine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Benjamin","Josephine","Earl"],"index":58828,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967603087,"difficulty":0.0032396913}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Willie can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alfred","Willie","Elsie","Rachel"],"index":10933,"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. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Charles's card is shown to Amy. Charles's card is shown to Charles. Amy's card is shown to Peter. Charles's card is shown to Peter. Peter's card is shown to Peter. 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) ] (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Peter can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Charles","Peter"],"index":52267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989997745,"difficulty":0.0010002255}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lavette's card is shown to Lavette. Lavette's card is shown to William. 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 William does not know whether William 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) ] Agenta knows that (Agentb knows that (1|2|3))","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":"Lavette can now know that William can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lavette","William","Becky"],"index":3018,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994422793,"difficulty":0.0005577207}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harry knows whether Harry is thirsty. It is publicly announced that Harry 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) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Nicholas can now know that Harry can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicholas","Jessica","Harry","Herbert"],"index":20678,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989745617,"difficulty":0.0010254383}
-{"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 Kevin. Antonio's card is shown to Kevin. David'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:2,3 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:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kevin","David","Antonio"],"index":24387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monroe knows whether or not nobody is thirsty. It is publicly announced that Keri 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 (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|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Darin can now know that Keri can know that Keri is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darin","Keri","Monroe"],"index":50070,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7082747221,"difficulty":1.7082747221}
-{"premise":"There are three persons. Everyone is visible 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 (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)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Raul can now know that Maureen can know that Raul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maureen","Raul","Betty"],"index":19518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9939723611,"difficulty":0.0060276389}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyrone's card is shown to Tyrone. Tyrone's card is shown to Ada. Ada'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:1 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:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tyrone can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tyrone","Ada","Michael"],"index":12926,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981422424,"difficulty":0.0018577576}
-{"premise":"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 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 (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":"Maribel can now know whether James can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maribel","Robert","Keith","James"],"index":5360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992020726,"difficulty":0.0007979274}
-{"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 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":"Howard can now know whether Danny can know that Mildred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mildred","Danny","Howard"],"index":19432,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9953715205,"difficulty":0.0046284795}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita is thirsty. It is publicly announced that Diane 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 (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 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Anita can now know that Diane can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shasta","Diane","Anita"],"index":55916,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8408268094,"difficulty":0.1591731906}
-{"premise":"There are four persons. Everyone is visible 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))) ] 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) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"David can now know whether Timothy can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","John","Moses","Timothy"],"index":51556,"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 Duane knows whether someone is thirsty. It is publicly announced that Thomas 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) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (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 1) ] 0","hypothesis":"Malissa can now know whether Malissa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Duane","Thomas","Malissa"],"index":28091,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.826126039,"difficulty":0.173873961}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida knows whether 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 Jeffery'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)) ] Agentc knows whether (Agentb 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ida can now know whether Patricia can know that Jeffery's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Patricia","Ida","Ronald"],"index":20651,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9455251098,"difficulty":0.0544748902}
-{"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 Donald is thirsty. It is publicly announced that John 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 1) ] [ ! ~(Agentc 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Donald can now know that William can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","William","John"],"index":41214,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999050796,"difficulty":0.000949204}
-{"premise":"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 Jose's forehead is muddy. It is publicly announced that Melissa knows whether Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Donna can now know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Donna","Jose","Melissa"],"index":29491,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992498755,"difficulty":0.0007501245}
-{"premise":"There are 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":"Mark can now know that Johnetta can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Johnetta","Erik","Mark"],"index":43066,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988675117,"difficulty":0.0011324883}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brain does not know whether Magdalena is 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&2&3&4))","n_announcements":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":"Magdalena can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Magdalena","Barbara","Brain","Justin"],"index":30355,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954953194,"difficulty":0.0045046806}
-{"premise":"There are three persons. Everyone is visible 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 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&2&3))","n_announcements":1,"pbcheck":"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":"Richard can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Marvel","Marietta"],"index":35457,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989958405,"difficulty":0.0010041595}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ricardo's card is shown to Walter. Walter's card is shown to Ricardo. It is publicly announced that someone picked a red card. It is publicly announced that Ricardo does not know whether Ricardo picked a red card. It is publicly announced that Ricardo does not know whether Ricardo 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 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":"Ricardo can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","Ricardo"],"index":12331,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988293052,"difficulty":0.0011706948}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Violette does not know whether Jennifer is thirsty. It is publicly announced that Violette 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 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":"Violette can now know that Walter can know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Violette","Walter"],"index":58783,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9900001884,"difficulty":0.0099998116}
-{"premise":"There are three 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 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 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":"Travis can now know that Holly can know that Holly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Travis","Holly"],"index":38247,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894984961,"difficulty":0.0105015039}
-{"premise":"There are four persons. Everyone is visible 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 Romona 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 (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)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Romona can now know whether Timothy can know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Romona","Timothy","Thomas","Kathleen"],"index":8033,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993730187,"difficulty":0.0006269813}
-{"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 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) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Maria can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ana","Maria","Christopher","Armando"],"index":5725,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990033507,"difficulty":0.0009966493}
-{"premise":"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 Ronnie does not know whether Ronnie's forehead 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 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 3) ] 0","hypothesis":"Charles can now know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Willie","Ronnie"],"index":60065,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963518381,"difficulty":0.0036481619}
-{"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 Elaine is thirsty. It is publicly announced that Christina does not know whether Andrea is thirsty.","smcdel_problem":"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) ] 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Elaine can now know that Christina can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christina","Elaine","Wendy","Andrea"],"index":8453,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993110895,"difficulty":0.0006889105}
-{"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 Sam. Scott's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Alexander 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 whether (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":"Sam can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","Sam","Scott"],"index":67483,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9673376679,"difficulty":0.0326623321}
-{"premise":"There are three persons. Everyone is visible 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 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":"Julie can now know whether Rolando's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","Rolando","Dayna"],"index":43967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993079901,"difficulty":0.0006920099}
-{"premise":"There are three 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 Lena's forehead is muddy. It is publicly announced that Aaron 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 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":"Aaron can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aaron","Glenn","Lena"],"index":16935,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6369109154,"difficulty":1.6369109154}
-{"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. Steven's card is shown to Barbara. Steven's card is shown to Earl. It is publicly announced that someone picked a red card. It is publicly announced that Julie 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 4)","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":"Barbara can now know that Earl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Steven","Barbara","Earl"],"index":12149,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967679977,"difficulty":0.0032320023}
-{"premise":"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 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 (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":"Curtis can now know that Tammy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sybil","Tammy","Curtis"],"index":66080,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994764924,"difficulty":0.0005235076}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether Suzanne's forehead is muddy. It is publicly announced that Ronni 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 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":"Michelle can now know that Ronni can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Suzanne","Michelle","Ronni"],"index":36464,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982158542,"difficulty":0.0017841458}
-{"premise":"There are three persons. Everyone is visible 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 Ahmad's forehead is muddy.","smcdel_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 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":"William can now know whether Ahmad can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Nichole","Ahmad"],"index":57736,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992491603,"difficulty":0.0007508397}
-{"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 Kathy. Michael's card is shown to Michael. Barbara's card is shown to Barbara. 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.","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)) ] (Agentb knows whether (1|2|3|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":"Michael can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathy","Michael","Linda","Barbara"],"index":27146,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994485974,"difficulty":0.0005514026}
-{"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 (~(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":"Randy can now know whether Kevin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danielle","Randy","Kevin","Antoinette"],"index":7925,"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). Shirley's card is shown to Shirley. April's card is shown to Shirley. Emmitt's card is shown to April. Emmitt's card is shown to Missy. Shirley's card is shown to Missy. It is publicly announced that someone picked a red card. It is publicly announced that April does not know whether or not everyone picked a red card. It is publicly announced that April does not know whether or not everyone picked a red card. It is publicly announced that Shirley knows whether Shirley picked a red card. It is publicly announced that April 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 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Emmitt can now know whether April picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Emmitt","Shirley","April","Missy"],"index":20807,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6417216063,"difficulty":0.3582783937}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Bertha. Kimberly's card is shown to Bertha. Bertha's card is shown to Kimberly. Bertha's card is shown to Elizabeth. Monica's card is shown to Elizabeth. Kimberly'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 Bertha 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 whether 2)","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":"Monica can now know whether Monica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bertha","Monica","Kimberly","Elizabeth"],"index":52375,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6304323077,"difficulty":0.3695676923}
-{"premise":"There are three persons. Everyone is visible 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 Eva's forehead is muddy.","smcdel_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 (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":"Gary can now know whether George can know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Eva","Gary"],"index":58671,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993587136,"difficulty":0.0006412864}
-{"premise":"There are two persons. Everyone is visible 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 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":"Jesse 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":["Jesse","Thomas"],"index":11360,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989632368,"difficulty":0.0010367632}
-{"premise":"There are three persons. Everyone is visible 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 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":"Christine can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christine","Jerry","Margaret"],"index":23703,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988897443,"difficulty":0.0011102557}
-{"premise":"There are two 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 Renee. It is publicly announced that someone picked a red card. It is publicly announced that Jason does not know whether Renee picked a red card. It is publicly announced that Jason does not know whether Renee 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 (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 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Renee can now know whether Jason can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jason","Renee"],"index":58095,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5311011076,"difficulty":1.5311011076}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beatrice's card is shown to James. James'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 James picked a red card. It is publicly announced that Stefan does not know whether Stefan 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) ] (Agentb knows that 2)","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":"James can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stefan","James","Beatrice"],"index":33827,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7740748525,"difficulty":1.7740748525}
-{"premise":"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 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) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb 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) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"John can now know whether Janet can know whether Wm's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wm","John","Andres","Janet"],"index":28531,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993077517,"difficulty":0.0006922483}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Francine'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 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":"Samuel can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephanie","Samuel","Francine"],"index":50691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988713861,"difficulty":0.0011286139}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelina'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 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":"Jason can now know that Eleanor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Eleanor","Angelina","Paula"],"index":25637,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982236028,"difficulty":0.0017763972}
-{"premise":"There are four 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 1,2,3,4 LAW Top OBS Agenta: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 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":"Kerri can now know that Joe can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kerri","Wayne","Esther","Joe"],"index":28613,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.951074779,"difficulty":0.048925221}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erlene'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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Erlene can now know that Edna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alan","Erlene","Benjamin","Edna"],"index":28195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979548454,"difficulty":0.0020451546}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luz's card is shown to Luz. Edward's card is shown to Edward. 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) ] 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) ] [ ! (1&2) ] 0","hypothesis":"Luz can now know that Edward can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Luz","Edward"],"index":66493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994341731,"difficulty":0.0005658269}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalee's forehead is muddy.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Rosalee can now know whether Vincent's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vincent","Patty","Rosalee"],"index":22700,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994786382,"difficulty":0.0005213618}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc knows whether 2) ] (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 2) ] 0","hypothesis":"Stephen can now know whether Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daniel","Stephen","Pamela"],"index":41339,"s-l":"forehead_mirror-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 is thirsty. It is publicly announced that Cathy 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) ] 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Larry can now know that Cathy can know that Anthony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Cathy","Nancy","Anthony"],"index":22998,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982458353,"difficulty":0.0017541647}
-{"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 Steven knows whether 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Debra can now know that Raymond can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Raymond","Debra","Jose"],"index":26238,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994691014,"difficulty":0.0005308986}
-{"premise":"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. 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 (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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Laura can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Michael","Jerald"],"index":36236,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994565845,"difficulty":0.0005434155}
-{"premise":"There are two persons. Everyone is visible 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 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) ] 0","hypothesis":"Justin can now know that Nicole can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nicole","Justin"],"index":57991,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989824891,"difficulty":0.0010175109}
-{"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 Dorothea is thirsty.","smcdel_problem":"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 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":"Robert can now know that Nicholas can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Arthur","Dorothea","Robert"],"index":60299,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993489385,"difficulty":0.0006510615}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paige does not know whether Jesus 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)","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":"Jesus can now know that Jesus is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesus","Krissy","Paige"],"index":7398,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9760422707,"difficulty":0.0239577293}
-{"premise":"There are three 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 Johnny 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta 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))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Johnny can now know that Larry can know that Elton is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Johnny","Larry","Elton"],"index":25115,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984415174,"difficulty":0.0015584826}
-{"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 William. Patricia's card is shown to William. Patricia's card is shown to Charles. Matthew's card is shown to Matthew. Charles'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 Matthew knows whether someone picked a red card. It is publicly announced that William picked a red card. It is publicly announced that Charles does not know whether Matthew 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) ] Agenta knows whether (Agentb knows whether (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":"William can now know whether Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Charles","Matthew","Patricia"],"index":58457,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5668174624,"difficulty":1.5668174624}
-{"premise":"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) ] [ ! 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":"Maria can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Maria","William","David"],"index":52874,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987986088,"difficulty":0.0012013912}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille does not know whether Gary 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 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":"Lucille can now know whether Gary can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lucille","Gary"],"index":41086,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993984699,"difficulty":0.0006015301}
-{"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 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":"Carol can now know whether John can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Carol","Silvia","John"],"index":13086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9838482738,"difficulty":0.0161517262}
-{"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 Jason 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":"Rodney can now know that Jason is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jason","Rodney"],"index":41980,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.947794497,"difficulty":0.052205503}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kaitlyn's card is shown to Kaitlyn. Amy's card is shown to Kaitlyn. Daniel's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Daniel picked a red card. It is publicly announced that Kellie does not know whether or not everyone picked a red card. It is publicly announced that Amy picked a red card. It is publicly announced that Kaitlyn does not know whether Kellie 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 (1&2&3&4))","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":"Kellie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kaitlyn","Kellie","Daniel","Amy"],"index":54057,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978755713,"difficulty":0.0021244287}
-{"premise":"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 knows whether or not nobody's forehead is muddy. It is publicly announced that Nicholas 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)) ] (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))) ] [ ! (Agentd knows whether (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":["Jessica","Margaret","John","Nicholas"],"index":58427,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999494195,"difficulty":0.000505805}
-{"premise":"There are three 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 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Joe can now know whether Elisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Elisa","Joe"],"index":45441,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.987742424,"difficulty":0.012257576}
-{"premise":"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 (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":"Willie can now know that Brenda can know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Willie","Debra","Brenda"],"index":52527,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947321415,"difficulty":0.0052678585}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genevieve knows whether or not nobody's forehead is muddy. It is publicly announced that Tony's forehead is muddy. It is publicly announced that Cheri does not know whether or not everyone's forehead is muddy. It is publicly announced that Cheri'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 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))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Cheri can now know that Tony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cheri","Genevieve","Tony","Richard"],"index":16531,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8236911297,"difficulty":0.1763088703}
-{"premise":"There are two persons. Everyone is visible 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 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":"Ramona can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ramona","Gary"],"index":59617,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988152981,"difficulty":0.0011847019}
-{"premise":"There are four persons. Everyone is visible 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 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":"Jason can now know that Michael can know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Alexis","Timothy","Michael"],"index":45626,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9904948473,"difficulty":0.0095051527}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charissa's card is shown to Charissa. Marissa's card is shown to Charissa. Charissa's card is shown to Marissa. Charissa'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:1,2 Agentb:1 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:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charissa","Marissa","Mildred","Ivan"],"index":26997,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993541837,"difficulty":0.0006458163}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 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":"Robbie can now know whether Terry can know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Pamela","Robbie","April"],"index":49117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9879505634,"difficulty":0.0120494366}
-{"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 Jessica. Carolyn's card is shown to Daniel. Carolyn's card is shown to Harry. Daniel'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 Carolyn does not know whether Jessica picked a red card. It is publicly announced that Jessica does not know whether or not everyone picked a red card. It is publicly announced that Carolyn does not know whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] 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 Agentb:2 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jessica can now know whether Daniel can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Carolyn","Daniel","Harry"],"index":22081,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994508624,"difficulty":0.0005491376}
-{"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 Eric. Shawnta's card is shown to Michael. Eric's card is shown to Beulah. Shawnta's card is shown to Beulah. Michael's card is shown to Shawnta. Shawnta's card is shown to Shawnta. It is publicly announced that someone picked a red card. It is publicly announced that Shawnta 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:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta 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:2 Agentb:4 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shawnta can now know whether Eric can know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Michael","Beulah","Shawnta"],"index":43932,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.987868607,"difficulty":0.012131393}
-{"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 Laura is thirsty. It is publicly announced that Laura does not know 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 3) ] [ ! ~(Agentc 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Judith can now know that Laura is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judith","Claudia","Laura","George"],"index":47955,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9943529367,"difficulty":0.0056470633}
-{"premise":"There are three persons. Everyone is visible 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'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 (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":"Alida can now know that Melissa can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alida","Edward","Melissa"],"index":35726,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993763566,"difficulty":0.0006236434}
-{"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 Gary. Mildred's card is shown to Mildred. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether 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 Gary 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 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":"Mildred can now know whether Mildred picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gary","Mildred"],"index":8178,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9551489353,"difficulty":0.0448510647}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Johnny'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 ] [ ! 4 ] [ ! ~(3) ] (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) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 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":["Richard","Esther","Robert","Johnny"],"index":62602,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999373138,"difficulty":0.000626862}
-{"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 Philip. 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 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|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Philip can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Philip","James"],"index":38887,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rona 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rona can now know whether Patricia can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rona","Patricia","Jennie","Jenny"],"index":5333,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8712188005,"difficulty":1.8712188005}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dewey's card is shown to Dewey. Ruth's card is shown to Dewey. Ruth's card is shown to Ruth. Verna's card is shown to Ella. 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 Agentc:3 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know that Verna can know whether Dewey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dewey","Ruth","Verna","Ella"],"index":61589,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8869317174,"difficulty":0.1130682826}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jerry can now know that George can know whether Jerry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jerry","George"],"index":50525,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7571238279,"difficulty":0.2428761721}
-{"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 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 (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":"Elsa can now know whether Brenda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brenda","Larry","Elsa"],"index":3520,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992850423,"difficulty":0.0007149577}
-{"premise":"There are four persons. Everyone is visible 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 Bryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Bryan can now know whether Edie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Victoria","Bryan","Edie"],"index":63892,"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. It is publicly announced that someone 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) ] [ ! 2 ] Agentd 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) ] [ ! 2 ] 0","hypothesis":"Lloyd can now know that George can know that George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brent","George","Mathew","Lloyd"],"index":49872,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.65031147,"difficulty":0.34968853}
-{"premise":"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 does not know 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) ] [ ! ~(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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know whether Elizabeth can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Thomas","Elizabeth"],"index":51479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9749346972,"difficulty":0.0250653028}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leticia does not know whether Leticia's forehead is muddy. It is publicly announced that Leticia does not know whether Leticia'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":"Jennifer can now know that Leticia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jennifer","Leticia"],"index":47584,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990562797,"difficulty":0.0009437203}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary 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) ] [ ! ~(Agentc knows whether 2) ] 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jessie can now know that Melvin can know that Jessie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melvin","Jessie","Gary"],"index":30670,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936967492,"difficulty":0.0063032508}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Kenneth can now know that Elsie can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Robert","Elsie"],"index":1958,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978346229,"difficulty":0.0021653771}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene knows whether Angelina 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 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":"Angelina can now know whether Irene can know that Irene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angelina","Irene"],"index":39142,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8384398818,"difficulty":0.1615601182}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Landon is 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 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":"Russell can now know that Landon can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Russell","Landon","Weston"],"index":5438,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990129471,"difficulty":0.0009870529}
-{"premise":"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 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) ] [ ! (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: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":"Carol can now know that Pauline can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Carol","Pauline","Lauretta"],"index":3600,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990109205,"difficulty":0.0009890795}
-{"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. Benjamin's card is shown to Nathan. Betty's card is shown to Betty. Benjamin's card is shown to Betty. Nathan's card is shown to Benjamin. 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 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:1,3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nathan can now know whether Benjamin can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nathan","Betty","Benjamin"],"index":44127,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993956089,"difficulty":0.0006043911}
-{"premise":"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 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 (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":"Mildred can now know that Tom can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gladys","Mildred","Tom","Robert"],"index":64717,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993770719,"difficulty":0.0006229281}
-{"premise":"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 everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","John","Joseph","Deborah"],"index":27856,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753981829,"difficulty":0.0246018171}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alonzo does not know whether Ronald is thirsty. It is publicly announced that Ronald 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Alonzo can now know that Anne can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aida","Alonzo","Anne","Ronald"],"index":64148,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990118742,"difficulty":0.0009881258}
-{"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 Betty 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] Agenta 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Barbara can now know whether Betty can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Brian","Betty","Robert"],"index":20748,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992639422,"difficulty":0.0007360578}
-{"premise":"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 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":"Mark can now know that Betty can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Betty","Robert","David"],"index":66379,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989523888,"difficulty":0.0010476112}
-{"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 Michael is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty. It is publicly announced that Luis does not know whether or not everyone 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) ] [ ! (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)) ] Agentc knows whether (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 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Luis can now know whether Paul can know whether Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pat","Paul","Luis","Michael"],"index":33384,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989427924,"difficulty":0.0010572076}
-{"premise":"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 Ila's forehead 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)","n_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":"David can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ila","David"],"index":4354,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824038744,"difficulty":0.0175961256}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maribeth 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) ] 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":"Maribeth can now know that Gloria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Maribeth","Gloria"],"index":47036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998839438,"difficulty":0.001160562}
-{"premise":"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 does not know whether Frances's forehead is muddy. It is publicly announced that Frances'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) ] 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Jesse can now know whether George can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","George","Blanche","Jesse"],"index":54140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9763433337,"difficulty":0.0236566663}
-{"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. John's card is shown to Thelma. Kenneth's card is shown to Kenneth. Thelma's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether Thelma 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 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":"John can now know whether Thelma can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","Kenneth","John"],"index":59081,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9251947999,"difficulty":0.0748052001}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brett 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 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) ] [ ! ~(2) ] 0","hypothesis":"Brett can now know whether Daniel can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Brett","Frederic"],"index":30200,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994925261,"difficulty":0.0005074739}
-{"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 Orville. John's card is shown to Joseph. Joseph's card is shown to Michael. Michael's card is shown to Michael. Joseph'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:4 Agentc:2,3 Agentd: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 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Orville can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Orville","Joseph","Michael","John"],"index":9120,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982415438,"difficulty":0.0017584562}
-{"premise":"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 Karen'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) ] 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) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Johnathan can now know that Juan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Juan","Johnathan"],"index":28369,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919223785,"difficulty":0.0080776215}
-{"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 Troy. Wanda's card is shown to Wanda. Troy's card is shown to Eldridge. Troy's card is shown to Mei. 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 whether (Agentb knows that 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":"Troy can now know whether Wanda can know that Eldridge picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Troy","Wanda","Eldridge","Mei"],"index":39546,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8297435641,"difficulty":0.1702564359}
-{"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 Ilona. Ilona's card is shown to Yvonne. Yvonne's card is shown to James. Philip's card is shown to James. James's card is shown to Philip. 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) ] Agentd knows whether (Agentb knows that 3)","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":"Philip can now know whether Yvonne can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ilona","Yvonne","James","Philip"],"index":39201,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9406256676,"difficulty":0.0593743324}
-{"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 Diana. Diana's card is shown to Teresa. Teresa's card is shown to Teresa. Diana's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Diana knows whether Teresa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 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:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that Diana can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Teresa","Richard","Mavis"],"index":51489,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989056587,"difficulty":0.0010943413}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ashton 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 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&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ashton can now know that Guy can know that Guy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Guy","Jason","Ashton"],"index":2561,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.96587044,"difficulty":0.03412956}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"George can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Debbie","Marcella","Chris"],"index":63000,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989074469,"difficulty":0.0010925531}
-{"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 Lawrence. Connie's card is shown to Connie. Franklin's card is shown to Yvonne. Lawrence'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:3 Agentc:1,2 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:4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Connie can now know whether Lawrence can know that Yvonne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Franklin","Lawrence","Connie","Yvonne"],"index":56547,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9038661122,"difficulty":0.0961338878}
-{"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. Augusta's card is shown to Nancy. Nancy's card is shown to Kelly. Nancy's card is shown to Augusta. Kelly's card is shown to Augusta. It is publicly announced that someone picked a red card. It is publicly announced that Nancy does not know whether Kelly picked a red card. It is publicly announced that Kelly knows whether or not everyone picked a red card. It is publicly announced that Augusta 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 (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":"Kelly can now know that Augusta can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Kelly","Augusta"],"index":37273,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8961539865,"difficulty":0.1038460135}
-{"premise":"There are four persons. Everyone is visible 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Chad can know whether Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judy","Henry","Chad","Christopher"],"index":17786,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992294312,"difficulty":0.0007705688}
-{"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 Keiko is thirsty. It is publicly announced that Keiko does not know whether Tracey is thirsty. It is publicly announced that Erica knows whether Erica is thirsty.","smcdel_problem":"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 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":"Julie can now know whether Tracey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keiko","Julie","Erica","Tracey"],"index":59965,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973518848,"difficulty":0.0026481152}
-{"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 Carole. James's card is shown to Carole. James's card is shown to Jeffrey. Carole'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 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 whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carole","Jeffrey","James"],"index":28944,"s-l":"explicit-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 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 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":"Steve can now know whether Tawnya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steve","Marlene","Tawnya","Clair"],"index":43206,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932141304,"difficulty":0.0067858696}
-{"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 Emily. Edith's card is shown to Edith. Emily's card is shown to Tina. William's card is shown to Tina. Emily'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:2 Agentc:1,4 Agentd:1 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 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edith can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Emily","Edith","Tina","William"],"index":5702,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973237514,"difficulty":0.0026762486}
-{"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 Walter does not know whether Carolyn is 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 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 1) ] 0","hypothesis":"Walter can now know whether Walter is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carolyn","Walter","Kathleen","Lee"],"index":42705,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973254204,"difficulty":0.0026745796}
-{"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 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 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Cynthia can now know that John can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cynthia","John","Robert"],"index":45252,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9746033549,"difficulty":0.0253966451}
-{"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 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) ] (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":"David can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Anthony","Joseph","David"],"index":41517,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990020394,"difficulty":0.0009979606}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monica does not know whether or not everyone is thirsty. It is publicly announced that Richard does not know whether Mary 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 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 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":"Richard can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Monica","Mary","Richard"],"index":61001,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997392416,"difficulty":0.002607584}
-{"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 Richard. Richard's card is shown to Amy. Manuel's card is shown to Marie. Amy'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:2 Agentb:1 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 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Manuel","Amy","Marie"],"index":57538,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9969393015,"difficulty":0.0030606985}
-{"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 (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":"William can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Alec","Desmond"],"index":21749,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994192123,"difficulty":0.0005807877}
-{"premise":"There are two 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. It is publicly announced that Betty 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 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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Edmund can now know that Betty can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edmund","Betty"],"index":29568,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989262223,"difficulty":0.0010737777}
-{"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. Emily's card is shown to Darrell. Matthew's card is shown to Darrell. Matthew's card is shown to Deanna. Darrell's card is shown to Emily. Darrell's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Deanna 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:1 Agentd:1 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:1,3,4 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Emily can now know that Deanna can know that Deanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darrell","Deanna","Emily","Matthew"],"index":3699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8355800509,"difficulty":0.1644199491}
-{"premise":"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 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 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":"Tracy 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","Tracy"],"index":6729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989410043,"difficulty":0.0010589957}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kara's card is shown to Kara. Leslie's card is shown to Kara. Anna's card is shown to Anna. Leslie's card is shown to Daniel. Kara's card is shown to Leslie. Anna's card is shown to Leslie. Leslie's card is shown to Leslie. 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) ] Agentb knows that (Agenta knows whether 4)","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":"Anna can now know that Kara can know whether Leslie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kara","Anna","Daniel","Leslie"],"index":55647,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8260161877,"difficulty":0.1739838123}
-{"premise":"There are four 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. It is publicly announced that Mona 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 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":"April can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marc","Claudia","Mona","April"],"index":29701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995033741,"difficulty":0.0004966259}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilson'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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Wilson can now know that Selma can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Selma","Joseph","Wilson","Charlotte"],"index":6088,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987804294,"difficulty":0.0012195706}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cedric 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Dorothea can now know that Cedric can know that Cedric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothea","Bobby","William","Cedric"],"index":54700,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979198575,"difficulty":0.0020801425}
-{"premise":"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 Robert 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 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":"Robert can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sue","Robert"],"index":24790,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6730127335,"difficulty":1.6730127335}
-{"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 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) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Kelly can now know that Alice can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alice","Kelly","Chase"],"index":36888,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987155199,"difficulty":0.0012844801}
-{"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 Linda. Dollie's card is shown to Linda. Miriam's card is shown to Richard. Dollie'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:2,4 Agentb: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:2,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Miriam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Richard","Miriam","Dollie"],"index":50471,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977706671,"difficulty":0.0022293329}
-{"premise":"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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Kyla can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kyla","Dolly","Barbara","Anne"],"index":34474,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989602566,"difficulty":0.0010397434}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann 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 (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 Ann can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Ann"],"index":19062,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9930917025,"difficulty":0.0069082975}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Oscar's card is shown to Oscar. 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 Leon knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Leon can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Leon","Oscar"],"index":32915,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990487695,"difficulty":0.0009512305}
-{"premise":"There are three persons. Everyone is visible 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 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 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 3) ] 0","hypothesis":"Melissa can now know that Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","John","Melissa"],"index":35999,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963363409,"difficulty":0.0036636591}
-{"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 Alysha is thirsty.","smcdel_problem":"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 (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":"Maurice can now know whether Donna can know whether Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maurice","Donna","Nancy","Alysha"],"index":12359,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956083894,"difficulty":0.0043916106}
-{"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. Margret's card is shown to Margret. Roberto's card is shown to Margret. Margret's card is shown to Roberto. 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 that (Agentb 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":"Donald can now know that Margret can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Margret","Roberto"],"index":31239,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9841992855,"difficulty":0.0158007145}
-{"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 Michael is not 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(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) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] 0","hypothesis":"Keith can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Keith","Nancy","Edward","Michael"],"index":37205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9958964586,"difficulty":0.0041035414}
-{"premise":"There are 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":"Anthony can now know that Wilton can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Anthony","Warren","Wilton"],"index":31757,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989472032,"difficulty":0.0010527968}
-{"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 Mercedes. Mary's card is shown to Mercedes. Mercedes's card is shown to Richard. Mercedes'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:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc 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":"Helen can now know that Richard can know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Mercedes","Richard","Mary"],"index":28417,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.788916111,"difficulty":1.788916111}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! 2 ] Agentc 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) ] [ ! 2 ] 0","hypothesis":"Henry can now know whether Karen can know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Carl","Henry","William"],"index":2154,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994389415,"difficulty":0.0005610585}
-{"premise":"There are three persons. Everyone is visible 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 Charles's forehead is muddy. It is publicly announced that Dorothy's forehead is not muddy. It is publicly announced that Danny 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) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] (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) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Danny can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Charles","Danny"],"index":39394,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9962972999,"difficulty":0.0037027001}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marianna does not know whether Jacob is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Jacob 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)) ] Agentb 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Frances can now know whether Marianna can know whether Marianna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jacob","Frances","Marianna"],"index":8794,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985786676,"difficulty":0.0014213324}
-{"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 Susan 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) ] [ ! (~(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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know that Todd can know whether Susan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Susan","Rachel","Todd"],"index":64977,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9538370967,"difficulty":1.9538370967}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allyson 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 2) ] 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Allyson can now know whether Leon can know whether Leon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sonya","Leon","Allyson"],"index":9022,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985969663,"difficulty":0.0014030337}
-{"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 Leslie. Christy's card is shown to Leslie. Gertrude's card is shown to Leslie. Christy's card is shown to Christy. 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 (~(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":"Christy can now know whether Leslie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leslie","Christy","Gertrude"],"index":19850,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992516637,"difficulty":0.0007483363}
-{"premise":"There are four persons. Everyone is visible 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 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":"Dorthy can now know whether Dawn can know whether Barb's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ophelia","Dorthy","Dawn","Barb"],"index":46680,"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.","smcdel_problem":"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":"Joe can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynda","Peter","Joe"],"index":54290,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9921328425,"difficulty":0.0078671575}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agenta knows whether 3) ] (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 3) ] 0","hypothesis":"Francisca can now know whether Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Francisca","Jeffrey","Tara"],"index":22687,"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's forehead is muddy. It is publicly announced that Amy 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":"Scott can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willa","Scott","Amy","Anastasia"],"index":59509,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994636178,"difficulty":0.0005363822}
-{"premise":"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's forehead is not muddy. It is publicly announced that Erin knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey does not know whether Tracey's forehead 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 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) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tracey can now know that Karen can know that Erin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","Erin","Karen"],"index":25217,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997497499,"difficulty":0.002502501}
-{"premise":"There are three persons. Everyone is visible 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 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 (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":"Birdie can now know that Patrice can know that Birdie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Birdie","Patrice"],"index":62775,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982125759,"difficulty":0.0017874241}
-{"premise":"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 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 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":"Juan can now know whether Shantel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shantel","Monica","Margaret","Juan"],"index":56803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9751944542,"difficulty":0.0248055458}
-{"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 Millard is thirsty. It is publicly announced that Desmond 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 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) ] [ ! ~(3) ] 0","hypothesis":"Nancy can now know whether Millard can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Millard","Nancy","Desmond"],"index":37696,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995005131,"difficulty":0.0004994869}
-{"premise":"There are four persons. Everyone is visible 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":"Irene can now know that Lula can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Lula","Irene","Florence"],"index":26659,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988434315,"difficulty":0.0011565685}
-{"premise":"There are four persons. Everyone is visible 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 Jill 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 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jill can now know whether Carmen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Carmen","Jill","Ronald"],"index":8516,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994196892,"difficulty":0.0005803108}
-{"premise":"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's forehead is muddy. It is publicly announced that Lorenza does not know whether Lorenza's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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) ] (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) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"James can now know that Anita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tom","James","Anita","Lorenza"],"index":27638,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9926615953,"difficulty":0.0073384047}
-{"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 or not nobody is thirsty. It is publicly announced that Helen does not know whether Jimmy is thirsty. It is publicly announced that Jimmy knows whether Helen 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|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":"Helen can now know that Jimmy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jimmy","Helen"],"index":1311,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994367957,"difficulty":0.0005632043}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathleen knows whether someone's forehead is muddy. It is publicly announced that Irene knows whether Myles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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) ] (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)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Melissa can now know that Cathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Myles","Irene","Cathleen"],"index":48586,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981185794,"difficulty":0.0018814206}
-{"premise":"There are three persons. Everyone is visible 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 Clarence's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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":"Clarence can now know that Calvin can know that Calvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clarence","Janice","Calvin"],"index":13089,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979448915,"difficulty":0.0020551085}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sue's card is shown to Jacob. Lois's card is shown to Lois. Jacob's card is shown to Sue. It is publicly announced that someone picked a red card. It is publicly announced that Sue picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 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:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Lois can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jacob","Lois","Sue"],"index":32743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994694591,"difficulty":0.0005305409}
-{"premise":"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 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 (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":"Robert can now know whether Alice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Sara","Robert","Alice"],"index":32942,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9369437099,"difficulty":0.0630562901}
-{"premise":"There are three persons. Everyone is visible 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 Audrey's forehead is muddy.","smcdel_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 (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 3) ] 0","hypothesis":"Rodrick can now know whether Audrey can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Rodrick","Audrey"],"index":14861,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992828965,"difficulty":0.0007171035}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lula'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 (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":"Lula can now know that Sean can know that Lula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lula","Sean","Deborah"],"index":38298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959949255,"difficulty":0.0040050745}
-{"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. Donald's card is shown to Donald. Larry's card is shown to Donald. Larry'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: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 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Donald","Larry"],"index":53280,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990020394,"difficulty":0.0009979606}
-{"premise":"There are four persons. Everyone is visible 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 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":"Christina can now know whether Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jane","Maria","Edith","Christina"],"index":67635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999417901,"difficulty":0.000582099}
-{"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 Tawana. Shelley's card is shown to Thelma. Shelley's card is shown to Shelley. Tawana's card is shown to Melissa. Thelma's card is shown to Melissa. It is publicly announced that someone picked a red card. It is publicly announced that Shelley 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 whether (Agentd knows whether 3)","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":"Tawana can now know whether Melissa can know whether Shelley picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tawana","Thelma","Shelley","Melissa"],"index":66632,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9971362352,"difficulty":0.0028637648}
-{"premise":"There are three persons. Everyone is visible 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 Eric's forehead is muddy.","smcdel_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&2&3))","n_announcements":1,"pbcheck":"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":"Eric can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Eric","Tony"],"index":22790,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989873767,"difficulty":0.0010126233}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alma does not know whether Byron is thirsty. It is publicly announced that Mark does not know whether Alma is thirsty. It is publicly announced that Mark does not know whether Byron 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 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 1) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Alma can now know that Byron can know whether Byron is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Byron","Alma","Mark"],"index":35837,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9838770032,"difficulty":0.0161229968}
-{"premise":"There are four persons. Everyone is visible 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":"Shawn can now know whether Sharon can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Monica","Shawn","Kim"],"index":315,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993671775,"difficulty":0.0006328225}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerome does not know whether Leon is 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 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":"Luis can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leon","Luis","Jerome","Michael"],"index":33239,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998759985,"difficulty":0.001240015}
-{"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 or not everyone is thirsty. It is publicly announced that Sheila does not know whether Leon 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 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 (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 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 (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Sheila can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leon","Donna","Sheila"],"index":66417,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990807772,"difficulty":0.0009192228}
-{"premise":"There are two persons. Everyone is visible 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 Ryan'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 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":"Ryan can now know whether Philip can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Philip","Ryan"],"index":47463,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993529916,"difficulty":0.0006470084}
-{"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 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":"Deborah can now know that Peter can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jon","Deborah","Peter"],"index":17247,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948769212,"difficulty":0.0051230788}
-{"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. Regina's card is shown to Andrew. Andrew's card is shown to Melanie. It is publicly announced that someone picked a red card. It is publicly announced that Andrew knows whether someone picked a red card. It is publicly announced that Andrew 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)) ] Agenta knows whether (Agentb knows that 2)","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":"Andrew can now know whether Regina can know that Regina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Regina","Melanie"],"index":61794,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6897882819,"difficulty":1.6897882819}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan does not know whether James is thirsty. It is publicly announced that Angelia does not know whether James is thirsty. It is publicly announced that Angelia 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)) ] (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) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Robert","James","Angelia"],"index":336,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995191097,"difficulty":0.0004808903}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Twila'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 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|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Helen","Harriett","Twila"],"index":24395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994136095,"difficulty":0.0005863905}
-{"premise":"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 Janice knows whether or not everyone's forehead is muddy. It is publicly announced that Janice 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":"Janice can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Janice"],"index":43843,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995028973,"difficulty":0.0004971027}
-{"premise":"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 Robert's forehead is not muddy. It is publicly announced that Sarah 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) ] [ ! ~(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":"Marie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sarah","Marie","Robert"],"index":59658,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9628264308,"difficulty":0.0371735692}
-{"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) ] [ ! ~(Agenta 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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Lester can now know that John can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lester","Theresa","Lance"],"index":40065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9961435795,"difficulty":0.0038564205}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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":"Rebecca can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Lauren","Rebecca","Matthew"],"index":34638,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994167089,"difficulty":0.0005832911}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rocco knows whether Nelson's forehead is muddy.","smcdel_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|2|3))","n_announcements":1,"pbcheck":"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":"Kerry can now know that Rocco can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rocco","Kerry","Nelson"],"index":39943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999345243,"difficulty":0.000654757}
-{"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 Francis. Lorita's card is shown to Francis. Francis's card is shown to Tonda. Tonda's card is shown to Jerry. Lorita's card is shown to Lorita. 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 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:3,4 Agentb:1 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tonda can now know that Jerry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Tonda","Jerry","Lorita"],"index":11752,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976161718,"difficulty":0.0023838282}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Doug's card is shown to Travis. Travis's card is shown to Ada. William's card is shown to Ada. Travis's card is shown to Doug. Travis'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:1,4 Agentc:1 Agentd: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:3 Agentb:1,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doug can now know that Travis can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Travis","Ada","Doug","William"],"index":40171,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988677502,"difficulty":0.0011322498}
-{"premise":"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 Vicky's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Lynne can now know whether Billy can know whether Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vicky","Billy","Laura","Lynne"],"index":10462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948242903,"difficulty":0.0051757097}
-{"premise":"There are three 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. It is publicly announced that Anita knows whether Mildred's forehead 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 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":"Anthony can now know that Anita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anita","Mildred","Anthony"],"index":45757,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994850159,"difficulty":0.0005149841}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Kimberly knows whether Eleanor's forehead is muddy. It is publicly announced that Kimberly 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&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)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","Mattie","Kimberly","Donald"],"index":11468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987457991,"difficulty":0.0012542009}
-{"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. Mildred's card is shown to Joesph. It is publicly announced that someone picked a red card. It is publicly announced that Mildred does not know whether Joesph 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 (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":"Mildred can now know that Joesph can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mildred","Joesph"],"index":13611,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994412065,"difficulty":0.0005587935}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mercedes knows whether Mercedes's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Angeles can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gloria","Mercedes","Jason","Angeles"],"index":30333,"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 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":"Enoch can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barbara","Jay","Cathy","Enoch"],"index":27287,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993100166,"difficulty":0.0006899834}
-{"premise":"There are three persons. Everyone is visible 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. 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) ] [ ! (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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"David can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Jason","Ryan"],"index":15052,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989318252,"difficulty":0.0010681748}
-{"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 Maria 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Richard can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Edna","Richard","Maria"],"index":19798,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.981259048,"difficulty":0.018740952}
-{"premise":"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 Lindsey's forehead is muddy. It is publicly announced that Lindsey 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)) ] (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 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Greg can now know that Lindsey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathy","Greg","Lindsey"],"index":41858,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7543849349,"difficulty":1.7543849349}
-{"premise":"There are three persons. Everyone is visible 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. 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 Beverly'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 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 (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"David can now know that Carolyn can know that Beverly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Beverly","Carolyn"],"index":234,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9747450352,"difficulty":0.0252549648}
-{"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 James. James's card is shown to Randy. Rhonda's card is shown to Randy. James's card is shown to Rhonda. 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) ] (Agentc 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":"Rhonda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Randy","Rhonda"],"index":36014,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943957329,"difficulty":0.0056042671}
-{"premise":"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 Nelly does not know whether Nelly'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":"Brenda can now know whether Nelly can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nelly","Brenda"],"index":59098,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9767966866,"difficulty":0.0232033134}
-{"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. Bettye's card is shown to Pamela. Lee's card is shown to Valarie. Pamela's card is shown to Lee. Valarie's card is shown to Lee. Bettye's card is shown to Bettye. It is publicly announced that someone picked a red card. It is publicly announced that Bettye does not know whether Pamela picked a red card. It is publicly announced that Lee 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)) ] Agentd knows that (Agenta knows whether 2)","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":"Bettye can now know that Pamela can know whether Valarie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Valarie","Lee","Bettye"],"index":55652,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6908904314,"difficulty":1.6908904314}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Agnes does not know whether Howard is thirsty. It is publicly announced that Dora does not know whether Howard 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 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Dora can now know that Agnes can know whether Dora is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Agnes","Dora","Howard"],"index":58175,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949368238,"difficulty":0.0050631762}
-{"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 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) ] [ ! (Agentb knows whether 2) ] 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) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know that Pat can know whether Joshua is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joshua","Margaret","Pat","Justin"],"index":30350,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8078511953,"difficulty":0.1921488047}
-{"premise":"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 does not know whether Joseph's forehead is muddy. It is publicly announced that Agustin knows whether Agustin's forehead is muddy. It is publicly announced that Agustin knows whether Agustin's forehead 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 (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 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Eileen can now know that Joseph can know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eileen","Joseph","Agustin"],"index":36899,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9293938875,"difficulty":0.0706061125}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Guadalupe's card is shown to Guadalupe. Melinda's card is shown to Guadalupe. Nellie's card is shown to Melinda. Melinda'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 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:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Melinda can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Guadalupe","Melinda","Nellie"],"index":22001,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994139671,"difficulty":0.0005860329}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Jessica can now know whether Gloria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Miriam","Edna","Jessica","Gloria"],"index":24265,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961382747,"difficulty":0.0038617253}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellis 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ellis can now know that Ellis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Jean","Ellis","Justin"],"index":49568,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976127148,"difficulty":0.0023872852}
-{"premise":"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 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 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":"Brenda can now know that James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","William","Brenda"],"index":65570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960653186,"difficulty":0.0039346814}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenny's card is shown to Edgar. Edgar's card is shown to Jenny. Thomas's card is shown to Jenny. Jenny's card is shown to Thomas. Willie'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 Agentb:1,3 Agentc:2,4 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:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jenny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edgar","Jenny","Thomas","Willie"],"index":19174,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988923669,"difficulty":0.0011076331}
-{"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 (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 that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesus","James","Josette"],"index":21359,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9875301123,"difficulty":0.0124698877}
-{"premise":"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'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 (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":"Frances can now know whether Angelica can know whether Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Angelica","Alberto","Frances"],"index":31506,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992799163,"difficulty":0.0007200837}
-{"premise":"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 Homer'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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] Agenta 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) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"George can now know whether Charles can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Homer","Charles"],"index":19924,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99931705,"difficulty":0.00068295}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Tara'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 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Tara can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Amanda","Tara"],"index":50444,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999322772,"difficulty":0.000677228}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Dwight can now know whether Nolan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Nolan","Dwight","Aileen"],"index":11682,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993453622,"difficulty":0.0006546378}
-{"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 Lorna. Lorna's card is shown to Elisa. Elisa's card is shown to Elisa. Tom's card is shown to Elisa. Elisa's card is shown to Tom. Jeri's card is shown to Jeri. It is publicly announced that someone picked a red card. It is publicly announced that Jeri picked a red card. It is publicly announced that Lorna 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) ] (Agentb knows that (~(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":"Elisa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorna","Elisa","Tom","Jeri"],"index":25046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990480542,"difficulty":0.0009519458}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myron knows whether someone is thirsty. It is publicly announced that Danielle does not know whether Myron 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 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)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Myron can now know that Myron is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Myron","Danielle","Ramon"],"index":19144,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9592183232,"difficulty":0.0407816768}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime does not know whether Jaime's forehead is muddy. It is publicly announced that Vicki 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":"Vicki can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jaime","Vicki"],"index":45878,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998906374,"difficulty":0.001093626}
-{"premise":"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 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) ] [ ! (Agentc knows whether 2) ] (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 2) ] 0","hypothesis":"Edith can now know whether Gabriel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edith","Lisa","Pamela","Gabriel"],"index":15867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993752837,"difficulty":0.0006247163}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lowell's card is shown to Pamela. Lowell's card is shown to Sarah. Kevin's card is shown to Lowell. 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) ] Agentb knows that (Agentc knows whether 3)","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":"Pamela can now know that Sarah can know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Pamela","Sarah","Lowell"],"index":67074,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8659090996,"difficulty":0.1340909004}
-{"premise":"There are four 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Joyce can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Joyce","Bernice","Roosevelt"],"index":42066,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909405708,"difficulty":0.0090594292}
-{"premise":"There are two persons. Everyone is visible 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 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)) ] [ ! (1|2) ] 0","hypothesis":"John can now know whether Gregory can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","John"],"index":4339,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99912709,"difficulty":0.00087291}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jenna's card is shown to Matthew. Matthew's card is shown to Jenna. Robert's card is shown to Robert. Matthew's card is shown to Bennett. 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:3 Agentd:1 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:2 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bennett can now know whether Jenna can know that Matthew picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Jenna","Robert","Bennett"],"index":62631,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8954231739,"difficulty":0.1045768261}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julian's card is shown to Holly. Maximina's card is shown to Holly. Julian's card is shown to Julian. Holly's card is shown to Maximina. Julian's card is shown to Maximina. 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 2)","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":"Maximina can now know that Julian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Holly","Julian","Maximina"],"index":46807,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995118022,"difficulty":0.004881978}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veda knows whether someone's forehead is muddy. It is publicly announced that Dorine knows whether or not nobody's forehead is muddy. It is publicly announced that Dorine knows whether Veda's forehead is muddy. It is publicly announced that Kevin 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 (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentc 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) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dorine can now know that Veda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Veda","Kevin","Dorine"],"index":57036,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.999042809,"difficulty":0.000957191}
-{"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 Marion. Joan's card is shown to Gregory. Mildred's card is shown to Gregory. Gregory's card is shown to Joan. Gregory'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:3 Agentb:3,4 Agentc:2 Agentd:2 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:3,4 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marion","Gregory","Joan","Mildred"],"index":57148,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8320430517,"difficulty":0.1679569483}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victorina knows whether Victorina 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))","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":"David can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victorina","David","Irene"],"index":22345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9775329232,"difficulty":0.0224670768}
-{"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.","smcdel_problem":"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":"Tammy can now know whether Tammy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Tammy","Benjamin","Wendy"],"index":44116,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978722334,"difficulty":0.0021277666}
-{"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 Denver. Aurora's card is shown to Denver. Denver's card is shown to Juan. Aurora's card is shown to Juan. Juan's card is shown to Michael. Aurora's card is shown to Michael. Denver's card is shown to Aurora. 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 whether (1&2&3&4))","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":"Juan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denver","Juan","Michael","Aurora"],"index":49235,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931266308,"difficulty":0.0068733692}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alisha 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) ] [ ! (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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Alisha can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alisha","William","Anthony"],"index":24271,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994388223,"difficulty":0.0005611777}
-{"premise":"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'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 Jennifer does not know whether Jennifer'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 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":"Craig can now know that Jennifer can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Craig","Jennifer"],"index":41510,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7008252144,"difficulty":1.7008252144}
-{"premise":"There are four persons. Everyone is visible 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 Raul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Raul can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Raul","Andrea","Elizabeth"],"index":53902,"s-l":"forehead_mirror-0","deberta_pred":0,"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. It is publicly announced that 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 ] (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":"Darrell can now know that Darrell's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicholas","Armando","Darrell","Barry"],"index":14707,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964635968,"difficulty":0.0035364032}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adam 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 (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) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Adam can now know whether Tommy can know whether Tommy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tommy","Adam","Lahoma"],"index":23294,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.985250473,"difficulty":0.014749527}
-{"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 Terry. Christopher's card is shown to Christopher. Beverly's card is shown to Christopher. 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 Philomena picked a red card. It is publicly announced that Terry does not know whether Christopher picked a red card. It is publicly announced that Beverly does not know whether or not everyone picked a red card. It is publicly announced that Christopher does not know whether Philomena 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 whether (1|2|3|4))","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":"Christopher can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Terry","Christopher","Beverly","Philomena"],"index":58246,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994634986,"difficulty":0.0005365014}
-{"premise":"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 3)","n_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":"Randal can now know whether Howard can know whether Randal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Oscar","Howard","Randal"],"index":13780,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9377750754,"difficulty":0.0622249246}
-{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Rudolph 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 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)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Dorothy can now know that Rudolph can know that Rudolph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Rudolph"],"index":40136,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8550742269,"difficulty":1.8550742269}
-{"premise":"There are two persons. Everyone is visible 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 Jennifer knows whether Charles'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) ] Agentb knows whether (Agenta knows that 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 2) ] [ ! (1&2) ] 0","hypothesis":"Charles 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","Charles"],"index":26069,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993535876,"difficulty":0.0006464124}
-{"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 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) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Daniel can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thomas","Linda","Daniel","James"],"index":18676,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996563971,"difficulty":0.003436029}
-{"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 Christina knows whether Christina is thirsty. It is publicly announced that Christina 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentb 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) ] [ ! ~(1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mark can now know whether Christina can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christina","Mark","Gertrude"],"index":40383,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8635549545,"difficulty":0.1364450455}
-{"premise":"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))) ] 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) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Betty 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":["John","Mark","Betty"],"index":2515,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992989302,"difficulty":0.0007010698}
-{"premise":"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 Dana'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 (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) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Paul can now know that Dana can know that Monte's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Monte","Paul","Dana","Joel"],"index":60189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943833351,"difficulty":0.0056166649}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Stephanie. Stephanie's card is shown to Maureen. Maureen's card is shown to Maureen. Joyce's card is shown to Maureen. 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 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:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stephanie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephanie","Maureen","Joyce"],"index":14512,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993203878,"difficulty":0.0006796122}
-{"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. It is publicly announced that Stephanie 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)) ] (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 (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Adam can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Lindy","Stephanie","Adam"],"index":12291,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995234013,"difficulty":0.0004765987}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jocelyn's card is shown to John. John's card is shown to Brain. Jocelyn's card is shown to Brain. It is publicly announced that someone picked a red card. It is publicly announced that John knows whether Jocelyn 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 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Brain","Jocelyn"],"index":45932,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990418553,"difficulty":0.0009581447}
-{"premise":"There are four 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 Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Melissa can now know that Roxann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Carlos","Melissa","Roxann"],"index":5337,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971297383,"difficulty":0.0028702617}
-{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Albert knows whether someone's forehead is muddy. It is publicly announced that Albert knows whether someone'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) ] [ ! (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)","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":"Seth can now know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Albert","Seth","Antonio"],"index":28922,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961990714,"difficulty":0.0038009286}
-{"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 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":"Ernesto can now know that Herbert can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Herbert","Elizabeth","Michael","Ernesto"],"index":5865,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963430762,"difficulty":0.0036569238}
-{"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. Forest's card is shown to Forest. Rose's card is shown to Forest. Anthony's card is shown to Rose. Forest's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Forest picked a black card. It is publicly announced that Anthony knows whether Anthony 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 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":"Forest can now know that Forest picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Forest","Rose"],"index":844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.965988338,"difficulty":0.034011662}
-{"premise":"There are four persons. Everyone is visible 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 Daniel 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) ] (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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Daniel can now know that Sterling's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Terry","Daniel","Sterling"],"index":39609,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9966204166,"difficulty":0.0033795834}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cesar 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 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":"Robert can now know that Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marcelle","Cesar","Larry","Robert"],"index":931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9482272267,"difficulty":0.0517727733}
-{"premise":"There are four persons. Everyone is visible 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 Lester 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 (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) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know whether William can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","William","Robert","Lester"],"index":2818,"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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elise does not know whether Elise's forehead is muddy. It is publicly announced that Elise does not know whether Elise'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 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":"Janet can now know that Elise can know whether Janet's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janet","Elise"],"index":4263,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9687350392,"difficulty":0.0312649608}
-{"premise":"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'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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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 whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maxwell","Peter","Karol","Joe"],"index":5011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9505724311,"difficulty":0.0494275689}
-{"premise":"There are 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 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":"Connie can now know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Connie","Elmer","Janet","Teresa"],"index":44788,"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. 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 Jeffery's forehead is muddy. It is publicly announced that Bobbie 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 (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 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jeffery can now know that Bobbie can know that Bobbie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bobbie","Jeffery","Shirley"],"index":42755,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978741407,"difficulty":0.0021258593}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Barbara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dana","Allison","Christinia","Barbara"],"index":49638,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988468885,"difficulty":0.0011531115}
-{"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 Rose. Fernando's card is shown to Rose. Fernando's card is shown to Sarah. Rose's card is shown to Fernando. Fernando's card is shown to Fernando. It is publicly announced that someone picked a red card. It is publicly announced that Rose does not know whether Rose 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 Fernando 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: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 whether (Agenta 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":"Fernando can now know whether Rose can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Sarah","Fernando"],"index":9960,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992280006,"difficulty":0.0007719994}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Luke 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))","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":"Martha can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Luke","Martha"],"index":53729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9887337685,"difficulty":0.0112662315}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott does not know whether Darla is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Leroy does not know whether Darla 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) ] (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 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Leroy can now know that Darla is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leroy","Scott","Darla"],"index":21489,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9931220412,"difficulty":0.0068779588}
-{"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 not thirsty. It is publicly announced that Michael knows whether Michael is thirsty. It is publicly announced that Michael does not know whether Clyde 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 (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":"Michael can now know that Clyde can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Clyde","Ezekiel"],"index":6675,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995144606,"difficulty":0.0004855394}
-{"premise":"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 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) ] [ ! ~(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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Josh can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Franklin","Daniel","Josh","Donald"],"index":42370,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
-{"premise":"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 knows whether Marie's forehead is muddy. It is publicly announced that Kenneth'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)","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":"Kenneth can now know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marie","Kenneth"],"index":1577,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5677478909,"difficulty":1.5677478909}
-{"premise":"There are three persons. Everyone is visible 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 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":"Gloria can now know whether Gladys can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gloria","Brett","Gladys"],"index":59887,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993386865,"difficulty":0.0006613135}
-{"premise":"There are four persons. Everyone is visible 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 Darla 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) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agenta 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) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Shirley can now know that Darla can know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Tyrone","Darla","Jamie"],"index":6303,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9923531413,"difficulty":0.0076468587}
-{"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 Evelyn. Rowena's card is shown to Rowena. Evelyn's card is shown to Erika. Roman's card is shown to Erika. Rowena's card is shown to Erika. It is publicly announced that someone picked a red card. It is publicly announced that Evelyn does not know whether Rowena 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) ] (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:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Rowena can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Roman","Rowena","Erika"],"index":4728,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99896276,"difficulty":0.00103724}
-{"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 someone is thirsty. It is publicly announced that Keith 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 (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":"Lisa can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Patricia","Keith","Mary"],"index":55880,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99949193,"difficulty":0.00050807}
-{"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 Deloris. Camille's card is shown to Elizabeth. Elizabeth's card is shown to Richard. Camille's card is shown to Richard. Deloris's card is shown to Camille. Elizabeth's card is shown to Camille. 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 that (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:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Elizabeth can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deloris","Elizabeth","Richard","Camille"],"index":10819,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992978573,"difficulty":0.0007021427}
-{"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. John's card is shown to Brian. John's card is shown to John. Brian's card is shown to Kelli. 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 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)) ] (Agentb knows that 1)","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 Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","John","Kelli"],"index":16931,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9301191568,"difficulty":0.0698808432}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Prince's card is shown to Prince. Walter's card is shown to Walter. 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 Prince picked a red card. It is publicly announced that Walter 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) ] 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 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Prince can now know that Michael can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Prince","Walter","Michael","Charles"],"index":20657,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989815354,"difficulty":0.0010184646}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jillian 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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Maurice can now know that Jillian can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cindi","Jillian","Maurice"],"index":26176,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989616871,"difficulty":0.0010383129}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Robbi's forehead is not muddy. It is publicly announced that Michiko knows whether Paul'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 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) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michiko","Terry","Paul","Robbi"],"index":10749,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9821433425,"difficulty":0.0178566575}
-{"premise":"There are three persons. Everyone is visible 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 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 3)","n_announcements":1,"pbcheck":"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 Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emma","Robert","Joe"],"index":46386,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994497895,"difficulty":0.0005502105}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Charles can now know that Matthew can know that Gloria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gloria","Matthew","Charles"],"index":64908,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942318797,"difficulty":0.0057681203}
-{"premise":"There are two persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Jean can now know whether Leona can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jean","Leona"],"index":43973,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994089603,"difficulty":0.0005910397}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Stacie does not know whether Stacie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Howard can now know that Roberto can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberto","Michael","Howard","Stacie"],"index":31036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9833956957,"difficulty":0.0166043043}
-{"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 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) ] [ ! ~(Agentc knows whether 2) ] (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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michael can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christine","Bridget","Michael","Irene"],"index":39154,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957677126,"difficulty":0.0042322874}
-{"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 Francis. Brian's card is shown to Francis. Francis's card is shown to Brian. Linda's card is shown to Brian. Paul'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:2,3 Agentb:2,4 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:2,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paul can now know that Francis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Francis","Brian","Linda"],"index":28148,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964026213,"difficulty":0.0035973787}
-{"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 Paula. Eboni's card is shown to Eboni. Roger's card is shown to Eboni. Phillis's card is shown to Eboni. Phillis's card is shown to Roger. Roger's card is shown to Phillis. It is publicly announced that someone picked a red card. It is publicly announced that Roger does not know whether Roger 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 that (Agenta knows whether (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":"Phillis can now know that Paula can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Eboni","Roger","Phillis"],"index":9940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994294047,"difficulty":0.0005705953}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Jennifer can now know whether Chester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cynthia","Chester","Jennifer"],"index":54951,"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. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Florida. Marvin's card is shown to Marvin. It is publicly announced that someone picked a red card. It is publicly announced that Florida knows whether someone picked a red card. It is publicly announced that Dan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb 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:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Florida can now know whether Dan can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dan","Florida","Marvin"],"index":20471,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.646851778,"difficulty":0.353148222}
-{"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 Bobby is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Anita does not know whether Agnes is thirsty. It is publicly announced that Kathie 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) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Agnes can now know whether Anita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anita","Kathie","Agnes","Bobby"],"index":58414,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994333148,"difficulty":0.005666852}
-{"premise":"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 (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":"Lawrence can now know whether Edith can know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Robert","Lawrence","Edith"],"index":6226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966509938,"difficulty":0.0033490062}
-{"premise":"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 knows whether or not nobody's forehead is muddy. It is publicly announced that Jaime knows whether or not nobody's forehead is muddy. It is publicly announced that Jaime 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 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))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jaime can now know that Joseph can know whether Jaime's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jaime","Joseph"],"index":32132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7438428402,"difficulty":0.2561571598}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marian's card is shown to Kelly. Kelly's card is shown to Billy. Billy's card is shown to Billy. Marian's card is shown to Billy. Kelly's card is shown to Marian. It is publicly announced that someone picked a red card. It is publicly announced that Marian 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)) ] Agentc 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:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marian can now know that Kelly can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelly","Billy","Marian"],"index":58270,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998929441,"difficulty":0.001070559}
-{"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 George. Michelle's card is shown to Michelle. Michelle's card is shown to Judith. Judith's card is shown to Judith. Judith's card is shown to Claudia. 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.","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))) ] (Agentd knows that (~(1|2|3|4)))","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":"Claudia can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Michelle","Judith","Claudia"],"index":4424,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990465045,"difficulty":0.0009534955}
-{"premise":"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) ] [ ! (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":"Rene can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rene","Rose","Kevin","Joshua"],"index":47183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892514348,"difficulty":0.0107485652}
-{"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. Robert's card is shown to Jennifer. Joel's card is shown to Gloria. Jennifer's card is shown to Robert. Joel's card is shown to Robert. Gloria's card is shown to Joel. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Jennifer picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joel does not know whether Robert 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) ] Agenta knows that (Agentd knows that 3)","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":"Jennifer can now know that Joel can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Gloria","Robert","Joel"],"index":41743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935488105,"difficulty":0.0064511895}
-{"premise":"There are three 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 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know whether Casandra can know whether Lee is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Casandra","Lee","Christopher"],"index":22204,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991420507,"difficulty":0.0008579493}
-{"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 Steven is thirsty. It is publicly announced that Desmond 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 1) ] [ ! ~(Agentd knows whether 1) ] (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) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Christopher can now know whether Desmond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Christopher","Maria","Desmond"],"index":48046,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9962915182,"difficulty":0.0037084818}
-{"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 (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":"Margaret can now know that Judith can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kay","Kimberly","Margaret","Judith"],"index":27039,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9849388599,"difficulty":0.0150611401}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ashley can now know that Lauren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Ashley","Lauren","Rafael"],"index":18854,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982536435,"difficulty":0.0017463565}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilbur does not know whether Wilbur's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Amy can now know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Wilbur","Amy","Vada"],"index":700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972923398,"difficulty":0.0027076602}
-{"premise":"There are two persons. Everyone is visible 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 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":"Tamra can now know that Elizabeth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elizabeth","Tamra"],"index":18749,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989652634,"difficulty":0.0010347366}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cesar does not know whether Cesar'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) ] [ ! ~(Agentb knows whether 2) ] [ ! (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 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Cesar","Daniel"],"index":62969,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983073473,"difficulty":0.0016926527}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Stanley's forehead is muddy. It is publicly announced that Stanley's forehead is muddy.","smcdel_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 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) ] [ ! 2 ] [ ! 2 ] 0","hypothesis":"Christopher can now know whether Eldon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eldon","Stanley","Christopher"],"index":3750,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994651675,"difficulty":0.0005348325}
-{"premise":"There are four persons. Everyone is visible 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 Lino's forehead is muddy. It is publicly announced that Lino knows whether Lino's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Emily can now know whether Otis can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Otis","Lino","Emily","Lewis"],"index":23639,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993603826,"difficulty":0.0006396174}
-{"premise":"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 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 (~(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":"Carol can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Travis","Flora"],"index":26552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994402528,"difficulty":0.0005597472}
-{"premise":"There are four persons. Everyone is visible 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 knows whether Krista's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Roy can now know that Caroline can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Krista","Nellie","Caroline","Roy"],"index":29420,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988971949,"difficulty":0.0011028051}
-{"premise":"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 Steven does not know whether Steven's forehead 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 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 1) ] 0","hypothesis":"Steven can now know that Dannette can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Jason","Dannette"],"index":51768,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999382019,"difficulty":0.000617981}
-{"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 Susana 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 whether (Agentb knows whether 1)","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":"Susana can now know whether Shirley can know whether Susana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susana","Shirley"],"index":21969,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989529848,"difficulty":0.0010470152}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latasha knows whether someone's forehead is muddy. It is publicly announced that Lawrence knows whether or not nobody's forehead is muddy. It is publicly announced that Lawrence knows whether Latasha'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: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 whether (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)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lawrence can now know whether Latasha can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Latasha","Christopher","Lawrence"],"index":50562,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992913008,"difficulty":0.0007086992}
-{"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 Theresa is thirsty. It is publicly announced that Nancy 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 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) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"William can now know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wilbert","Theresa","Nancy","William"],"index":19372,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8861814737,"difficulty":0.1138185263}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Len 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)","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":"Len can now know whether Len's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Len","Robin","Sheridan"],"index":67504,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9892116785,"difficulty":0.0107883215}
-{"premise":"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'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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Virginia can now know that William can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Sharon","Virginia","William"],"index":49397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998978138,"difficulty":0.001021862}
-{"premise":"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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Irma can now know that Annie can know whether Irma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annie","Irma"],"index":42923,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8835327625,"difficulty":1.8835327625}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne 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 (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":"April can now know that Wayne can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","April","Thomas","Stacy"],"index":42295,"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 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) ] [ ! 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) ] [ ! 4 ] 0","hypothesis":"Derrick can now know that Keith can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Howard","Michael","Keith","Derrick"],"index":43816,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995200634,"difficulty":0.0004799366}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathy's card is shown to Tad. Billy'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:4 Agentb:1 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:4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know that Billy can know whether Billy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Billy","Amy","Tad","Cathy"],"index":19086,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.867321074,"difficulty":0.132678926}
-{"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 Jacqueline 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)) ] Agenta 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) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jacqueline can now know that David can know that Jacqueline is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jacqueline","David","Jamison"],"index":57671,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9686008096,"difficulty":0.0313991904}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kam 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 3) ] 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 3) ] 0","hypothesis":"Blanca can now know that Kam can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Kam","Joyce","Blanca"],"index":15066,"s-l":"forehead_mirror-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 is thirsty. It is publicly announced that Brett does not know whether Frances is thirsty. It is publicly announced that Laura 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) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Laura can now know whether Zane can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Zane","Brett","Frances"],"index":9623,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994235039,"difficulty":0.0005764961}
-{"premise":"There are three persons. Everyone is visible 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 Leo knows whether someone's forehead is muddy. It is publicly announced that Leo 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 (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) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Patrick can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leo","Patrick","Joanne"],"index":47847,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999075532,"difficulty":0.000924468}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roxanne's card is shown to Roxanne. Roxanne's card is shown to Mark. 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":"Mark can now know that Roxanne can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Roxanne","Mark"],"index":4793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988837838,"difficulty":0.0011162162}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roxie 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))) ] (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":"Ronald can now know that Toni's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Toni","Ronald","Amanda","Roxie"],"index":9205,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977254272,"difficulty":0.0022745728}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Howard. Brian's card is shown to Howard. Howard's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Howard 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 that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Howard can now know whether Brian can know that Howard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Howard","Brian"],"index":39222,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9524357319,"difficulty":0.0475642681}
-{"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 (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":"Charles can now know whether Christopher can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Christopher","Charles","Richard"],"index":36996,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984878302,"difficulty":0.0015121698}
-{"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 Jerilyn. Michael's card is shown to Michael. Jim's card is shown to Michael. Jerilyn's card is shown to Jim. 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:3 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that 1)","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":"Jim can now know that Jerilyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerilyn","Michael","Jim"],"index":37369,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8900204897,"difficulty":0.1099795103}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Babette does not know whether or not everyone is thirsty. It is publicly announced that Babette does not know whether Sam 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 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":"Babette can now know whether Sam can know that Sam is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Babette","Sam"],"index":24558,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9277381897,"difficulty":1.9277381897}
-{"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. It is publicly announced that Janet does not know whether James is thirsty. It is publicly announced that John 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) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 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) ] [ ! 4 ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"George can now know that George is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","George","James","Janet"],"index":7643,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9781463742,"difficulty":0.0218536258}
-{"premise":"There are two 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 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 (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":"Mack can now know whether Sarah can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mack","Sarah"],"index":33929,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8785643578,"difficulty":1.8785643578}
-{"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 Bill. Bill'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 Clarence knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Bill does not know whether Clarence 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":"Bill can now know that Clarence can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bill","Clarence"],"index":58528,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994621873,"difficulty":0.0005378127}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Connie does not know whether Connie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Denise can now know that Doug can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","Doug","Connie","Denise"],"index":22634,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994385839,"difficulty":0.0005614161}
-{"premise":"There are three persons. Everyone is visible 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 Tanya's forehead is muddy.","smcdel_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 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":"Naomi can now know that Christopher can know that Naomi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Naomi","Tanya","Christopher"],"index":36364,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982206225,"difficulty":0.0017793775}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laticia 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 (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":"Chung can now know whether Carol can know that Carol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chung","Carol","William","Laticia"],"index":67662,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991301894,"difficulty":0.0008698106}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Clyde. Clyde's card is shown to Heather. Heather'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 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:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clyde can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Clyde","Heather","Janet"],"index":14399,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993312359,"difficulty":0.0006687641}
-{"premise":"There are four persons. Everyone is visible 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 Eric's forehead is muddy. It is publicly announced that Eric knows whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Barbara can now know that Eric can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Benjamin","Eric","Barbara","William"],"index":14816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9793242812,"difficulty":0.0206757188}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harry knows whether Harry 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 (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":"Harry can now know whether William can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Harry","William"],"index":59759,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994859695,"difficulty":0.0005140305}
-{"premise":"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. 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 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)) ] (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 2) ] [ ! (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":["Mary","Christopher","May"],"index":35281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980345368,"difficulty":0.0019654632}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanne knows whether or not nobody'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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Sonya can now know that Nicholas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeanne","Sonya","Nicholas"],"index":53998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9909558892,"difficulty":0.0090441108}
-{"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 Cynthia is thirsty. It is publicly announced that Sandra does not know whether Sylvia is thirsty. It is publicly announced that Sandra does not know whether Sylvia is thirsty. It is publicly announced that Tanya 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 (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) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentc knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sylvia can now know whether Tanya can know whether Sylvia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Tanya","Sandra","Sylvia"],"index":39053,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988222718,"difficulty":0.0011777282}
-{"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 Marguerite knows whether Marguerite is thirsty. It is publicly announced that Marguerite 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 that 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":"Rhoda can now know that Marguerite is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Rhoda","Marguerite"],"index":57659,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9905006886,"difficulty":0.0094993114}
-{"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) ] [ ! ~(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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Elisa can now know that Elisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Elisa","Jeannie","Kenneth"],"index":46054,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7051749229,"difficulty":0.2948250771}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Goldie 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) ] [ ! 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) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Goldie","Iva","David"],"index":44687,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995027781,"difficulty":0.0004972219}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burl's card is shown to Daniel. Burl's card is shown to Leticia. Leticia's card is shown to Leticia. It is publicly announced that someone picked a red card. It is publicly announced that Burl knows whether someone picked a red card. It is publicly announced that Burl does not know whether or not everyone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Burl 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)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 2 ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] [ ! 2 ] 0","hypothesis":"Burl can now know whether Leticia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daniel","Burl","Leticia"],"index":7930,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8617038727,"difficulty":0.1382961273}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexander 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 (1|2|3|4))","n_announcements":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":"Alexander can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Judy","Max","Alexander","Joseph"],"index":48932,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995243549,"difficulty":0.0004756451}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raven's card is shown to Michael. Raven's card is shown to Raven. Lana's card is shown to Raven. Michael's card is shown to Jack. Jack's card is shown to Jack. Michael's card is shown to Lana. 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) ] (Agenta knows that 1)","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":"Michael can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Raven","Jack","Lana"],"index":26973,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930816293,"difficulty":0.0069183707}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Jack can now know that James can know that Ervin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jack","James","John","Ervin"],"index":22462,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979315996,"difficulty":0.0020684004}
-{"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 Richard. Susan'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 Richard 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 whether 1)","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":"Richard can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Richard","Susan"],"index":6426,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964841604,"difficulty":0.0035158396}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tiffany 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 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":"Kevin can now know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tiffany","Jeanne","Kevin"],"index":46958,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9950430393,"difficulty":0.0049569607}
-{"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 Leroy. Leroy's card is shown to Martin. Joseph'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:1,3 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Leroy can now know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leroy","Martin","Joseph"],"index":57519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8165162802,"difficulty":0.1834837198}
-{"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 Charles. Charley's card is shown to Charles. Nathaniel's card is shown to Nathaniel. Charles's card is shown to Charley. 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 whether 2)","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":"Nathaniel can now know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Charles","Nathaniel","Charley"],"index":42448,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6762297153,"difficulty":0.3237702847}
-{"premise":"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 (~(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 that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","John","Mary"],"index":34656,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994071722,"difficulty":0.0005928278}
-{"premise":"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 Antonio 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 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":"Lauren can now know that Antonio can know whether Antonio's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lauren","Antonio","Katherine"],"index":16618,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.90926373,"difficulty":0.09073627}
-{"premise":"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 muddy. It is publicly announced that Philip 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)) ] (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) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Todd can now know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Philip","Christina","Todd","Bonnie"],"index":21217,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9613324404,"difficulty":0.0386675596}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maude knows whether Derrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Derrick can now know that Ethel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ethel","Derrick","Kenneth","Maude"],"index":60656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998920083,"difficulty":0.001079917}
-{"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 Sharon. Sharon's card is shown to Herbert. Herbert's card is shown to Herbert. Angela's card is shown to Herbert. Herbert's card is shown to Angela. Angela's card is shown to Angela. It is publicly announced that someone picked a red card. It is publicly announced that Herbert knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2,3 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 Agentb:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Herbert can now know whether Sharon can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Herbert","Angela"],"index":61493,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994589686,"difficulty":0.0005410314}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Marsha can now know that Antonia can know that Frederick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Marsha","Antonia"],"index":30823,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9920984507,"difficulty":0.0079015493}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clarence 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 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":"Clarence can now know that Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","David","James","Clarence"],"index":29641,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984074235,"difficulty":0.0015925765}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rolland 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)) ] 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) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Michael can now know whether Rolland can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lee","Michael","Rolland"],"index":6627,"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 Sharon does not know whether Sharon'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 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 (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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ashley can now know whether Sharon can know that Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Ashley","Christine"],"index":59873,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6574962735,"difficulty":1.6574962735}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether or not everyone is thirsty. It is publicly announced that Stephen does not know whether Vicky 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) ] (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)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Vicky can now know that Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Vicky","Stephen"],"index":65446,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.982635498,"difficulty":0.017364502}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amelia's card is shown to Amelia. John's card is shown to Amelia. Amelia's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Isabel 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 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:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Amelia can now know whether Isabel can know whether Isabel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amelia","Isabel","John"],"index":39571,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9117289186,"difficulty":0.0882710814}
-{"premise":"There are two persons. Everyone is visible 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 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 (1&2)) ] [ ! 1 ] 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)) ] [ ! 1 ] 0","hypothesis":"Benjamin can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Benjamin"],"index":62651,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.5412655473,"difficulty":1.5412655473}
-{"premise":"There are two persons. Everyone is visible 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 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 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":"Keith can now know that Katie can know whether Keith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Katie","Keith"],"index":10200,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993767142,"difficulty":0.0006232858}
-{"premise":"There are two persons. Everyone is visible 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 Gary'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 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":"David can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gary","David"],"index":57914,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9900084734,"difficulty":0.0099915266}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ginger's card is shown to Christopher. Ginger's card is shown to Ginger. Mike's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Mike knows whether Mike picked a red card. It is publicly announced that Ginger 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 whether (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":"Ginger can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Ginger","Mike"],"index":13928,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9230903983,"difficulty":1.9230903983}
-{"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 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 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":"James can now know that Kimberly can know that Kimberly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kimberly","James"],"index":22461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9906861186,"difficulty":0.0093138814}
-{"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 James. James's card is shown to Gerald. Gerald's card is shown to Gerald. Raymond's card is shown to Raymond. It is publicly announced that someone picked a red card. It is publicly announced that Raymond 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:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Gerald","Raymond"],"index":61383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986832738,"difficulty":0.0013167262}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jackie's card is shown to Luke. Jackie's card is shown to Linda. Linda's card is shown to Fabian. Linda's card is shown to Jackie. Jackie's card is shown to Jackie. 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 (~(1|2|3|4)))","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":"Luke can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Luke","Linda","Fabian","Jackie"],"index":46332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989625216,"difficulty":0.0010374784}
-{"premise":"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 Eva's forehead is muddy. It is publicly announced that Kenneth knows whether Marion's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Kenneth can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","Marion","Kenneth","Eva"],"index":38319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972116351,"difficulty":0.0027883649}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Xavier 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) ] [ ! (Agenta knows whether 2) ] 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 2) ] 0","hypothesis":"Xavier can now know that Thomas can know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Xavier","Thomas","Kevin"],"index":58421,"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 Guadalupe 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 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":"Joseph can now know whether Darrin can know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrin","Guadalupe","Joseph","Catherine"],"index":49351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991724491,"difficulty":0.0008275509}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby 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 Ruby knows whether Bobby'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 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":"Bobby can now know whether Ruby can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bobby","Ruby"],"index":64263,"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 is thirsty. It is publicly announced that Gregory 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 (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":"Luis can now know whether Nancy can know that Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Gregory","Luis"],"index":56588,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9817259908,"difficulty":0.0182740092}
-{"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 Michael. Russel's card is shown to Ruby. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Ruby 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 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Ruby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Timothy","Ruby","Russel"],"index":33039,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948815107,"difficulty":0.0051184893}
-{"premise":"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 Christopher does not know whether Christopher's forehead is muddy. It is publicly announced that Clarence 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Clarence","Charles","Leslie"],"index":54849,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925774932,"difficulty":0.0074225068}
-{"premise":"There are 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 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":"Ruthie can now know whether Jon can know whether Ruthie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruthie","Zachary","Kelly","Jon"],"index":40341,"s-l":"forehead_mirror-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's forehead is muddy. It is publicly announced that Milton knows whether 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 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 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|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marvin can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Milton","Marvin","Robert"],"index":10308,"s-l":"forehead-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 Michael knows whether Michael's forehead is muddy. It is publicly announced that Janice 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 whether 2) ] 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 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Patricia can now know that Victor can know that Victor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janice","Michael","Patricia","Victor"],"index":25643,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979840517,"difficulty":0.0020159483}
-{"premise":"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 Joel 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)","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":"Joel can now know whether Joel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joel","Charles"],"index":49980,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8791248798,"difficulty":0.1208751202}
-{"premise":"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 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 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":"Sara can now know that Sara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darren","Sara","Rachel"],"index":32649,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968478084,"difficulty":0.0031521916}
-{"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 thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc: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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Christopher can now know whether Jason can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Regina","Christopher"],"index":64249,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9846137762,"difficulty":0.0153862238}
-{"premise":"There are three persons. Everyone is visible 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 Gregory'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 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) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Betty can now know that Kevin can know that Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Gregory","Kevin"],"index":39535,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9892392159,"difficulty":0.0107607841}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lillian's card is shown to Helen. Rhonda's card is shown to Helen. Helen's card is shown to Helen. Maria's card is shown to Helen. Helen'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:1,2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lillian can now know that Rhonda picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillian","Rhonda","Helen","Maria"],"index":4810,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998296082,"difficulty":0.001703918}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Eva. Eva's card is shown to Joann. Joann's card is shown to Joann. 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)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Joann can now know that Eva can know whether Eva picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eva","Joann"],"index":40617,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8318006396,"difficulty":0.1681993604}
-{"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 Lisa. Emily's card is shown to Emily. Allen's card is shown to Emily. Emily's card is shown to Allen. Allen's card is shown to Allen. It is publicly announced that someone picked a red card. It is publicly announced that Allen picked a red card. It is publicly announced that Allen does not know whether Lisa picked a red card. It is publicly announced that Allen 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) ] (Agenta 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":"Lisa can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Emily","Allen"],"index":1798,"s-l":"explicit-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 Gerald knows whether Gerald'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)) ] 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) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Richard can now know that Gerald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Marilyn","Gerald","Harry"],"index":59774,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993329644,"difficulty":0.0006670356}
-{"premise":"There are four persons. Everyone is visible 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 Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 4) ] 0","hypothesis":"Ashley 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":["Daniel","Michael","Ashley","Phyllis"],"index":24770,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975520968,"difficulty":0.0024479032}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isaiah is thirsty. It is publicly announced that Evelyn knows whether Isaiah 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 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":"Isaiah can now know that Jo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Jo","Isaiah"],"index":22970,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9885649085,"difficulty":0.0114350915}
-{"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 Jonathan is thirsty. It is publicly announced that Cynthia knows whether Cynthia 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 whether 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) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Johnny can now know that Johnny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jonathan","Johnny","Cynthia"],"index":37493,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9880111814,"difficulty":0.0119888186}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Juanita can now know that Vicki can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Vicki","Robert","Juanita"],"index":25079,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993118048,"difficulty":0.0006881952}
-{"premise":"There are two persons. Everyone is visible 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 Edgar'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":"Edgar can now know that Jean can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edgar","Jean"],"index":2582,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991592169,"difficulty":0.0008407831}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Judith. Judith's card is shown to Rosemary. Rosemary's card is shown to Rosemary. It is publicly announced that someone picked a red card. It is publicly announced that Judith picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Rosemary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Judith","Rosemary"],"index":14612,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994731545,"difficulty":0.0005268455}
-{"premise":"There are three persons. Everyone is visible 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 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&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":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cindy","David","Oscar"],"index":26623,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986690283,"difficulty":0.0013309717}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elodia knows whether someone is thirsty. It is publicly announced that Carmelo 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 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":"Elodia can now know that Carmelo can know that Carmelo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Elodia","Carmelo"],"index":50119,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937505126,"difficulty":0.0062494874}
-{"premise":"There are four persons. Everyone is visible 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 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":"Andre can now know whether Jacquelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Jacquelyn","Heriberto","Andre"],"index":9089,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993044138,"difficulty":0.0006955862}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heath does not know whether Bruce is thirsty. It is publicly announced that Erica 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 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 (1&2&3&4)) ] 0","hypothesis":"Erica can now know whether Heath is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Heath","Bruce","Flora","Erica"],"index":62564,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.990431726,"difficulty":0.009568274}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brittney 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) ] 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know whether Brittney can know that Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Brittney","Robert","Thomas"],"index":34944,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9797213078,"difficulty":0.0202786922}
-{"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 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":"Sandy can now know that Sarah can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandy","Nathaniel","Sarah","James"],"index":50152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999392271,"difficulty":0.000607729}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corey 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)) ] 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) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Eugene can now know whether Richard can know whether Corey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Eugene","Corey"],"index":61201,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991565943,"difficulty":0.0008434057}
-{"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 Michael is thirsty. It is publicly announced that Amanda 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 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 (1|2|3)) ] 0","hypothesis":"Peter can now know that Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peter","Amanda","Michael"],"index":62078,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997015357,"difficulty":0.002984643}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dale 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) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Daniel can now know that Kathy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathy","Dale","Daniel"],"index":31323,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998912096,"difficulty":0.001087904}
-{"premise":"There are two persons. Everyone is visible 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 George 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 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":"George can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["George","Vickie"],"index":40459,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9988898635,"difficulty":0.0011101365}
-{"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 Meta. Henrietta's card is shown to Tina. Henrietta's card is shown to Henrietta. It is publicly announced that someone picked a red card. It is publicly announced that Henrietta knows whether someone picked a red card. It is publicly announced that Tina does not know whether Meta 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)) ] [ ! ~(Agentb 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:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Tina can now know that Meta can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Meta","Tina","Henrietta"],"index":49498,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903038144,"difficulty":0.0096961856}
-{"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 nobody is thirsty. It is publicly announced that Ralph does not know whether David 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 (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ralph can now know that Linda can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ralph","David","Linda"],"index":8417,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994885921,"difficulty":0.0005114079}
-{"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 Alton is thirsty. It is publicly announced that Cindy does not know whether Kathryn is thirsty. It is publicly announced that Linda 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 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) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alton can now know that Cindy can know whether Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alton","Linda","Kathryn","Cindy"],"index":59987,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7637126446,"difficulty":0.2362873554}
-{"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 Glen is 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":"Glen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marcia","Charlene","Linda","Glen"],"index":37421,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988561869,"difficulty":0.0011438131}
-{"premise":"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'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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Ronald can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Ronald","Daniel","Shari"],"index":60716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986544847,"difficulty":0.0013455153}
-{"premise":"There are four persons. Everyone is visible 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Connie can now know that Linda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kent","Connie","Linda","Karen"],"index":51169,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992104769,"difficulty":0.0007895231}
-{"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 Edward. Rosa's card is shown to Rosa. Edward's card is shown to Alfonso. 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 (Agenta 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":"Alfonso can now know whether Edward can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Rosa","Alfonso"],"index":34202,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8572249413,"difficulty":1.8572249413}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlene's card is shown to Marlene. Don's card is shown to Marlene. Marlene's card is shown to Don. 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 Marlene 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)) ] (Agenta knows whether (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":"Thomas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Marlene","Don"],"index":49913,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994804263,"difficulty":0.0005195737}
-{"premise":"There are three persons. Everyone is visible 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 Hortencia 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 (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":"John can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Ciera","Hortencia"],"index":56693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988646507,"difficulty":0.0011353493}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheri knows whether or not nobody's forehead is muddy. It is publicly announced that Sheri does not know whether Sheri's forehead is muddy. It is publicly announced that Sheri 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)) ] (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 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sheri can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peter","Sheri","Perry"],"index":52381,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999047339,"difficulty":0.000952661}
-{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Brian 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)","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":"Brian can now know whether Ray can know whether Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","Ray"],"index":5155,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994027615,"difficulty":0.0005972385}
-{"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 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) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jim can now know whether David can know that Shirley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","John","Jim","Shirley"],"index":18180,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9919370413,"difficulty":0.0080629587}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Retta does not know whether Glory 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 (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":"Glory can now know whether Retta can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frank","Retta","Glory"],"index":48434,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9935624599,"difficulty":0.0064375401}
-{"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. Basil's card is shown to Michael. Basil's card is shown to Basil. 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 Basil 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)) ] Agenta knows that (Agentb knows that 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":"Michael can now know that Basil can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Basil"],"index":59651,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.542273581,"difficulty":1.542273581}
-{"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.","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 (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 (1&2&3&4)) ] 0","hypothesis":"Michael can now know that Lloyd can know whether Lloyd is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Shirley","Doris","Lloyd"],"index":56265,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.893401444,"difficulty":0.106598556}
-{"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 Harry. Harry's card is shown to Ginger. Francisco's card is shown to Ginger. Harry's card is shown to Francisco. It is publicly announced that someone picked a red card. It is publicly announced that Harry does not know whether Colleen picked a red card. It is publicly announced that Colleen does not know whether Ginger picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 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:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Colleen can now know whether Ginger can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Colleen","Ginger","Francisco"],"index":35416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9862653613,"difficulty":0.0137346387}
-{"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 Alfred is thirsty. It is publicly announced that Amanda 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 whether 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) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Alfred can now know that David can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Alfred","Trudy","David"],"index":7679,"s-l":"internal-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 Samuel'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 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":"Veronica can now know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Samuel","Veronica","Luther"],"index":30189,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983652234,"difficulty":0.0016347766}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Freda's card is shown to Freda. Freda's card is shown to Thomas. Clarence's card is shown to Thomas. 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 Agentb:1,3 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:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Clarence can now know whether Thomas can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Freda","Thomas","Clarence"],"index":29144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6643324494,"difficulty":0.3356675506}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Neva does not know whether Rosalie is thirsty.","smcdel_problem":"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 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":"Kate can now know whether Rosalie can know whether Neva is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosalie","Neva","Mark","Kate"],"index":44422,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991107583,"difficulty":0.0008892417}
-{"premise":"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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (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":"Helen can now know whether Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marjorie","Linda","Bradley","Helen"],"index":46831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992359877,"difficulty":0.0007640123}
-{"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 Todd. Ricky's card is shown to Kenneth. Catherine's card is shown to Kenneth. Ricky's card is shown to Ricky. Catherine's card is shown to Ricky. Kenneth's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Ricky does not know whether Kenneth picked a red card. It is publicly announced that Ricky does not know whether Kenneth picked a red card. It is publicly announced that Catherine 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 that (Agentc knows whether (~(1|2|3|4)))","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":"Kenneth can now know that Ricky can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Todd","Kenneth","Ricky","Catherine"],"index":55860,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994284511,"difficulty":0.0005715489}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney knows whether Bradley's forehead is muddy. It is publicly announced that Courtney 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 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":"Bradley can now know that Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Bradley","Courtney"],"index":53036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9620041847,"difficulty":0.0379958153}
-{"premise":"There are 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 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":"Michelle can now know that Thomas can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Roma","Kristin","Thomas"],"index":32967,"s-l":"forehead_mirror-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 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 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":"Samuel can now know that William can know that Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chris","Samuel","Ronald","William"],"index":23554,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9909850359,"difficulty":0.0090149641}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kaylee 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 (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":"David can now know whether Catherine can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kaylee","Catherine","Michael","David"],"index":30220,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994390607,"difficulty":0.0005609393}
-{"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 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":"Wanda can now know whether Cecil can know that Cecil's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wanda","Charles","Cecil"],"index":17907,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967409968,"difficulty":0.0032590032}
-{"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 Susan. Alex's card is shown to Susan. Leonard's card is shown to Leonard. Susan's card is shown to Alex. Leonard's card is shown to Alex. 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) ] (Agentb knows whether 1)","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":"Leonard can now know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susan","Leonard","Alex"],"index":42105,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6993653774,"difficulty":1.6993653774}
-{"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 or not everyone is thirsty. It is publicly announced that Barbra knows whether Barbra 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 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Barbra can now know whether Glenn can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glenn","Barbra","Robert"],"index":63798,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999297142,"difficulty":0.000702858}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen knows whether Kathleen is thirsty. It is publicly announced that Deborah 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kathleen can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Tim","Deborah"],"index":38694,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932740927,"difficulty":0.0067259073}
-{"premise":"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 Elbert knows whether Lucy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Elbert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Lucy","Stanley","Elbert"],"index":16539,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976332188,"difficulty":0.0023667812}
-{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that Doyle 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 (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":"Doyle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Doyle","Jose"],"index":4816,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989753962,"difficulty":0.0010246038}
-{"premise":"There are three persons. Everyone is visible 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 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":"Brent can now know that Carl can know that Brent's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Danielle","Brent","Carl"],"index":2726,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948714972,"difficulty":0.0051285028}
-{"premise":"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. It is publicly announced that Paul 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 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 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jonathan can now know whether Hilda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kyle","Jonathan","Hilda","Paul"],"index":59698,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993382096,"difficulty":0.0006617904}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney does not know whether Sidney's forehead is muddy. It is publicly announced that Sidney 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 (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) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Sidney can now know whether George can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sidney","George"],"index":41621,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6819629669,"difficulty":1.6819629669}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kara knows whether or not everyone's forehead is muddy. It is publicly announced that Wanda'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":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","William","Wanda","Kara"],"index":24107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986584187,"difficulty":0.0013415813}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Vada can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joan","Charles","Vada","Christopher"],"index":32522,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990043044,"difficulty":0.0009956956}
-{"premise":"There are three 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 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 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":"Jack can now know that Lisa can know that Jack's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Mary","Jack"],"index":1186,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8052418828,"difficulty":1.8052418828}
-{"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 Paul 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 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":"Paul can now know whether Jennie can know that Paul is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennie","Paul","Erica","Blake"],"index":63561,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9871000051,"difficulty":0.0128999949}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiesha's card is shown to Tiesha. Sharon's card is shown to Tiesha. Tiesha'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 LAW Top OBS Agenta:1,2 Agentb:1,2 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:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Tiesha can now know whether Sharon can know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tiesha","Sharon"],"index":26790,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99704355,"difficulty":0.00295645}
-{"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.","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":"Toya can now know that Maryann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maryann","Shawn","Louis","Toya"],"index":65158,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974550605,"difficulty":0.0025449395}
-{"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 James is thirsty. It is publicly announced that Phyllis does not know whether or not everyone is thirsty. It is publicly announced that Phyllis does not know whether Hugh is thirsty. It is publicly announced that James 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentc 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"James can now know that Gina can know that Gina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hugh","Gina","James","Phyllis"],"index":64221,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9317137003,"difficulty":0.0682862997}
-{"premise":"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 does not know whether Wm's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Chong can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kim","Chong","Joseph","Wm"],"index":26841,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976201653,"difficulty":0.0023798347}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 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":"Donna can now know whether Deborah can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lori","Deborah","Donna","Susan"],"index":26978,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
-{"premise":"There are four persons. Everyone is visible 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 Vernon knows whether Vernon's forehead is muddy. It is publicly announced that Wendi knows whether Vernon's forehead is muddy. It is publicly announced that Vernon knows whether Luther's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"John can now know that Wendi can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wendi","Luther","Vernon","John"],"index":10740,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999388814,"difficulty":0.000611186}
-{"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 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":"Jeanette can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Veronica","Jeanette","Robert","Joseph"],"index":65562,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957142472,"difficulty":0.0042857528}
-{"premise":"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 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":"Rose can now know whether Patricia can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Rose","Robert","Sarah"],"index":14362,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991624355,"difficulty":0.0008375645}
-{"premise":"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 Maria knows whether or not everyone's forehead is muddy. It is publicly announced that Heather knows whether Viola's forehead 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|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":"Heather can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Heather","Viola"],"index":39310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994565845,"difficulty":0.0005434155}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie does not know whether or not everyone's forehead is muddy. It is publicly announced that Keith 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 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":"Melanie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melanie","Ivan","Keith"],"index":3172,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.579816103,"difficulty":1.579816103}
-{"premise":"There are four persons. Everyone is visible 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 Rebecca's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenda 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) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (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) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glenda can now know that Rebecca can know whether Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","George","Glenda","Kelli"],"index":46497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993934631,"difficulty":0.0006065369}
-{"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 Pat is thirsty. It is publicly announced that Charles does not know whether Justin 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 whether (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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Charles can now know whether Justin can know whether Justin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pat","Justin","Charles"],"index":25739,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988225102,"difficulty":0.0011774898}
-{"premise":"There are four persons. Everyone is visible 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 Raquel's forehead is muddy. It is publicly announced that Clay'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 (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 3) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know that Clay can know that Clay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clay","Richard","Raquel","Mary"],"index":53262,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952577949,"difficulty":0.0047422051}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Mario. Mario's card is shown to Theresa. It is publicly announced that someone picked a red card. It is publicly announced that Mario picked a red card. It is publicly announced that Theresa 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) ] [ ! 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) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mario can now know whether Theresa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mario","Theresa"],"index":6735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9492769837,"difficulty":0.0507230163}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gloria's card is shown to Betsy. Betsy'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 knows whether or not nobody picked a red card. It is publicly announced that Betsy knows whether Gloria 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) ] (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))) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gloria can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Betsy","Gloria"],"index":29973,"s-l":"explicit-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 Christian'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 (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":"Christian can now know that Paula can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","John","Paula","Christian"],"index":39120,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986876845,"difficulty":0.0013123155}
-{"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 Sarah is thirsty. It is publicly announced that Melissa 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))) ] Agentd knows that (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&2&3&4) ] [ ! 3 ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melissa can now know that Sarah can know that Melissa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Jana","Sarah","Melissa"],"index":2479,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9944981933,"difficulty":0.0055018067}
-{"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. Stacy'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 Stacy picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 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 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Stacy can now know whether Matthew can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stacy","Matthew"],"index":1527,"s-l":"explicit-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's forehead is muddy. It is publicly announced that Deborah knows whether Buddy's forehead is muddy. It is publicly announced that Annie knows whether 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) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (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) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Deborah can now know whether Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Pamela","Annie","Buddy"],"index":54331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992949963,"difficulty":0.0007050037}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Kyle. Gustavo's card is shown to Kyle. Kyle's card is shown to Gustavo. It is publicly announced that someone picked a red card. It is publicly announced that Kyle knows whether or not everyone picked a red card. It is publicly announced that Gustavo 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) ] [ ! (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:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gustavo can now know that Gustavo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kyle","Gustavo"],"index":56319,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8929852843,"difficulty":0.1070147157}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gregg's card is shown to Regina. John's card is shown to John. Craig's card is shown to Gregg. It is publicly announced that someone picked a red card. It is publicly announced that Craig does not know whether Gregg picked a red card. It is publicly announced that John does not know whether Gregg picked a red card. It is publicly announced that John does not know whether Craig picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] 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":["Regina","John","Craig","Gregg"],"index":45775,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.988806963,"difficulty":0.011193037}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Craig 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 2) ] 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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Craig can now know that Norman can know that Craig is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Craig","Joseph","Norman"],"index":9895,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967519045,"difficulty":0.0032480955}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danette 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 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|2|3|4)) ] 0","hypothesis":"Tyler can now know whether Catherine can know whether Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Catherine","Tina","Tyler","Danette"],"index":396,"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 Amy knows whether or not nobody's forehead is muddy. It is publicly announced that Brian'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 (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":"Amy can now know whether Brian can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brian","Amy"],"index":50790,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993656278,"difficulty":0.0006343722}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lonnie's card is shown to Anthony. Betty's card is shown to Lonnie. Anthony's card is shown to Betty. 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:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","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":"Anthony can now know that Lonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anthony","Lonnie","Betty"],"index":54466,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982661605,"difficulty":0.0017338395}
-{"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 Travis 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 Travis 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) ] [ ! ~(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 (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":"Manuel can now know that John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Manuel","Travis","Chester","John"],"index":40221,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986732006,"difficulty":0.0013267994}
-{"premise":"There are two persons. Everyone is visible 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 knows whether or not nobody's forehead is muddy. It is publicly announced that Arthur 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 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":"Arthur can now know whether Holly can know whether Holly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arthur","Holly"],"index":61381,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994199276,"difficulty":0.0005800724}
-{"premise":"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 Moises 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 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":"Moises can now know that Audrey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Shannon","Moises","Audrey"],"index":39048,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968140721,"difficulty":0.0031859279}
-{"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 James. Justin's card is shown to Andrew. Andrew's card is shown to Harold. Harold's card is shown to Harold. Andrew'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:2 Agentb:4 Agentc:2,3 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:2 Agentb:4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrew can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Andrew","Harold","Justin"],"index":39751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989076853,"difficulty":0.0010923147}
-{"premise":"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 Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Spencer can now know that Albert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Robert","Spencer","Albert"],"index":25569,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972802401,"difficulty":0.0027197599}
-{"premise":"There are three persons. Everyone is visible 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 Gayle's forehead is muddy.","smcdel_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 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":"Jacqueline can now know that Vicki can know that Vicki's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gayle","Jacqueline","Vicki"],"index":56896,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980043769,"difficulty":0.0019956231}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Courtney 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 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":"Nathan can now know whether Courtney is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Courtney","Nathan","Deborah","Julie"],"index":36372,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938182235,"difficulty":0.0061817765}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cristina's card is shown to David. Alana's card is shown to David. David's card is shown to Cristina. David's card is shown to Alana. 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":"Cristina can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Cristina","Alana"],"index":14561,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963155389,"difficulty":0.0036844611}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony 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&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":"Tony can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tony","Renae","Diane"],"index":64520,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972244501,"difficulty":0.0027755499}
-{"premise":"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.","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":"Eddie can now know that Angela can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Eddie","Angela"],"index":67401,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994458556,"difficulty":0.0005541444}
-{"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 Shawn. Shawn's card is shown to Jimmie. Lawrence's card is shown to Jimmie. Jimmie's card is shown to Lawrence. Lawrence's card is shown to Lawrence. It is publicly announced that someone picked a red card. It is publicly announced that Shawn does not know whether or not everyone picked a red card. It is publicly announced that Lawrence 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 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":"Jimmie can now know whether Shawn can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shawn","Leonila","Jimmie","Lawrence"],"index":11535,"s-l":"explicit-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'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 (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":"Christine can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christine","George","John"],"index":4015,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9939517379,"difficulty":0.0060482621}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katerine knows whether someone's forehead is muddy. It is publicly announced that Gerald'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) ] (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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Katerine can now know whether Guillermo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Guillermo","Gerald","Katerine","Robert"],"index":55054,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994024038,"difficulty":0.0005975962}
-{"premise":"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 William'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|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":"William can now know that Ronald can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Ronald"],"index":47173,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990099669,"difficulty":0.0009900331}
-{"premise":"There are four persons. Everyone is visible 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Lenny can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Monica","Lenny","Rebecca","Willis"],"index":32036,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9875026345,"difficulty":0.0124973655}
-{"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 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":"Helga can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Helga"],"index":48630,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918473959,"difficulty":0.0081526041}
-{"premise":"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 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Clark can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","James","Jose","Clark"],"index":27964,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988547564,"difficulty":0.0011452436}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Crystal knows whether Crystal is thirsty. It is publicly announced that Crystal 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 3) ] [ ! ~(Agentc 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jerry can now know that Crystal can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Brian","Crystal","Alanna"],"index":30931,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99949646,"difficulty":0.00050354}
-{"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 Ilda. Ilda's card is shown to Joshua. Joshua's card is shown to Joshua. Ilda's card is shown to Michael. Joshua'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 Agentb:1,2 Agentc:1,2 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:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ilda","Joshua","Floyd","Michael"],"index":39706,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917125702,"difficulty":0.0082874298}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Marta","Patricia"],"index":18041,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986802936,"difficulty":0.0013197064}
-{"premise":"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 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know that Michael can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Michael","Kevin"],"index":21296,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991909862,"difficulty":0.0008090138}
-{"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. Teresa's card is shown to William. Delphine's card is shown to Teresa. Kevin's card is shown to Delphine. Teresa's card is shown to Delphine. 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) ] (Agentc knows whether (1&2&3&4))","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":"Teresa can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Kevin","Teresa","Delphine"],"index":15511,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958491325,"difficulty":0.0041508675}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Timmy. Delores's card is shown to Timmy. Delores's card is shown to Delores. 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 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:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juanita can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Timmy","Abigail","Delores"],"index":66970,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994161129,"difficulty":0.0005838871}
-{"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 Debbie is 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 (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) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Steven can now know that Gerald can know that Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Debra","Gerald","Debbie"],"index":67589,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974671602,"difficulty":0.0025328398}
-{"premise":"There are four 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"Pedro can now know that Jimmy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmy","Dorothy","Pedro","Karla"],"index":12103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989675283,"difficulty":0.0010324717}
-{"premise":"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 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) ] 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Larry can now know whether Fredrick can know that Sara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sara","Larry","Fredrick"],"index":66322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9403616786,"difficulty":0.0596383214}
-{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Carlos 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 (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (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 (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Regina can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Regina","Mark","Gary","Carlos"],"index":37999,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958835244,"difficulty":0.0041164756}
-{"premise":"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 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 (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":"Larry can now know whether Eric can know that Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Joyce","Larry","Eric"],"index":36136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9479919076,"difficulty":0.0520080924}
-{"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 Melissa. Christina's card is shown to Amy. Melissa'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 Christina does not know whether Amy picked a red card. It is publicly announced that Melissa does not know whether Christina 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:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christina can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Amy","Christina"],"index":37351,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963920712,"difficulty":0.0036079288}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latonya 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 3)","n_announcements":1,"pbcheck":"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":"Douglas can now know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Latonya","Sally","Douglas"],"index":64451,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982037544,"difficulty":0.0017962456}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernestina's card is shown to Ernestina. Anthony'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 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ernestina can now know that Daniel can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernestina","Daniel","Anthony"],"index":26906,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948621392,"difficulty":0.0051378608}
-{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Shanae knows whether Shanae's forehead is muddy. It is publicly announced that not everyone'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) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (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) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Bryan can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Shanae","Bryan"],"index":66159,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990291595,"difficulty":0.0009708405}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erik 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":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Erik","James"],"index":66719,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988289475,"difficulty":0.0011710525}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sheryll 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 (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":"Marilyn can now know whether Sheryll can know whether Jean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheryll","Marilyn","Renee","Jean"],"index":49139,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991057515,"difficulty":0.0008942485}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clyde's card is shown to Clyde. Clyde's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Clyde knows whether Clyde picked a red card. It is publicly announced that Clyde knows whether William 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) ] (Agentb knows that 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":"William can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clyde","William"],"index":14826,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.95094347,"difficulty":1.95094347}
-{"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 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 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Paul can now know that Linda can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Brian","Paul","Victoria"],"index":59500,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999293685,"difficulty":0.000706315}
-{"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) ] [ ! 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) ] [ ! 4 ] 0","hypothesis":"James can now know that Michelle can know that Michelle is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Stephen","Marie","James"],"index":40942,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8316512108,"difficulty":0.1683487892}
-{"premise":"There are four persons. Everyone is visible 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 Jimmy's forehead is muddy. It is publicly announced that Sharon knows whether Jimmy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know whether Sandra can know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Jimmy","Sandra","Martha"],"index":47925,"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. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Jerry. Penny's card is shown to Jerry. Jerry's card is shown to Annette. Penny's card is shown to Annette. Jerry's card is shown to Linda. Annette'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:3,4 Agentb:1,4 Agentc:1,2 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:3,4 Agentb:1,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know that Jerry can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Annette","Linda","Penny"],"index":3071,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993718266,"difficulty":0.0006281734}
-{"premise":"There are four persons. Everyone is visible 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 not everyone's forehead is muddy. It is publicly announced that 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) ] [ ! (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":"Alan can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Bonnie","Alan","Patricia"],"index":19153,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993439317,"difficulty":0.0006560683}
-{"premise":"There are four 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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd: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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Leslie can now know whether Steven is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leslie","Helen","Jason","Steven"],"index":11271,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979431033,"difficulty":0.0020568967}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brett does not know whether Mary is thirsty. It is publicly announced that Brett 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)) ] (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) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Dorothy can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dorothy","Mary","Brett"],"index":27141,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994574189,"difficulty":0.0005425811}
-{"premise":"There are four persons. Everyone is visible 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 Stephen'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 (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) ] [ ! (1&2&3&4) ] 0","hypothesis":"Stephen can now know that Christopher can know whether Stephen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Christopher","Amanda","Steven"],"index":62742,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994317889,"difficulty":0.0005682111}
-{"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. Donald's card is shown to Sharon. Sharon's card is shown to Donald. Dorothy'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 LAW Top OBS Agenta:1,3 Agentb: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:1,3 Agentb:1,2,3 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":["Sharon","Dorothy","Donald"],"index":40261,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990001321,"difficulty":0.0009998679}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul knows whether Paul is thirsty. It is publicly announced that Paul 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) ] (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 3) ] [ ! ~(3) ] 0","hypothesis":"Neil can now know that Donna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Neil","Paul"],"index":16885,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953936338,"difficulty":0.0046063662}
-{"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 or not everyone is thirsty.","smcdel_problem":"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":"Alfred can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mildred","Alfred","Sheila","Barbara"],"index":37160,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995260239,"difficulty":0.0004739761}
-{"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. Warren's card is shown to Dorothy. Dorothy's card is shown to Yolanda. Warren's card is shown to Yolanda. Yolanda's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Brian can now know that Warren picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dorothy","Yolanda","Brian","Warren"],"index":40974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9812672138,"difficulty":0.0187327862}
-{"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 Steve. Jessica's card is shown to Steve. Steve's card is shown to Harriet. Harriet's card is shown to Harriet. Jessica's card is shown to Harriet. Steve's card is shown to Jessica. 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 whether (Agentb knows that 2)","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":"Jessica can now know whether Harriet can know that Harriet picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steve","Harriet","Jessica"],"index":33794,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5609778166,"difficulty":0.4390221834}
-{"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 Edward. Edward's card is shown to Michael. William'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 Edward does not know whether Edward 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 (1&2&3&4))","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":"Michael can now know that William can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","William","Michael","Barbara"],"index":17091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988553524,"difficulty":0.0011446476}
-{"premise":"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 knows whether Rosemary's forehead is muddy. It is publicly announced that Ashley 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 (~(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":"Ashley can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosemary","Richard","Ashley"],"index":19277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990377426,"difficulty":0.0009622574}
-{"premise":"There are three persons. Everyone is visible 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":"Angela can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Angela","George","Betty"],"index":30603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989941716,"difficulty":0.0010058284}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! 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) ] [ ! (1&2&3) ] [ ! 1 ] 0","hypothesis":"Bessie can now know whether Francis can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bessie","Cecelia","Francis"],"index":65081,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991101623,"difficulty":0.0008898377}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Madonna'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":"Alva can now know that Madonna can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Madonna","Patricia","Alva"],"index":60313,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99947685,"difficulty":0.00052315}
-{"premise":"There are three persons. Everyone is visible 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 (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":"Steve can now know that George can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Steve","Jeff"],"index":66156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948320389,"difficulty":0.0051679611}
-{"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 Ashley knows whether Zachary 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 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":"Zachary can now know that Ashley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Zachary","Ashley"],"index":21899,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9936675429,"difficulty":0.0063324571}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darla knows whether Talia's forehead is muddy. It is publicly announced that Jimmie does not know whether Jimmie's forehead is muddy. It is publicly announced that Mattie knows whether Talia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] Agentd 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) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jimmie can now know whether Talia can know whether Talia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Talia","Mattie","Darla","Jimmie"],"index":55503,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989959598,"difficulty":0.0010040402}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sterling knows whether Anna's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead is muddy. It is publicly announced that Anna knows whether Sterling'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 (~(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":"Anna can now know that Sterling can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sterling","Anna"],"index":65758,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999088645,"difficulty":0.000911355}
-{"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 (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":"Diane can now know that Kevin can know whether Valentin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kevin","Walter","Diane","Valentin"],"index":11883,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982784986,"difficulty":0.0017215014}
-{"premise":"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 Bryan knows 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) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 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) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kelley can now know that Barbara can know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelley","Barbara","Bryan"],"index":60879,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971541166,"difficulty":0.0028458834}
-{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that 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) ] [ ! ~(3) ] [ ! 2 ] [ ! 2 ] (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) ] [ ! 2 ] [ ! 2 ] 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":["John","Sandra","Lee"],"index":59136,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993915558,"difficulty":0.0006084442}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell 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) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Catherine can now know that Catherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darrell","Catherine","Glenn"],"index":62802,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971830845,"difficulty":0.0028169155}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 1) ] (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":"Daniel can now know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Victoria","Karen"],"index":9949,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998364985,"difficulty":0.001635015}
-{"premise":"There are four persons. Everyone is visible 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 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":"Joel can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Migdalia","Carl","Joel","Jorge"],"index":27685,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989705086,"difficulty":0.0010294914}
-{"premise":"There are two persons. Everyone is visible 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 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":"Phyllis can now know that Charles can know whether Phyllis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charles","Phyllis"],"index":5874,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993746877,"difficulty":0.0006253123}
-{"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 Deborah. James's card is shown to Deborah. Deborah's card is shown to Margaret. James's card is shown to Margaret. Margaret'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 Deborah 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 2)","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":"Deborah can now know whether James can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Margaret","James"],"index":41338,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.998898387,"difficulty":0.001101613}
-{"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. David'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 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Josephine can now know that Josephine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Josephine","David","Patricia"],"index":31310,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9937847853,"difficulty":0.0062152147}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore knows whether or not everyone's forehead is muddy. It is publicly announced that Theodore does not know whether Theodore's forehead 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|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":"Rebecca can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Earnest","Rebecca","Theodore"],"index":64196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990625978,"difficulty":0.0009374022}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ross's card is shown to Arletta. Arletta's card is shown to Ross. Ross's card is shown to Ross. It is publicly announced that someone picked a red card. It is publicly announced that Ross picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Ross can now know that Arletta can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arletta","Ross"],"index":23301,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994539618,"difficulty":0.0005460382}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen 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 (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":"Percy can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Percy","Doris","Helen"],"index":15170,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995102882,"difficulty":0.0004897118}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melisa does not know whether or not everyone is thirsty. It is publicly announced that Melisa does not know whether Louise is thirsty. It is publicly announced that Leighann does not know whether Louise 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)) ] (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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Melisa can now know that Leighann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Leighann","Louise","Melisa"],"index":38787,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9917518497,"difficulty":0.0082481503}
-{"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 (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":"Louis can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Louis","Michelle","Daniel"],"index":27077,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9934656024,"difficulty":0.0065343976}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Etta's card is shown to Etta. Jack's card is shown to Jack. Jack's card is shown to Christopher. Etta'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 Agentb:2 Agentc:2 Agentd:1 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 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Etta","Jack","Christopher","Joseph"],"index":55662,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7712291479,"difficulty":1.7712291479}
-{"premise":"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 Fannie does not know whether Fannie's forehead 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 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 2) ] 0","hypothesis":"James can now know whether Fannie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Fannie","James"],"index":36695,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994356036,"difficulty":0.0005643964}
-{"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 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 2) ] (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 2) ] 0","hypothesis":"Maria can now know whether Jerry is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Thomas","William","Maria"],"index":6927,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971633554,"difficulty":0.0028366446}
-{"premise":"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 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) ] [ ! (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":"Kerry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Joe","Kerry"],"index":61341,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954622388,"difficulty":0.0045377612}
-{"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. Ronald's card is shown to Guadalupe. Michael's card is shown to Guadalupe. Michael's card is shown to Arthur. Guadalupe's card is shown to Ronald. Arthur's card is shown to Michael. Ronald's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Ronald 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) ] Agentb knows whether (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Arthur can now know whether Michael can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Guadalupe","Arthur","Ronald","Michael"],"index":25770,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9914225936,"difficulty":0.0085774064}
-{"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 Chris. Susana's card is shown to Susana. Tony's card is shown to Susana. Tony's card is shown to Tony. It is publicly announced that someone picked a red card. It is publicly announced that Tony does not know whether Susana 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|2|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":"Chris can now know that Tony can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chris","Susana","Tony"],"index":67032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994202852,"difficulty":0.0005797148}
-{"premise":"There are three persons. Everyone is visible 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 muddy.","smcdel_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)","n_announcements":1,"pbcheck":"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 that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Robert","Stephen"],"index":59745,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964048862,"difficulty":0.0035951138}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Olga knows whether Viola's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (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) ] 0","hypothesis":"Viola can now know that Paul can know that Olga's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Viola","Olga","Elsa","Paul"],"index":60182,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972983003,"difficulty":0.0027016997}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice does not know whether Jesse is thirsty. It is publicly announced that Janice 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)) ] 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&2)) ] 0","hypothesis":"Jesse can now know that Janice can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesse","Janice"],"index":57198,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994754195,"difficulty":0.0005245805}
-{"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. It is publicly announced that Joseph does not know whether Angela is thirsty. It is publicly announced that James knows whether James 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)) ] (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":"Joseph can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Angela","James"],"index":41663,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981831908,"difficulty":0.0018168092}
-{"premise":"There are three persons. Everyone is visible 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":"Debbie can now know that Elaine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debbie","Elaine","Rigoberto"],"index":10945,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9931203127,"difficulty":0.0068796873}
-{"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 Robert does not know whether Maria is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Maria does not know whether Carol 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) ] (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) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Carol can now know that Carol is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carol","Maria","Robert"],"index":63473,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9809910059,"difficulty":0.0190089941}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mollie knows whether Mollie is 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) ] (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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Maria can now know whether Vance is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawn","Maria","Mollie","Vance"],"index":62656,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980424643,"difficulty":0.0019575357}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Homer 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":"Homer can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Homer","David","Dorothy"],"index":30132,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989845157,"difficulty":0.0010154843}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sam does not know whether Tammy 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 Sam is thirsty. It is publicly announced that Sam 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":"Janet can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janet","Tammy","Sam"],"index":65833,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994956255,"difficulty":0.0005043745}
-{"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. Herbert's card is shown to Betty. Alex's card is shown to William. Betty's card is shown to Herbert. William's card is shown to Alex. Herbert'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:1,3 Agentb:4 Agentc:1 Agentd:2,3 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:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alex can now know that Herbert can know that Betty picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","William","Herbert","Alex"],"index":7652,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983776808,"difficulty":0.0016223192}
-{"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 Carlos. John's card is shown to Margery. Carlos's card is shown to Margery. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Carlos 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 that (1&2&3&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":"John can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Carlos","Margery","Margaret"],"index":66550,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998570919,"difficulty":0.001429081}
-{"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 Roy knows whether 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) ] [ ! (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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Roy can now know that Roy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roy","Roxanne","Christopher","Lorenzo"],"index":59312,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8058168292,"difficulty":0.1941831708}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvia 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 (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":"Sylvia can now know that Floyd can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Floyd","Barbara","Sylvia"],"index":36452,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992771745,"difficulty":0.0007228255}
-{"premise":"There are four persons. Everyone is visible 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 Tamara'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) ] (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))) ] [ ! ~(4) ] 0","hypothesis":"Michael can now know whether Deanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christy","Deanna","Michael","Tamara"],"index":1857,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994413257,"difficulty":0.0005586743}
-{"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 Carl. Carl's card is shown to Carl. Edith's card is shown to Carl. Frances's card is shown to Edith. 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) ] (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 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bill can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Bill","Carl","Edith"],"index":54618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989988208,"difficulty":0.0010011792}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnnie knows whether someone is thirsty. It is publicly announced that Joseph does not know whether Johnnie is thirsty. It is publicly announced that Joseph is thirsty. It is publicly announced that Lidia 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Joseph can now know that Clarence is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clarence","Joseph","Johnnie","Lidia"],"index":35483,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9940511584,"difficulty":0.0059488416}
-{"premise":"There are four persons. Everyone is visible 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Hubert can now know whether Edwin can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edwin","Hubert","Jan","Arthur"],"index":20230,"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 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) ] [ ! ~(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) ] [ ! ~(3) ] 0","hypothesis":"Ashley can now know that Ashley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grace","James","Ashley","Lance"],"index":58713,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9918149114,"difficulty":0.0081850886}
-{"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. Josephine's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Josephine does not know whether Edith 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 whether (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":"Sandra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Josephine","Edith"],"index":48084,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949765205,"difficulty":0.0050234795}
-{"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. Cherly's card is shown to Patrick. Patrick's card is shown to Cherly. It is publicly announced that someone picked a red card. It is publicly announced that Patrick does not know whether Timothy 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 (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":"Patrick can now know whether Maria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Patrick","Timothy","Cherly"],"index":24539,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9863134623,"difficulty":0.0136865377}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Natalie 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 (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) ] [ ! 3 ] 0","hypothesis":"Henry can now know whether Dana can know that Henry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dana","Henry","Natalie"],"index":54743,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9730451703,"difficulty":0.0269548297}
-{"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 Jennifer. Lance's card is shown to Thomas. Jennifer's card is shown to Victoria. Lance's card is shown to Victoria. 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) ] 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:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know whether Thomas can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Thomas","Lance","Victoria"],"index":44825,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993767142,"difficulty":0.0006232858}
-{"premise":"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. 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)) ] [ ! ~(Agentd knows whether (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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Rex can now know that Earl can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Earl","Rex","Eunice","Maria"],"index":65603,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987108707,"difficulty":0.0012891293}
-{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that Diane 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 (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)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Troy can now know that Diane can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Troy","Carolyn"],"index":21047,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994713664,"difficulty":0.0005286336}
-{"premise":"There are four persons. Everyone is visible 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 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) ] (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) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Joseph can now know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Peter","George","Susan"],"index":49960,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981757402,"difficulty":0.0018242598}
-{"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 Ebony. Ebony's card is shown to John. John's card is shown to Joseph. It is publicly announced that someone picked a red card. It is publicly announced that Ebony picked a red card. It is publicly announced that not everyone 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: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":"Ebony can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Ebony","John","Joseph"],"index":8837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9907485843,"difficulty":0.0092514157}
-{"premise":"There are four persons. Everyone is visible 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 Darlene's forehead is muddy. It is publicly announced that Darlene'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 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":"Robert can now know that Darlene can know whether Darlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darlene","John","Joshua","Robert"],"index":40133,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994689822,"difficulty":0.0005310178}
-{"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 Cindy is thirsty. It is publicly announced that Cindy does not know whether Tina is thirsty.","smcdel_problem":"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 (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":"Cindy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clyde","William","Tina","Cindy"],"index":10467,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960398674,"difficulty":0.0039601326}
-{"premise":"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 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":"Barbara can now know whether Carol can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Carla","Courtney","Carol"],"index":43501,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995064199,"difficulty":0.004935801}
-{"premise":"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 Brenda'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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brenda can now know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brenda","Juan"],"index":58,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9760277271,"difficulty":0.0239722729}
-{"premise":"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.","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 (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":"William can now know whether Jesus can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Jesus","William"],"index":49229,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5975600481,"difficulty":0.4024399519}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernadette 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 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":"Bernadette can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mario","Faye","Bernadette","Carlos"],"index":14941,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990047812,"difficulty":0.0009952188}
-{"premise":"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 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|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":"Angela can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Aurelio","Rosa"],"index":1328,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988724589,"difficulty":0.0011275411}
-{"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 Ginny does not know whether Thomas is thirsty. It is publicly announced that Ginny does not know whether or not everyone is thirsty. It is publicly announced that James 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 (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta 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)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"James can now know that Ginny is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Ginny","Thomas"],"index":49788,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9762831926,"difficulty":1.9762831926}
-{"premise":"There are four 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 muddy. It is publicly announced that Clyde knows whether someone's forehead is muddy. It is publicly announced that Alberto knows whether Elizabeth'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) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (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":"Alberto can now know whether Richard can know whether Alberto's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Alberto","Richard","Clyde"],"index":26295,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977699518,"difficulty":0.0022300482}
-{"premise":"There are two persons. Everyone is visible 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 knows whether Jeremy'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)","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":"Drew can now know that Drew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Drew","Jeremy"],"index":4458,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977049232,"difficulty":0.0022950768}
-{"premise":"There are four persons. Everyone is visible 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 Sandi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Julia can now know that Stephen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephen","Julia","Sandi","Alisa"],"index":55447,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988167286,"difficulty":0.0011832714}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 (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) ] [ ! ~(2) ] 0","hypothesis":"Lyn can now know whether Pamela can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pamela","Anna","Lyn","Willia"],"index":56187,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly's forehead is muddy.","smcdel_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 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":"Brittany can now know that Beverly can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brittany","Joan","Beverly"],"index":17169,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993815422,"difficulty":0.0006184578}
-{"premise":"There are two persons. Everyone is visible 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 Dominique'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 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":"Audrey can now know that Dominique's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Audrey","Dominique"],"index":21167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994549334,"difficulty":0.005450666}
-{"premise":"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 Kim's forehead 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 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 2) ] 0","hypothesis":"Harry can now know that Kim can know whether Harry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Kim","Darci"],"index":4921,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954093099,"difficulty":0.0045906901}
-{"premise":"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 does not know whether Fernando'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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ann can now know whether Fernando's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fernando","Joyce","Jose","Ann"],"index":57920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979034662,"difficulty":0.0020965338}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (~(1&2&3)) ] [ ! 1 ] (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":"Julie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julie","Carl","Patricia"],"index":33538,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9866284132,"difficulty":0.0133715868}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Della is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 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 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Olivia can now know that Della can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Olivia","Della"],"index":8270,"s-l":"internal-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). Anna's card is shown to Anna. Anna's card is shown to Roberta. Vennie's card is shown to Roberta. 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 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":"Marlene can now know whether Roberta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Marlene","Vennie","Roberta"],"index":27736,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9522659779,"difficulty":0.0477340221}
-{"premise":"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 Joyce 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)) ] 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) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joyce can now know that Becky can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","John","Becky","Joyce"],"index":46156,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9530969858,"difficulty":0.0469030142}
-{"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.","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 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":"Jayne can now know whether Jayne is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Jayne","Zelma","Michael"],"index":34293,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971687198,"difficulty":0.0028312802}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"Annabel can now know that Teresa can know that Nicole's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Nicole","Teresa","Annabel"],"index":5622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939869642,"difficulty":0.0060130358}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Zelma's card is shown to Zelma. Tammy's card is shown to Zelma. Lynn's card is shown to Zelma. Zelma's card is shown to Tammy. Tammy's card is shown to Tammy. Bill's card is shown to Tammy. Lynn's card is shown to Tammy. Zelma's card is shown to Bill. Lynn's card is shown to Bill. Zelma's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Lynn does not know whether Tammy picked a red card. It is publicly announced that Lynn does not know whether Bill picked a red card. It is publicly announced that Zelma does not know whether Bill picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] Agentd knows that (Agentc knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,2,3,4 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lynn can now know that Bill can know whether Lynn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Zelma","Tammy","Bill","Lynn"],"index":55039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6278433204,"difficulty":0.3721566796}
-{"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 David knows whether David 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 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":"David can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Danny","David"],"index":51041,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8651890159,"difficulty":0.1348109841}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Judy is thirsty. It is publicly announced that Jessie knows whether or not nobody is thirsty. It is publicly announced that Judy 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agentb 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jessie can now know whether Judy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judy","Jessie","Gary"],"index":34541,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994238615,"difficulty":0.0005761385}
-{"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 Della is thirsty. It is publicly announced that Erin does not know whether Della is thirsty.","smcdel_problem":"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) ] 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Erin can now know whether Randolph can know that Alan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randolph","Alan","Della","Erin"],"index":18147,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9910054207,"difficulty":0.0089945793}
-{"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 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":"Christine can now know whether Billy can know whether Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Christine","Billy","Mary"],"index":26830,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994260788,"difficulty":0.005739212}
-{"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 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":"Burma can now know whether Justin can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Burma","Karen","James","Justin"],"index":62271,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9882506132,"difficulty":0.0117493868}
-{"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 Lorraine. Lorraine's card is shown to Robert. Robert's card is shown to Robert. Lorraine's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Nancy picked a red card. It is publicly announced that Robert 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 3) ] [ ! 2 ] Agentc knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Nancy can now know that Lorraine can know that Lorraine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lorraine","Robert","Nancy"],"index":34303,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8919941187,"difficulty":0.1080058813}
-{"premise":"There are four persons. Everyone is visible 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 Maureen'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:1,2,3,4 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 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 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Maureen can now know that Bill can know that Bill's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeannette","Richard","Maureen","Bill"],"index":40243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976186156,"difficulty":0.0023813844}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Betty'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 (~(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":"Francis can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Virginia","Francis"],"index":18170,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990259409,"difficulty":0.0009740591}
-{"premise":"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 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 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":"Mike can now know that Jack can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jack","Mike"],"index":63320,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994599223,"difficulty":0.0005400777}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernest 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 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":"Lenore can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Lenore","Douglas","Ernest"],"index":2044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994662404,"difficulty":0.0005337596}
-{"premise":"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 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Wanda can now know that Kristy can know whether Kristy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Kristy","Wanda","Joseph"],"index":9465,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5130884051,"difficulty":1.5130884051}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vivian's card is shown to Brad. Vivian's card is shown to Vivian. It is publicly announced that someone picked a red card. It is publicly announced that Brad knows whether Vivian picked a red card. It is publicly announced that Brad 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 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:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Vivian can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brad","Vivian"],"index":9383,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973022938,"difficulty":0.0026977062}
-{"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 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":"Bonnie can now know that John can know whether Bonnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ashley","John","Bonnie"],"index":10105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9931001663,"difficulty":0.0068998337}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 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 4) ] 0","hypothesis":"John can now know that Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","John","George","Raymond"],"index":59063,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967349172,"difficulty":0.0032650828}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether Rachel'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) ] (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 1) ] [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rachel","Frances","Kenneth"],"index":41821,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898277521,"difficulty":0.0101722479}
-{"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 David. David's card is shown to Rachel. Frank's card is shown to Rachel. Rachel's card is shown to Frank. John'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 Agentb:1,3 Agentc:2,4 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:1,3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rachel can now know whether Frank picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Rachel","Frank","John"],"index":30635,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8417631984,"difficulty":1.8417631984}
-{"premise":"There are four 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.","smcdel_problem":"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)","n_announcements":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":"Diane can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Kristina","Diane","Bertha"],"index":2842,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9586309791,"difficulty":0.0413690209}
-{"premise":"There are four persons. Everyone is visible 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 Pamela 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 (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) ] [ ! 4 ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Kenyatta can now know that Kevin can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenyatta","Pamela","Kevin","Charles"],"index":56796,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9894605279,"difficulty":1.9894605279}
-{"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)","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":"Lorenzo can now know that Myron can know that Lorenzo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lorenzo","Myron","Quinn","Steven"],"index":42277,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975002408,"difficulty":0.0024997592}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elvira does not know whether or not everyone is thirsty. It is publicly announced that Gertrude 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 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&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Gertrude can now know that Shauna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gertrude","Shauna","Elvira"],"index":59579,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9919227362,"difficulty":0.0080772638}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie knows whether Verna's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)) ] (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) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Verna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","John","Carrie","Verna"],"index":32512,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989407659,"difficulty":0.0010592341}
-{"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 James. Elizabeth's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that James picked a red card. It is publicly announced that James knows whether James picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mildred can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Mildred","Elizabeth"],"index":5975,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990386963,"difficulty":0.0009613037}
-{"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 Charlie. Charlie's card is shown to Virginia. Virginia's card is shown to Virginia. Darin's card is shown to Virginia. Charlie's card is shown to Darin. Darin's card is shown to Darin. Charlie'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 Agentb:1,2,3 Agentc:1,3 Agentd:1 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 Agentb:1,2,3 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darin can now know that Virginia can know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlie","Virginia","Darin","Norman"],"index":35201,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979192615,"difficulty":0.0020807385}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emmett is thirsty. It is publicly announced that Richard is not thirsty. It is publicly announced that Kevin does not know whether Glen is thirsty. It is publicly announced that Emmett does not know whether 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 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 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) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Richard can now know that Glen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emmett","Kevin","Glen","Richard"],"index":45998,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990475774,"difficulty":0.0009524226}
-{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Yvonne does not know 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&2&3)) ] [ ! ~(Agenta knows whether 1) ] (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&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Yvonne can now know whether Vincent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yvonne","James","Vincent"],"index":26810,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989321828,"difficulty":0.0010678172}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether John is thirsty. It is publicly announced that Marget 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))) ] (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 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"John can now know whether Gary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gary","John","Marget"],"index":5888,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974967837,"difficulty":0.0025032163}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delores's card is shown to Charles. Priscilla's card is shown to Alta. Charles's card is shown to Priscilla. Priscilla'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 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 whether (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:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Alta can now know whether Priscilla can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Alta","Priscilla","Delores"],"index":11766,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994354844,"difficulty":0.0005645156}
-{"premise":"There are four persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows 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 ] 0","hypothesis":"Hallie can now know whether Hallie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Phyllis","Charles","Hallie"],"index":42848,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994663596,"difficulty":0.0005336404}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Howard. Kyle's card is shown to Kyle. 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 that (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Kyle can now know that Howard can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Howard","Kyle"],"index":53286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993982315,"difficulty":0.0006017685}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Fernando can now know that David can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janessa","Fernando","David","Barbara"],"index":58461,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979233146,"difficulty":0.0020766854}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Archie knows whether or not nobody's forehead is muddy. It is publicly announced that Shane 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":"Shane can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Shane","Archie"],"index":62825,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993565679,"difficulty":0.0006434321}
-{"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 someone is thirsty. It is publicly announced that Pedro 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)) ] 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Pedro can now know that Robert can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heather","Ruth","Robert","Pedro"],"index":63293,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.989539206,"difficulty":0.010460794}
-{"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 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) ] [ ! ~(Agentc knows whether 1) ] 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) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Marie can now know that Jeff can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marie","Patricia","David","Jeff"],"index":15589,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984040856,"difficulty":0.0015959144}
-{"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 (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":"Sherie can now know whether Tracy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Serena","David","Tracy","Sherie"],"index":56412,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993951321,"difficulty":0.0006048679}
-{"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 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":"Beverly can now know whether Rene can know that Beverly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Rene","Amber","Perla"],"index":23308,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9359377623,"difficulty":0.0640622377}
-{"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 John. Chester's card is shown to Chester. 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)) ] 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) ] [ ! (~(1&2)) ] 0","hypothesis":"Chester 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":["John","Chester"],"index":45250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999378562,"difficulty":0.000621438}
-{"premise":"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 Andy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Pamela can now know that Andy can know whether Andy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andy","Patricia","James","Pamela"],"index":64577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7395863533,"difficulty":0.2604136467}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janie does not know whether or not everyone's forehead is muddy. It is publicly announced that Janie does not know whether or not everyone'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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Janie can now know whether Thomas can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Janie"],"index":59914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.524274826,"difficulty":0.475725174}
-{"premise":"There are two persons. Everyone is visible 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 Charlotte'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":"Charlotte can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charlotte","Celia"],"index":43172,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936088324,"difficulty":0.0063911676}
-{"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 (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":"Anne can now know that Edmund can know that Edmund is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edmund","Anne","Carolyn","Roberta"],"index":30432,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9952189326,"difficulty":0.0047810674}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Lydia'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 (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) ] [ ! ~(2) ] 0","hypothesis":"Edna can now know that Jennifer can know whether Edna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edna","Lydia","Jennifer","Aileen"],"index":47505,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994396567,"difficulty":0.0005603433}
-{"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 Maria. Dennis's card is shown to Maria. Christine's card is shown to Christine. Christine's card is shown to Dennis. It is publicly announced that someone picked a red card. It is publicly announced that Christine knows whether Christine 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 Maria 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)) ] Agentb knows whether (Agentc knows whether 2)","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":"Christine can now know whether Dennis can know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Christine","Dennis"],"index":37954,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980667233,"difficulty":0.0019332767}
-{"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 Amy is thirsty. It is publicly announced that Lenora does not know whether Jeffrey is thirsty. It is publicly announced that Lori 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))) ] Agentb knows that (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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lori can now know that Lenora can know that Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amy","Lori","Jeffrey","Lenora"],"index":1561,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980524778,"difficulty":0.0019475222}
-{"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 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) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 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) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Carlos can now know whether Elizabeth can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","David","Elizabeth","Kenneth"],"index":49643,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994634986,"difficulty":0.0005365014}
-{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Valerie'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":"Vickie can now know that Christopher can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Valerie","Christopher","Vickie"],"index":27269,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986680746,"difficulty":0.0013319254}
-{"premise":"There are two persons. Everyone is visible 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 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. It is publicly announced that Pamela 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)) ] (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) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Pamela can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Pamela"],"index":43479,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948323965,"difficulty":0.0051676035}
-{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Mona knows whether Mona's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Erik 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)) ] (Agentb knows whether 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":"Erik can now know whether Erik's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mona","Erik"],"index":14204,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9987297654,"difficulty":0.0012702346}
-{"premise":"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 someone's forehead is muddy. It is publicly announced that Darrell knows whether Dale'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) ] Agentb 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)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know that Jeanne can know that Jeanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeanne","Frank","Dale","Darrell"],"index":20765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972321391,"difficulty":0.0027678609}
-{"premise":"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'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 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) ] [ ! ~(3) ] 0","hypothesis":"Shannon can now know whether Ernest can know that Ernest's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shannon","Rachel","Ernest"],"index":6682,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9898938537,"difficulty":0.0101061463}
-{"premise":"There are three persons. Everyone is visible 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 Matthew's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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":"Mark can now know that Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Richard","Matthew"],"index":50587,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964275956,"difficulty":0.0035724044}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delma knows whether or not everyone's forehead is muddy. It is publicly announced that Delma does not know whether Delma's forehead 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 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":"Sharon can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delma","Chris","Sharon"],"index":10215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9691187739,"difficulty":0.0308812261}
-{"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 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":"Betty can now know that Carol can know whether Laura is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Betty","Carol"],"index":28425,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9970476031,"difficulty":0.0029523969}
-{"premise":"There are four 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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Charles can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","Michael","Harry","Charles"],"index":29128,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989418387,"difficulty":0.0010581613}
-{"premise":"There are three persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Beulah'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|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":"Beulah can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lois","Teresa","Beulah"],"index":57039,"s-l":"forehead_mirror-0","deberta_pred":0,"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 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) ] [ ! 2 ] (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":"Kelly can now know that Luther's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Kelly","Luther"],"index":24103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9787422419,"difficulty":0.0212577581}
-{"premise":"There are three persons. Everyone is visible 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 Kim's forehead is muddy.","smcdel_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 (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":"Cathy can now know that Kim can know that Kim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cathy","Michelle","Kim"],"index":53329,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947063327,"difficulty":0.0052936673}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gertrude does not know whether Gertrude's forehead is muddy. It is publicly announced that Brenda does not know whether Brenda's forehead is muddy. It is publicly announced that Gertrude 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 (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 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gertrude can now know that Sara can know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Patricia","Gertrude","Sara"],"index":36074,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965923429,"difficulty":0.0034076571}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elliott's forehead is muddy.","smcdel_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":"Elliott can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Elliott","John"],"index":20327,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9896664619,"difficulty":0.0103335381}
-{"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 Michael. Michael's card is shown to Ardith. 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 (Agentc knows that (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":"Michael can now know whether Ardith can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Michael","Ardith"],"index":57936,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999404788,"difficulty":0.000595212}
-{"premise":"There are four persons. Everyone is visible 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 Tammy's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 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) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"Stacy can now know whether Rita can know whether Stacy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stacy","Larry","Tammy","Rita"],"index":63577,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994276166,"difficulty":0.0005723834}
-{"premise":"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'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":"Travis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Jack","Travis"],"index":15909,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994562268,"difficulty":0.0005437732}
-{"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 Georgina. Jose's card is shown to Tom. 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 Agentb:2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jose can now know that Georgina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Georgina","Jose","Tom"],"index":64912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998467505,"difficulty":0.001532495}
-{"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. Velma's card is shown to Richard. Richard's card is shown to Robin. Richard's card is shown to Velma. Velma's card is shown to Velma. 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 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":"Richard can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Robin","Velma"],"index":55487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989365935,"difficulty":0.0010634065}
-{"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 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":"Vincent can now know that Emma can know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Andrea","Emma","Vincent"],"index":18016,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982680082,"difficulty":0.0017319918}
-{"premise":"There are four persons. Everyone is visible 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 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":"William can now know that Wilbert can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Kevin","Vernon","Wilbert"],"index":44617,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982193112,"difficulty":0.0017806888}
-{"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. Joyce's card is shown to Carol. Carol's card is shown to Donnette. Donnette's card is shown to Donnette. Carol's card is shown to Joyce. 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 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":"Joyce can now know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carol","Donnette","Joyce"],"index":25946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5031784177,"difficulty":0.4968215823}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Candace knows whether or not nobody is thirsty. It is publicly announced that Candace does not know whether Tammy is thirsty. It is publicly announced that Alexander knows whether or not everyone is thirsty. It is publicly announced that Tammy knows whether Tammy 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)","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":"Candace can now know that Candace is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Candace","Alexander","Tammy"],"index":51320,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6587040424,"difficulty":0.3412959576}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tara's card is shown to James. James's card is shown to Tara. Albert's card is shown to Tara. Tara'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:1,3 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:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Tara","Albert"],"index":6123,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.996009469,"difficulty":0.003990531}
-{"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 Elizabeth knows 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Rudolph can now know whether Elizabeth can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rudolph","Norman","Michael","Elizabeth"],"index":1648,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9911382794,"difficulty":0.0088617206}
-{"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 Rose. Brandon's card is shown to Jean. Erick's card is shown to Jean. Rose's card is shown to Brandon. Jean's card is shown to Brandon. Jean's card is shown to Erick. Brandon's card is shown to Erick. 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 (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:1,2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brandon can now know that Rose can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Jean","Brandon","Erick"],"index":13130,"s-l":"explicit-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). Carole's card is shown to James. James's card is shown to Carole. It is publicly announced that someone picked a red card. It is publicly announced that Carole does not know whether Carole 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 (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":"James can now know whether Carole can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Carole"],"index":63497,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8417441845,"difficulty":1.8417441845}
-{"premise":"There are four persons. Everyone is visible 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 John'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 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":"Helen can now know that Freda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Freda","Clay","John","Helen"],"index":10696,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997875452,"difficulty":0.002124548}
-{"premise":"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 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Luis can now know that Luis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brad","Anthony","Justin","Luis"],"index":50399,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953332543,"difficulty":0.0046667457}
-{"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. Todd's card is shown to Kevin. Kevin's card is shown to Todd. Todd's card is shown to Todd. Douglas's card is shown to Todd. Todd'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:2,3,4 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:2,3 Agentb:2,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Kevin","Todd","Douglas"],"index":39515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990081191,"difficulty":0.0009918809}
-{"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. Liz's card is shown to Karen. Karen's card is shown to Liz. 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 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":"Karen can now know whether Liz picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Karen","Liz"],"index":37310,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5833329558,"difficulty":1.5833329558}
-{"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 Gary. Irene's card is shown to Gary. Gary's card is shown to Lisa. Lisa's card is shown to Irene. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether Gary 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) ] 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gary can now know whether Irene can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Lisa","Irene"],"index":43949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993962049,"difficulty":0.0006037951}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luanna's forehead is not muddy. It is publicly announced that Luanna's forehead is not muddy. It is publicly announced that Luanna'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|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":"Mckenzie can now know whether Robert can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mckenzie","Luanna","Robert","Raul"],"index":59482,"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. 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 Charles knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Amy can now know whether Betty can know whether Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Doris","Charles","Amy"],"index":5356,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990782738,"difficulty":0.0009217262}
-{"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. Jeffrey's card is shown to Andrew. Sharda's card is shown to Sharda. Sharda's card is shown to Jeffrey. Jeffrey's card is shown to Stephen. 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. It is publicly announced that Jeffrey does not know whether Jeffrey picked a red card. It is publicly announced that Andrew knows whether Jeffrey 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 whether (Agentc knows whether (1&2&3&4))","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":"Sharda can now know whether Jeffrey can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Sharda","Jeffrey","Stephen"],"index":54963,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8514096141,"difficulty":0.1485903859}
-{"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. It is publicly announced that Cesar does not know whether Billy 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 (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)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kenneth can now know that Cesar can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Billy","Kenneth","Cesar"],"index":35193,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993935823,"difficulty":0.0006064177}
-{"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 Tara is thirsty. It is publicly announced that Tara does not know whether Albert is thirsty. It is publicly announced that Albert does not know whether Tara is thirsty.","smcdel_problem":"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 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":"Albert can now know that Tara can know that Kelly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tara","Albert","Kelly","Danielle"],"index":25828,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983573556,"difficulty":0.0016426444}
-{"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 Blake is thirsty. It is publicly announced that Avery is 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 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":"Thomas can now know that Jordan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jordan","Avery","Thomas","Blake"],"index":35864,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961198568,"difficulty":0.0038801432}
-{"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. Olga's card is shown to Sara. Robert's card is shown to Sara. Olga's card is shown to Louisa. Olga's card is shown to Olga. Olga's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Sara does not know whether Louisa 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 that 4)","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":"Sara can now know that Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sara","Louisa","Olga","Robert"],"index":41758,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960946441,"difficulty":0.0039053559}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ward's card is shown to Lillian. Lillian's card is shown to Ward. Ward's card is shown to Ward. Lillian's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Ward does not know whether William picked a red card. It is publicly announced that Ward 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 3) ] [ ! 2 ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"William can now know whether Ward can know whether Ward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lillian","Ward","William"],"index":1402,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979806542,"difficulty":0.0020193458}
-{"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 Corene. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card. It is publicly announced that Corene 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 2) ] Agenta knows whether (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 2) ] 0","hypothesis":"Corene can now know whether Pamela can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Corene","Pamela"],"index":67354,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9882655144,"difficulty":0.0117344856}
-{"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 Elizabeth. Robert's card is shown to Robert. 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 that 1)","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":"Elizabeth can now know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Robert","Thomas"],"index":1231,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9871789217,"difficulty":0.0128210783}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beth's card is shown to Beth. Theresa's card is shown to Beth. Tammi's card is shown to Theresa. Beth's card is shown to Tammi. Tammi's card is shown to Tammi. It is publicly announced that someone picked a red card. It is publicly announced that Theresa picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 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 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Tammi can now know that Theresa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Beth","Theresa","Tammi"],"index":57711,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990039468,"difficulty":0.0009960532}
-{"premise":"There are 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 (~(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":"Bryon can now know whether Evelyn can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Bryon","Evelyn"],"index":29030,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992383718,"difficulty":0.0007616282}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackson'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":"Jackson can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Valentin","Theodora","John","Jackson"],"index":39352,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999304533,"difficulty":0.000695467}
-{"premise":"There are two 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 someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Brittany 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)) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 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)) ] [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Edward can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brittany","Edward"],"index":45701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994963408,"difficulty":0.0005036592}
-{"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. Timothy's card is shown to Christopher. Christopher's card is shown to Christopher. 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 that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Timothy can now know that Christopher can know whether Joanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Christopher","Joanne"],"index":62442,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995693922,"difficulty":0.004306078}
-{"premise":"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 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) ] 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":"James can now know that Annie can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annie","James","Dianne"],"index":3866,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994427562,"difficulty":0.0005572438}
-{"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 Jonathan. Ella's card is shown to Jonathan. Jonathan's card is shown to Barbara. Ella's card is shown to Barbara. Jonathan's card is shown to Ella. 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) ] (Agentb knows that 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 Ella picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jonathan","Barbara","Ella"],"index":392,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945561886,"difficulty":0.0054438114}
-{"premise":"There are three persons. Everyone is visible 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 John'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) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentc 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":"John 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","Joyce","John"],"index":33909,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989976287,"difficulty":0.0010023713}
-{"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 Pauline. Jerry's card is shown to Pauline. Joyce's card is shown to Joyce. Joyce's card is shown to Jean. Jerry's card is shown to Jerry. 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) ] Agentc knows whether (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 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jean can now know whether Jerry can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Joyce","Jean","Jerry"],"index":45150,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993616939,"difficulty":0.0006383061}
-{"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 or not everyone is thirsty. It is publicly announced that Andre does not know whether or not everyone is thirsty. It is publicly announced that Sal knows 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)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd 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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Sherry can now know whether Sal is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andre","David","Sherry","Sal"],"index":37629,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.979254365,"difficulty":0.020745635}
-{"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 Sally. Viola's card is shown to Sally. Gertrude's card is shown to Stella. Stella's card is shown to Stella. 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) ] (Agentb 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":"Viola can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sally","Viola","Gertrude","Stella"],"index":48398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993335605,"difficulty":0.0006664395}
-{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Mary knows whether Laura's forehead is muddy. It is publicly announced that Brian 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) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (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 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know whether Patricia can know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Brian","Mary","Laura"],"index":3675,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994350076,"difficulty":0.0005649924}
-{"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 Marjorie. David's card is shown to Benjamin. Marjorie's card is shown to Benjamin. 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:1 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:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Marjorie","Benjamin"],"index":13228,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990192652,"difficulty":0.0009807348}
-{"premise":"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 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 (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":"Jennifer can now know that William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Tracey","Fred","William"],"index":24350,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994740665,"difficulty":0.005259335}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emilio's card is shown to James. Emilio's card is shown to Emilio. It is publicly announced that someone picked a red card. It is publicly announced that Emilio does not know whether James 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 that (Agenta 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":"Emilio can now know that James can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Emilio"],"index":34989,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994215965,"difficulty":0.0005784035}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara is 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 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":"Ralph can now know that Elizabeth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gilbert","Tara","Elizabeth","Ralph"],"index":37382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9881049395,"difficulty":0.0118950605}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Glynis can now know that Carol can know that Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","Glynis","Keith","Carol"],"index":11151,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997916162,"difficulty":0.002083838}
-{"premise":"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 does not know whether Jerome's forehead is muddy. It is publicly announced that Jerome 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 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":"Jerome can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Guy","Jerome"],"index":36931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994531274,"difficulty":0.0005468726}
-{"premise":"There are three persons. Everyone is visible 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 Carri's forehead is muddy.","smcdel_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 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) ] 0","hypothesis":"Lucinda can now know whether Carri can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carri","David","Lucinda"],"index":19500,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994193316,"difficulty":0.0005806684}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaiah does not know whether Isaiah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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":"Elizabeth can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Patricia","Jan","Isaiah"],"index":48786,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993738532,"difficulty":0.0006261468}
-{"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 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":"Pamela can now know whether Kurt can know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Kurt","Pamela"],"index":48290,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9410943389,"difficulty":0.0589056611}
-{"premise":"There are two persons. Everyone is visible 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 Earl'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 (~(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&2)) ] 0","hypothesis":"Jesse can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jesse","Earl"],"index":67223,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990003705,"difficulty":0.0009996295}
-{"premise":"There are four persons. Everyone is visible 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's forehead is muddy. It is publicly announced that William knows whether Amanda's forehead is muddy. It is publicly announced that Sharon 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 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agenta 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 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Gloria can now know that Amanda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Sharon","William","Amanda"],"index":58094,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990286827,"difficulty":0.0009713173}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sophie's card is shown to Sophie. Wilmer's card is shown to Sophie. Sophie's card is shown to Charles. Sophie's card is shown to Wilmer. Wilmer's card is shown to Wilmer. 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 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":"Charles can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sophie","Charles","Wilmer"],"index":61884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9942427278,"difficulty":0.0057572722}
-{"premise":"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 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Hannah can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judy","Sharon","Dinah","Hannah"],"index":56132,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990235567,"difficulty":0.0009764433}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"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))","n_announcements":1,"pbcheck":"VARS 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":"Erin can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Erin","Gary"],"index":48238,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992871881,"difficulty":0.0007128119}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristy's card is shown to Marjorie. Marjorie's card is shown to Marjorie. It is publicly announced that someone picked a red card. It is publicly announced that Kristy 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kristy can now know whether Kristy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kristy","Marjorie"],"index":41880,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6116583347,"difficulty":1.6116583347}
-{"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 or not everyone is thirsty. It is publicly announced that Irvin knows whether someone is thirsty. It is publicly announced that Gail does not know whether Irvin is thirsty. It is publicly announced that Gail does not know whether Leslie is thirsty.","smcdel_problem":"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 (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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Gail can now know that Irvin can know that Leslie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irvin","Leslie","Gail","Henry"],"index":30770,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9607998729,"difficulty":0.0392001271}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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":"Lue can now know whether Lue's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Lue","Peter","Traci"],"index":27020,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.991483748,"difficulty":0.008516252}
-{"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 or not everyone is thirsty. It is publicly announced that Manuel 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 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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"David can now know that Manuel can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Jesse","David","Manuel"],"index":14709,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9845293164,"difficulty":0.0154706836}
-{"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 Donald. Joshua's card is shown to Donald. Donald's card is shown to Denise. Joshua's card is shown to Denise. Denise's card is shown to Billy. Billy's card is shown to Billy. Denise's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Denise 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 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:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Donald can now know whether Billy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Denise","Billy","Joshua"],"index":907,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992832541,"difficulty":0.0007167459}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandon does not know whether Erika is thirsty. It is publicly announced that Mildred does not know whether Erika 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 (~(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 1) ] 0","hypothesis":"Brandon can now know whether Erika can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erika","Brandon","Mildred"],"index":21205,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! ~(2) ] 0","hypothesis":"Michelle can now know whether Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gilberto","Michelle","Russell"],"index":27420,"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. Each person draws a card, face unrevealed (red or black). Christopher's card is shown to Anna. Christopher's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether Anna 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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anna can now know whether Anna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","Christopher"],"index":27453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.90768677,"difficulty":0.09231323}
-{"premise":"There are four persons. Everyone is visible 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 knows whether Eileen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Holly can now know that Andrea can know that Lorene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eileen","Andrea","Holly","Lorene"],"index":18040,"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. 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 not muddy. It is publicly announced that Craig's forehead is not muddy. It is publicly announced that Craig'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 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) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Summer can now know whether Edward can know whether Craig's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Summer","Craig","Edward","Joseph"],"index":37868,"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. 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 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":"Carlos can now know that Collette can know that Collette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Collette","Michael","Carlos"],"index":2758,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984543324,"difficulty":0.0015456676}
-{"premise":"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 muddy. It is publicly announced that David 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) ] [ ! 2 ] [ ! (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: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":"Brian can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Brian","Richard","David"],"index":59948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987745881,"difficulty":0.0012254119}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damon's forehead is muddy. It is publicly announced that Damon knows whether someone's forehead is muddy. It is publicly announced that Belinda'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)","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":"Damon can now know whether Belinda can know that Belinda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Belinda","Damon"],"index":4927,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993036985,"difficulty":0.0006963015}
-{"premise":"There are four persons. Everyone is visible 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'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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Kevin can now know that Norma can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norma","Kevin","Lillian","Robert"],"index":48604,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988462925,"difficulty":0.0011537075}
-{"premise":"There are two persons. Everyone is visible 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. 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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 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))) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know whether Gregory can know whether Gregory's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Gregory"],"index":51655,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994588494,"difficulty":0.0005411506}
-{"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.","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":"Eva can now know whether Christopher can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christopher","Eva"],"index":34235,"s-l":"internal-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 Lucille does not know 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) ] [ ! ~(Agentd knows whether 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 4) ] 0","hypothesis":"Lucille can now know that Lucille's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Paul","Yvonne","Lucille"],"index":39226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892302155,"difficulty":0.0107697845}
-{"premise":"There are three persons. Everyone is visible 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 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":"Jon can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Latisha","Wayne","Jon"],"index":42723,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986080527,"difficulty":0.0013919473}
-{"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 Grace. Kelly's card is shown to Julie. Randy's card is shown to Julie. Grace's card is shown to Randy. Julie's card is shown to Randy. 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 whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelly can now know whether Julie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Grace","Kelly","Julie","Randy"],"index":53032,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8063346148,"difficulty":0.1936653852}
-{"premise":"There are four persons. Everyone is visible 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 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":"Judy can now know whether Ronald can know that Judy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","Judy","Ronald","Gabriela"],"index":3260,"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). David's card is shown to Marisa. David's card is shown to Bessie. Lionel's card is shown to David. Marisa's card is shown to Lionel. David's card is shown to Lionel. It is publicly announced that someone picked a red card. It is publicly announced that Bessie 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)) ] Agentc knows whether (Agentd 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":"David can now know whether Lionel can know whether David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marisa","Bessie","David","Lionel"],"index":19520,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983024597,"difficulty":0.0016975403}
-{"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 4)","n_announcements":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":"Penelope can now know whether Penelope is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Valorie","Maria","John","Penelope"],"index":30622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9936572909,"difficulty":0.0063427091}
-{"premise":"There are three persons. Everyone is visible 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 muddy. It is publicly announced that Dolores knows whether someone's forehead is muddy. It is publicly announced that Dolores knows whether Bruno's forehead is muddy. It is publicly announced that Dolores 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 (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":"Bruno can now know that Dolores can know that Dolores's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amber","Bruno","Dolores"],"index":66855,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940696955,"difficulty":0.0059303045}
-{"premise":"There are four persons. Everyone is visible 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) ] (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":"Rebecca can now know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Rebecca","Mark","Linda"],"index":59601,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9802016616,"difficulty":0.0197983384}
-{"premise":"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'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) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Thomas can now know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Catherine","Thomas"],"index":66542,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992644191,"difficulty":0.0007355809}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (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":"Dora can now know whether Bonnie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bonnie","Gary","Dora","Claudia"],"index":54028,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993213415,"difficulty":0.0006786585}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronnie's card is shown to Laurie. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Laurie does not know whether Laurie 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) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Laurie can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laurie","Ronnie","Mary"],"index":60678,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964829683,"difficulty":0.0035170317}
-{"premise":"There are three persons. Everyone is visible 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 Wm's forehead is muddy.","smcdel_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":"Heather can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Heather","Wm","John"],"index":54701,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990135431,"difficulty":0.0009864569}
-{"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 Toby does not know whether Jonathan 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)","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":"Toby can now know whether Jonathan can know that Jonathan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jonathan","Toby"],"index":4826,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9426320791,"difficulty":1.9426320791}
-{"premise":"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 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) ] [ ! (Agentd 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: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":"Bonnie can now know whether Lillie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lillie","David","Bonnie"],"index":37983,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994412065,"difficulty":0.0005587935}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maricela's card is shown to Maricela. Ray's card is shown to Maricela. Dave's card is shown to Maricela. Dave's card is shown to Ray. Dave's card is shown to Dave. 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) ] Agentb 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:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ray can now know that Maricela can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maricela","Ray","Dave"],"index":27054,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994152784,"difficulty":0.0005847216}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antonette's card is shown to Louise. Marva's card is shown to Louise. Paula's card is shown to Antonette. Paula's card is shown to Marva. Antonette's card is shown to Marva. 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) ] 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:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Antonette can now know whether Louise can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Louise","Antonette","Marva"],"index":57092,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9932821989,"difficulty":0.0067178011}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doyle does not know whether Kenyatta is thirsty. It is publicly announced that Doyle 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 (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":"Doyle can now know that Kenyatta can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenyatta","Doyle"],"index":34603,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994986057,"difficulty":0.0005013943}
-{"premise":"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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Joey can now know that Nancy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Joey","Barbara","Andres"],"index":27959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993816614,"difficulty":0.0006183386}
-{"premise":"There are four persons. Everyone is visible 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 Jonathan'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 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":"Shannon can now know whether Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jonathan","Kevin","Joyce","Shannon"],"index":21838,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999345839,"difficulty":0.000654161}
-{"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) ] [ ! (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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Arnold can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Arnold","Mark","Mary"],"index":9580,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993300438,"difficulty":0.0006699562}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalyn's card is shown to Rosalyn. Priscilla's card is shown to Rosalyn. Priscilla's card is shown to Priscilla. 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 that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Rosalyn can now know that Rosalyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rosalyn","Priscilla"],"index":60949,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9903772473,"difficulty":0.0096227527}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ralph's card is shown to Malcolm. Juliette's card is shown to Juliette. Manuel's card is shown to Juliette. Manuel's card is shown to Ralph. Malcolm's card is shown to Manuel. Juliette's card is shown to Manuel. Ralph'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:3 Agentb:2,4 Agentc:4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 2)","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":"Manuel can now know whether Malcolm can know that Juliette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Malcolm","Juliette","Ralph","Manuel"],"index":5777,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9358462095,"difficulty":0.0641537905}
-{"premise":"There are 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 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":"Christine can now know whether Erlene can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erlene","Christine","John"],"index":19291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993579984,"difficulty":0.0006420016}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rae's card is shown to Rae. Naomi's card is shown to Rae. Naomi's card is shown to Dana. Anderson's card is shown to Anderson. 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 Agentc: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:1,2 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rae can now know whether Dana can know that Dana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rae","Naomi","Dana","Anderson"],"index":57988,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9848756194,"difficulty":1.9848756194}
-{"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 Kathryn. Kathryn's card is shown to Mark. Mark's card is shown to Mark. James's card is shown to Mark. Kathryn'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 Mark knows whether James 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) ] Agenta knows whether (Agentb knows that 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":"Kathryn can now know whether Mark can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathryn","Mark","James"],"index":8501,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9692941308,"difficulty":1.9692941308}
-{"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 (Agentb 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":"Judy can now know that Howard can know whether Howard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Howard","Judy","Gwendolyn"],"index":57052,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5437602401,"difficulty":1.5437602401}
-{"premise":"There are three persons. Everyone is visible 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's forehead is muddy. It is publicly announced that Ray 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) ] [ ! 3 ] [ ! (Agentc knows whether 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) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ray can now know that Erin can know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Erin","Marilyn","Ray"],"index":45835,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9819876552,"difficulty":0.0180123448}
-{"premise":"There are 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)","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":"Jason can now know that Sarah can know that Ilda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ilda","Christopher","Sarah","Jason"],"index":64379,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972475171,"difficulty":0.0027524829}
-{"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 Darlene. Bryan's card is shown to Darlene. Darlene's card is shown to Carlos. Agnes's card is shown to Carlos. Agnes's card is shown to Agnes. Agnes's card is shown to Bryan. It is publicly announced that someone picked a red card. It is publicly announced that Agnes 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)) ] (Agentb knows that 1)","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":"Carlos can now know that Darlene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darlene","Carlos","Agnes","Bryan"],"index":46317,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.968334496,"difficulty":0.031665504}
-{"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 Doris. Johnny's card is shown to Johnny. Mark's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether Christopher picked a red card. It is publicly announced that Johnny does not know whether Christopher picked a red card. It is publicly announced that Johnny does not know whether Mark picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mark can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Johnny","Mark","Christopher"],"index":3008,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.966920197,"difficulty":0.033079803}
-{"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. Alice's card is shown to Theodore. Keith's card is shown to Theodore. Theodore's card is shown to Alice. 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:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Keith can now know that Theodore can know that Keith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theodore","Alice","Keith"],"index":56074,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958181977,"difficulty":0.0041818023}
-{"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 Randy. Steven's card is shown to Peter. 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:1 Agentb:2,3 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:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether Randy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Steven","Peter","Geraldine"],"index":32185,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9867239594,"difficulty":0.0132760406}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim knows whether or not nobody'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) ] [ ! (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:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jim can now know whether Robert can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Jim"],"index":34907,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992461205,"difficulty":0.0007538795}
-{"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 William. Jaqueline's card is shown to Jaqueline. Agnes's card is shown to Jaqueline. Agnes's card is shown to Agnes. William's card is shown to Annie. 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:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta 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:3 Agentb:2,3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Agnes can know that William picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jaqueline","Agnes","Annie"],"index":53055,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7887471914,"difficulty":0.2112528086}
-{"premise":"There are two 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. It is publicly announced that Esther knows whether or not nobody's forehead is muddy. It is publicly announced that Esther 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":"Esther can now know that Joshua can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Esther","Joshua"],"index":58560,"s-l":"forehead-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 Wanda is thirsty. It is publicly announced that Mary is not thirsty. It is publicly announced that William does not know whether Randy is thirsty. It is publicly announced that Wanda 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) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (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) ] [ ! 1 ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Wanda can now know whether William can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wanda","William","Randy","Mary"],"index":5596,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994846582,"difficulty":0.0005153418}
-{"premise":"There are four persons. Everyone is visible 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 Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Jennifer can now know that Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Paul","Mildred","Laurie"],"index":11926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948900938,"difficulty":0.0051099062}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chester's card is shown to Chester. Gregory's card is shown to Gregory. Mercedes's card is shown to Mercedes. 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 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":"Gregory can now know that Chester can know whether Mercedes picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Chester","Gregory","Mercedes"],"index":44168,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5496553779,"difficulty":1.5496553779}
-{"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 Julius. Emily's card is shown to Danny. Marsha's card is shown to Marsha. Emily's card is shown to Marsha. 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 whether (Agentc knows that 1)","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":"Danny can now know whether Marsha can know that Julius picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julius","Danny","Marsha","Emily"],"index":65915,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8948574066,"difficulty":0.1051425934}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicole knows whether or not nobody is thirsty. It is publicly announced that Jeannette knows whether Nicole 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))) ] [ ! (Agenta knows whether 2) ] [ ! (~(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))) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jeannette can now know that Nicole can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeannette","Nicole"],"index":38907,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994100332,"difficulty":0.0005899668}
-{"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 Paul. Sheila's card is shown to Paul. Nancy's card is shown to Nancy. Paul's card is shown to Sheila. Nancy'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:2,3 Agentb:2 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:2,3 Agentb:2 Agentc:1,2,3 VALID? [ ! (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":["Paul","Nancy","Sheila"],"index":40560,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989956021,"difficulty":0.0010043979}
-{"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 Emma. 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 whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Emma can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Emma","Steven","Joyce"],"index":33440,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.995582521,"difficulty":0.004417479}
-{"premise":"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.","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)","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":"Mark can now know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Mark"],"index":1357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989174604,"difficulty":0.0010825396}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cesar knows whether Cesar'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 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":"Cesar can now know whether Carrie can know whether Cesar's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Carrie","Cesar"],"index":17954,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993993044,"difficulty":0.0006006956}
-{"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 Wm. Wm's card is shown to Josefina. Justin's card is shown to Josefina. Russel's card is shown to Justin. Justin'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:2 Agentb:1,4 Agentc:2,4 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:1,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wm can now know that Russel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Wm","Russel","Josefina","Justin"],"index":49495,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961793423,"difficulty":0.0038206577}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nichole's card is shown to Jerry. Jerry's card is shown to Jerry. Jennifer's card is shown to Jerry. Nichole's card is shown to Jennifer. Jerry'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:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know whether Nichole can know that Jerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nichole","Jerry","Jennifer"],"index":21389,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7624345422,"difficulty":0.2375654578}
-{"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 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 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":"Daniel can now know that Cynthia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cynthia","Daniel"],"index":66583,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993478656,"difficulty":0.0006521344}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Donald can now know that Harold can know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Tammy","Harold","Donald"],"index":13381,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972873926,"difficulty":0.0027126074}
-{"premise":"There are four persons. Everyone is visible 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 (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 2) ] 0","hypothesis":"Marc can now know that Leland can know that Marc's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leland","William","Elizabeth","Marc"],"index":51574,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983969331,"difficulty":0.0016030669}
-{"premise":"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 or not everyone'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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb 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 (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Caitlyn can now know whether Caitlyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Caitlyn","Ruth","Justin"],"index":24592,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823964834,"difficulty":0.0176035166}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chelsea 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) ] (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":"David can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tobias","William","Chelsea","David"],"index":34246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987387061,"difficulty":0.0012612939}
-{"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 Tamra. Tamra's card is shown to Peter. Vera's card is shown to Peter. Michael's card is shown to Vera. Peter's card is shown to Vera. 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) ] (Agentb knows that (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":"Michael can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tamra","Michael","Peter","Vera"],"index":41238,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989621639,"difficulty":0.0010378361}
-{"premise":"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 (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":"Carol can now know whether William can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amber","William","Sadie","Carol"],"index":9046,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978271127,"difficulty":0.0021728873}
-{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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 that Claudia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Claudia","Nolan","Angela"],"index":21495,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989745617,"difficulty":0.0010254383}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Walter's card is shown to Walter. Donna's card is shown to Willis. Walter's card is shown to Willis. Samuel's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc: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 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Walter can now know that Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Walter","Willis","Samuel"],"index":54377,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7362667918,"difficulty":1.7362667918}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clement's card is shown to Clement. Clement's card is shown to Eric. It is publicly announced that someone picked a red card. It is publicly announced that Clement knows whether someone picked a red card. It is publicly announced that Eric knows whether Eric 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) ] (Agentb 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":"Eric can now know whether Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Clement","Eric"],"index":11276,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7937288284,"difficulty":0.2062711716}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julian knows whether someone's forehead is muddy. It is publicly announced that Marsha 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":"Marsha can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marsha","Julian"],"index":12724,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990090132,"difficulty":0.0009909868}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 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":"Robin 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":["Anne","Robin","James","Renee"],"index":40596,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8148954511,"difficulty":1.8148954511}
-{"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 Marie 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) ] [ ! (~(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) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robbie can now know that Teresa can know that Marie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robbie","Marie","Harvey","Teresa"],"index":58760,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964233041,"difficulty":0.0035766959}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sally's forehead is not muddy. It is publicly announced that Sally's forehead is not muddy. It is publicly announced that Sally'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 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":"Melissa can now know whether Roland can know whether Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roland","Sally","James","Melissa"],"index":66219,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994618297,"difficulty":0.0005381703}
-{"premise":"There are 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":"Sheron can now know that Louis can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheron","Harvey","Louis"],"index":27944,"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 Juan'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":"Annie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Juan","Hermelinda","Kendra","Annie"],"index":29805,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988492727,"difficulty":0.0011507273}
-{"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. Marla's card is shown to Debra. Marla's card is shown to Ashley. 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:1,4 Agentb:4 Agentc:3 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:1,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Debra can now know whether Ashley can know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Ashley","Paul","Marla"],"index":595,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984771609,"difficulty":0.0015228391}
-{"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 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":"Loretta can now know that Howard can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Loretta","Howard"],"index":17117,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9926925898,"difficulty":0.0073074102}
-{"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 or not nobody is thirsty. It is publicly announced that Arthur 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 (~(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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Barbara can now know that Arthur can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arthur","Barbara","Cecilia"],"index":27043,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942287207,"difficulty":0.0057712793}
-{"premise":"There are two 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 Jodee knows whether or not nobody is thirsty. It is publicly announced that Jodee 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)) ] [ ! (Agenta knows whether (~(1|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 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jodee can now know whether Charles can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jodee","Charles"],"index":60570,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993953705,"difficulty":0.0006046295}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Quincy's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jess knows whether Quincy's forehead is muddy.","smcdel_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 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":"Quincy can now know that Jess can know that Quincy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jess","Alton","Quincy"],"index":6807,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9605138302,"difficulty":0.0394861698}
-{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (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":"Cindy can now know whether Sarah can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Sarah","Jesus","Ernest"],"index":30631,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994847775,"difficulty":0.0005152225}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marina 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&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":"Richard can now know that Marina can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Marina"],"index":51637,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988065958,"difficulty":0.0011934042}
-{"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 David 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb 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)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anthony","David","Sonya","Alicia"],"index":1923,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993718266,"difficulty":0.0006281734}
-{"premise":"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 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 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":"Jean can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","James","Doris"],"index":55619,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7564204931,"difficulty":1.7564204931}
-{"premise":"There are three persons. Everyone is visible 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 (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":"Charlene can now know that Shirley can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charlene","Shirley","Cathleen"],"index":38546,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947636127,"difficulty":0.0052363873}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derek 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 (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":"Barbara can now know that Timothy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Timothy","Derek"],"index":47078,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995168447,"difficulty":0.0004831553}
-{"premise":"There are four persons. Everyone is visible 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 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 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":"Jose can now know that Jesus can know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Marie","Jesus","Jose"],"index":49818,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994156361,"difficulty":0.0005843639}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leisa knows whether or not everyone is thirsty. It is publicly announced that Leisa knows whether Suzette 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 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) ] [ ! (1|2) ] 0","hypothesis":"Suzette can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Suzette","Leisa"],"index":33721,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990549684,"difficulty":0.0009450316}
-{"premise":"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 Edwin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (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) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Erik can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erik","Edwin"],"index":50793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987506866,"difficulty":0.0012493134}
-{"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 Dewey 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 (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 3) ] 0","hypothesis":"Dewey can now know whether Cynthia can know that Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cynthia","Thomas","Dewey"],"index":27924,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9920523167,"difficulty":0.0079476833}
-{"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 (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":"William can now know that Jana can know whether Jana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jana","William","Christina","John"],"index":56527,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5281531811,"difficulty":1.5281531811}
-{"premise":"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) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that Jorge can know that Jorge's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Martha","Jorge"],"index":41811,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959852695,"difficulty":0.0040147305}
-{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Mark can now know that Joe can know that Lien's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Melvin","Mark","Lien"],"index":38441,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955137372,"difficulty":0.0044862628}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cedric knows whether Cedric 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 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":"Elsa can now know whether Cedric can know that Edna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elsa","Cedric","Edna"],"index":22304,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9917581677,"difficulty":0.0082418323}
-{"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 Daniel. Daniel'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 someone picked a red card. It is publicly announced that Daniel picked a red card. It is publicly announced that Francine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (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:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 1 ] [ ! 2 ] 0","hypothesis":"Daniel can now know that Francine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Francine"],"index":53957,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989652634,"difficulty":0.0010347366}
-{"premise":"There are three persons. Everyone is visible 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'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 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":"Kenneth can now know that Gene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Gene","Julian"],"index":22812,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945181012,"difficulty":0.0054818988}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"John can now know whether Alfred can know whether Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfred","John","Tina"],"index":32974,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993020296,"difficulty":0.0006979704}
-{"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 Kim. Dorothy's card is shown to Dorothy. Lucille's card is shown to Lucille. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy 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 Dorothy does not know whether Kim 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 whether (Agentc knows that 1)","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":"Kim can now know whether Lucille can know that Kim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Dorothy","Lucille"],"index":23902,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7321740389,"difficulty":1.7321740389}
-{"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 (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":"Nancy can now know that Willie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Nancy","Willie","Lawrence"],"index":10686,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9920727611,"difficulty":0.0079272389}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dusty 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 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":"Brian can now know that Daniel can know that Dusty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Brian","Dusty","Daniel"],"index":10464,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982982278,"difficulty":0.0017017722}
-{"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|2|3|4))","n_announcements":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":"Orlando can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Yvonne","Orlando","Guy","Katherine"],"index":10109,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999499321,"difficulty":0.000500679}
-{"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 Pearlie. Edith's card is shown to Pearlie. Pearlie's card is shown to Aaron. Edith's card is shown to Aaron. Benjamin's card is shown to Benjamin. Aaron's card is shown to Edith. It is publicly announced that someone picked a red card. It is publicly announced that Pearlie knows whether or not nobody picked a red card. It is publicly announced that Pearlie 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 whether (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":"Pearlie can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Pearlie","Aaron","Benjamin","Edith"],"index":34039,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994468093,"difficulty":0.0005531907}
-{"premise":"There are four 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 1,2,3,4 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 (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) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know whether Lillie can know that Lillie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Lillie","Colleen","Charles"],"index":25519,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940438867,"difficulty":0.0059561133}
-{"premise":"There are two 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.","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 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":"Joyce can now know whether Gwendolyn can know that Joyce is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joyce","Gwendolyn"],"index":8532,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9518741369,"difficulty":1.9518741369}
-{"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 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":"Kathy can now know that Veronica can know that Barbara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathy","Fernando","Barbara","Veronica"],"index":51308,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997009635,"difficulty":0.002990365}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gertrude's card is shown to Gertrude. Elmer's card is shown to Gertrude. Billy's card is shown to Elmer. Billy's card is shown to Billy. Billy's card is shown to Sonia. It is publicly announced that someone picked a red card. It is publicly announced that Billy picked a red card. It is publicly announced that Gertrude 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|2|3|4))","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":"Gertrude can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gertrude","Elmer","Billy","Sonia"],"index":2032,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994546771,"difficulty":0.0005453229}
-{"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 Marie is thirsty. It is publicly announced that Frank 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)) ] (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) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Marie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Frank","Marie"],"index":41845,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990000129,"difficulty":0.0009999871}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Albert knows whether someone is thirsty. It is publicly announced that Frances knows whether or not nobody is thirsty. It is publicly announced that Richard knows whether Richard is thirsty. It is publicly announced that Frances 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 (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (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 (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Albert can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Richard","Frances","William"],"index":15491,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9935238361,"difficulty":0.0064761639}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurence 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 (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":"Eilene can now know whether Laurence can know whether Helen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laurence","Helen","Eilene","Simone"],"index":23954,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993983507,"difficulty":0.0006016493}
-{"premise":"There are three persons. Everyone is visible 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 Matthew's forehead is muddy.","smcdel_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 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 Matthew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lillian","Matthew","Edith"],"index":63314,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9960926175,"difficulty":0.0039073825}
-{"premise":"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 or not nobody's forehead is muddy. It is publicly announced that Ashley's forehead is not muddy. It is publicly announced that Brenda'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) ] 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Ashley can now know that Scott can know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Scott","Jo","Brenda"],"index":59966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992092252,"difficulty":0.0007907748}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwina knows whether or not everyone's forehead is muddy. It is publicly announced that Edwina does not know whether Edwina's forehead 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":"Wilma can now know that Edwina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wilma","William","Edwina"],"index":9234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9414023161,"difficulty":0.0585976839}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor does not know whether or not everyone's forehead is muddy. It is publicly announced that Margie knows whether Eleanor's forehead is muddy. It is publicly announced that Margie knows whether Eleanor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Margie can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margie","Karen","Eleanor","Thomas"],"index":66812,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994693398,"difficulty":0.0005306602}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas 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 4)","n_announcements":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":"Vernell can now know whether Patrick can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Vernell","Patrick","Robert"],"index":66868,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992613196,"difficulty":0.0007386804}
-{"premise":"There are four persons. Everyone is visible 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 John can know that Thurman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","John","Mary","Thurman"],"index":56418,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9909471273,"difficulty":0.0090528727}
-{"premise":"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 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 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":"William can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","William"],"index":8225,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994552732,"difficulty":0.0005447268}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Lori can now know that Arnita can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Arnita","Lori"],"index":29815,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999329567,"difficulty":0.000670433}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cyrus knows whether Tricia's forehead is muddy.","smcdel_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 (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 3) ] 0","hypothesis":"Laurie can now know whether Cyrus can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cyrus","Laurie","Tricia"],"index":31022,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992762208,"difficulty":0.0007237792}
-{"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 William. William's card is shown to Hector. Hector's card is shown to Hector. Michael's card is shown to Hector. Hector's card is shown to Michael. Hector's card is shown to Thomas. Michael's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that William picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(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:3 Agentb:1,2,3 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know that Hector can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Hector","Michael","Thomas"],"index":62354,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999011755,"difficulty":0.000988245}
-{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Nancy can now know that Ruth can know whether Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Ruth"],"index":31810,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994613528,"difficulty":0.0005386472}
-{"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 Delores 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) ] Agentc 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 1) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"James can now know that Delores can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Delores","Abraham","James","Robert"],"index":47116,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994789958,"difficulty":0.0005210042}
-{"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 (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":"Jennette can now know whether Matthew can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Jennette","Ralph"],"index":58954,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993066788,"difficulty":0.0006933212}
-{"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 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 (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":"Andrew can now know that Brian can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexa","Brian","Andrew"],"index":5726,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992600083,"difficulty":0.0007399917}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rita 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 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":"Sophia can now know whether Rita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sophia","Rita","Hugh"],"index":32916,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9851796627,"difficulty":0.0148203373}
-{"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. Rachel's card is shown to Michelle. Rachel's card is shown to Rachel. Michelle's card is shown to Heidi. Heidi's card is shown to Heidi. Rachel'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 someone picked a red card. It is publicly announced that Rachel picked a red card. It is publicly announced that Rachel 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 whether (Agenta knows whether 2)","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":"Heidi can now know whether Michelle can know whether Rachel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Rachel","Heidi","Marie"],"index":30117,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987333417,"difficulty":0.0012666583}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse knows whether someone is thirsty. It is publicly announced that Susan does not know whether Paul 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Karen can now know whether Jesse is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Jesse","Susan","Paul"],"index":65987,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9461240172,"difficulty":0.0538759828}
-{"premise":"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 Robert's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Kathleen does not know 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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (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 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Brad can know that Brad's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brad","Robert","Kathleen"],"index":4237,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9968727231,"difficulty":1.9968727231}
-{"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 Jennifer is thirsty. It is publicly announced that Jennifer 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agentd 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Jennifer can now know whether Laura can know that Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Robert","Laura","Jennifer"],"index":23064,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9934509993,"difficulty":0.0065490007}
-{"premise":"There are three persons. Everyone is visible 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 muddy.","smcdel_problem":"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":"Bernice can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marion","Bernice","Edward"],"index":64168,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988541603,"difficulty":0.0011458397}
-{"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 Mary. Matthew's card is shown to Matthew. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether or not everyone picked a red card. It is publicly announced that 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:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Matthew can now know whether Mary can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Matthew"],"index":12306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994180202,"difficulty":0.0005819798}
-{"premise":"There are four 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.","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) ] (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 3) ] 0","hypothesis":"Toni can now know that Tracy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Lee","Jennifer","Toni"],"index":31307,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966729879,"difficulty":0.0033270121}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arla's forehead is muddy.","smcdel_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 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":"Mark can now know that Arla can know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Betty","Arla"],"index":52812,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9920896292,"difficulty":0.0079103708}
-{"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 Amanda. Thomas's card is shown to Thomas. Amanda's card is shown to Margaret. Thomas'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 Amanda 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:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether Amanda can know whether Margaret picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Mary","Thomas","Margaret"],"index":28187,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987246394,"difficulty":0.0012753606}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Concetta 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Concetta can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Deanna","Concetta","Hattie"],"index":17729,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988433123,"difficulty":0.0011566877}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andres 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 4)","n_announcements":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 Hazel can know that Hazel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Andres","Robert","Hazel"],"index":4074,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8144268394,"difficulty":0.1855731606}
-{"premise":"There are two 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Steven can now know that Andrea can know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Andrea"],"index":7908,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6105528474,"difficulty":1.6105528474}
-{"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 or not everyone is thirsty.","smcdel_problem":"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 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":"Kimberly can now know that Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tracy","Lawrence","Kimberly","Roger"],"index":63586,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6982523799,"difficulty":0.3017476201}
-{"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 Walter. Cassandra's card is shown to Cassandra. Jenny's card is shown to Cassandra. Wayne's card is shown to Jenny. It is publicly announced that someone 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 Jenny does not know whether Walter picked a red card. It is publicly announced that Walter does not know whether Wayne 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) ] (Agenta knows whether 4)","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":"Walter can now know whether Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Cassandra","Jenny","Wayne"],"index":56991,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.971288085,"difficulty":0.028711915}
-{"premise":"There are three persons. Everyone is visible 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 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 (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":"Jordan can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Jordan","Cindy"],"index":59902,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990842342,"difficulty":0.0009157658}
-{"premise":"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) ] [ ! ~(2) ] 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) ] [ ! ~(2) ] 0","hypothesis":"Lizette can now know whether Mary can know that Valerie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lizette","Mary","Valerie"],"index":55564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9865292311,"difficulty":0.0134707689}
-{"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 Marjorie. Larry's card is shown to Marjorie. Mildred's card is shown to Larry. Joseph's card is shown to Mildred. Mildred'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:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know whether Joseph can know whether Mildred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marjorie","Larry","Mildred","Joseph"],"index":52564,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985585809,"difficulty":0.0014414191}
-{"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 Elliot is thirsty. It is publicly announced that Rita 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)) ] 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Sylvia can now know that Rita can know that Rita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Crystal","Rita","Elliot"],"index":56992,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7909383178,"difficulty":1.7909383178}
-{"premise":"There are two 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 John. John'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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 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:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Rose can now know that Rose picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rose","John"],"index":15060,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9353154898,"difficulty":0.0646845102}
-{"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 Dona 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) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Karen can now know that Dona can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Karen","Jeanie","Dona"],"index":31914,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990171194,"difficulty":0.0009828806}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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 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":"Sharon can now know that David can know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","David","William"],"index":37214,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998408854,"difficulty":0.001591146}
-{"premise":"There are four persons. Everyone is visible 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 Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"George can now know that Betty can know that Melody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Karen","George","Melody"],"index":42623,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981349707,"difficulty":0.0018650293}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eileen does not know whether or not everyone is thirsty. It is publicly announced that Juliet does not know whether Asuncion is thirsty. It is publicly announced that Asuncion does not know whether or not everyone is thirsty. It is publicly announced that Asuncion does not know whether Juliet 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) ] (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 (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Asuncion can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Asuncion","Eileen","Juliet"],"index":61128,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9850121737,"difficulty":0.0149878263}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sidney's card is shown to Jennifer. Whitney's card is shown to Jennifer. Jennifer's card is shown to Sidney. Jennifer's card is shown to Whitney. Sidney's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Sidney does not know whether Sidney 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) ] (Agenta 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 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jennifer can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jennifer","Sidney","Whitney","Robert"],"index":26596,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989635944,"difficulty":0.0010364056}
-{"premise":"There are three persons. Everyone is visible 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))) ] (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":"Steve can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gary","Betty","Steve"],"index":14005,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989638329,"difficulty":0.0010361671}
-{"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 Dawn is thirsty. It is publicly announced that Chad knows 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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Matthew can now know whether Elsie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elsie","Dawn","Matthew","Chad"],"index":32035,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994730353,"difficulty":0.0005269647}
-{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Thomas knows whether someone's forehead is muddy. It is publicly announced that Gail'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&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":"Gail can now know whether Thomas can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gail","Thomas"],"index":12778,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994022846,"difficulty":0.0005977154}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether someone's forehead is muddy. It is publicly announced that Denise 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (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)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Beverly can now know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Denise","George","Beverly","Robert"],"index":36761,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983073473,"difficulty":0.0016926527}
-{"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 Abel. Abel's card is shown to Yvonne. Yvonne's card is shown to Yvonne. Yvonne's card is shown to Katheryn. 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) ] 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 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yvonne can now know whether Kenneth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Abel","Yvonne","Katheryn"],"index":39753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8946009874,"difficulty":0.1053990126}
-{"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 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 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 (1&2&3)) ] 0","hypothesis":"Robert can now know whether Janice can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Janice","Virgil"],"index":43510,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9938200116,"difficulty":0.0061799884}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar does not know whether or not everyone's forehead is muddy. It is publicly announced that Suzanna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Everett can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Everett","Mollie","Suzanna","Edgar"],"index":30193,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994800687,"difficulty":0.0005199313}
-{"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 Patricia. Ethel's card is shown to Ethel. Eldon's card is shown to Ethel. Ethel'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 Patricia 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) ] (Agenta 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":"Patricia can now know that Ethel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Ethel","Eldon"],"index":19846,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9479324818,"difficulty":0.0520675182}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Juan can now know that Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Juan","Judy","Michael"],"index":29093,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9930637479,"difficulty":0.0069362521}
-{"premise":"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 Krista 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 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":"Mark can now know that Jessie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Krista","Mark"],"index":7716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9781980515,"difficulty":0.0218019485}
-{"premise":"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. It is publicly announced that Wanda'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) ] [ ! 3 ] [ ! 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) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Wanda can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tiffany","Thomas","Wanda","Keith"],"index":7122,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989732504,"difficulty":0.0010267496}
-{"premise":"There are two persons. Everyone is visible 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 Lynn 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 that 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":"Lynn can now know that Edna can know that Lynn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edna","Lynn"],"index":61403,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.987682879,"difficulty":0.012317121}
-{"premise":"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 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 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":"Donna can now know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Carolyn","Edward"],"index":54577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9789284468,"difficulty":0.0210715532}
-{"premise":"There are three persons. Everyone is visible 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 Norman'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|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":"Norman can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sharon","Anita","Norman"],"index":65908,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994303584,"difficulty":0.0005696416}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eun's card is shown to Rachel. Sherry's card is shown to James. Rachel's card is shown to Eun. Rachel's card is shown to Sherry. 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 that (Agenta knows whether 3)","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":"James can now know that Rachel can know whether Eun picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","James","Eun","Sherry"],"index":64885,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6429770589,"difficulty":1.6429770589}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Debra. Gretchen's card is shown to Debra. Debra's card is shown to Gretchen. It is publicly announced that someone 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)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Debra can now know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Reginald","Gretchen"],"index":13174,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8409997821,"difficulty":1.8409997821}
-{"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 Ruby. Ruby'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 Ruby knows whether Marie 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 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":"Ruby can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruby","Marie"],"index":26153,"s-l":"explicit-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). Jeffrey's card is shown to Earl. Earl's card is shown to Kerry. Earl'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 2)","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":"Kerry can now know whether Earl can know that Earl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Earl","Kerry","Shirley"],"index":17765,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8795042634,"difficulty":0.1204957366}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lula 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) ] [ ! (Agenta 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:1,2,3,4 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":"Margaret 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":["Lula","Brenda","Margaret","William"],"index":53465,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993535876,"difficulty":0.0006464124}
-{"premise":"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 Matthew knows whether Kimberley's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy. It is publicly announced that Kimberley'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) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Norma can now know that Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Norma","Kimberley"],"index":3679,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.985182941,"difficulty":0.014817059}
-{"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 or not everyone is thirsty. It is publicly announced that David knows whether someone is thirsty. It is publicly announced that Dennis 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 (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (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)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Joanne can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Dennis","Joanne"],"index":63865,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9440400004,"difficulty":0.0559599996}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lakiesha's card is shown to Larry. Michael's card is shown to Larry. Lakiesha's card is shown to Lakiesha. 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 Larry picked a red card. It is publicly announced that Lakiesha knows whether Lakiesha picked a red card. It is publicly announced that Lakiesha does not know whether or not everyone picked a red card. It is publicly announced that Michael knows whether Lakiesha 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) ] (Agentc knows whether (1&2&3))","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":"Michael can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Lakiesha","Michael"],"index":23439,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5789123774,"difficulty":0.4210876226}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irma 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) ] [ ! ~(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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Anthony can now know that Irma can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ana","Irma","Marie","Anthony"],"index":42415,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990257025,"difficulty":0.0009742975}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shelly's card is shown to Shelly. David's card is shown to Shelly. Shelly's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Shelly 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 (Agenta knows whether (1&2&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":"Shelly can now know whether Jewel can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jewel","Shelly","David"],"index":22447,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8008099794,"difficulty":0.1991900206}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gennie knows whether Gennie's forehead 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":"Gennie can now know whether Walter can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Walter","Robert","Gennie"],"index":59627,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9672124982,"difficulty":0.0327875018}
-{"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 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":"Ernest can now know that Francesca can know whether Wanda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Ernest","Wanda","Francesca"],"index":7357,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998239398,"difficulty":0.001760602}
-{"premise":"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 muddy.","smcdel_problem":"VARS 1,2,3,4 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 (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) ] [ ! 3 ] 0","hypothesis":"Janet can now know whether Jeffrey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Jeffrey","Janet","Iris"],"index":43591,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992797971,"difficulty":0.0007202029}
-{"premise":"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 Peggy does not know whether Peggy's forehead 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 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":"Tenisha can now know that Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Tenisha","Peggy"],"index":46327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960557222,"difficulty":0.0039442778}
-{"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 Tina is thirsty.","smcdel_problem":"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) ] 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Tina can now know that David can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Tina","Barbara","James"],"index":65344,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8394255042,"difficulty":0.1605744958}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamie 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) ] [ ! 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) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jamie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Jamie","Rick","Ronald"],"index":67297,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981713295,"difficulty":0.0018286705}
-{"premise":"There are two 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 Hazel. It is publicly announced that someone picked a red card. It is publicly announced that Hazel does not know whether or not everyone picked a red card. It is publicly announced that Hazel does not know whether or not everyone picked a red card. It is publicly announced that Joe knows whether or not nobody picked a red card. It is publicly announced that Joe 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 (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb 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 (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Hazel can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joe","Hazel"],"index":37121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994503856,"difficulty":0.0005496144}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clara's card is shown to Nancy. Andrew's card is shown to Nancy. Clara's card is shown to Clara. Nancy's card is shown to Andrew. It is publicly announced that someone picked a red card. It is publicly announced that Nancy knows whether Clara 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) ] (Agentb 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":"Clara can now know that Clara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Clara","Andrew"],"index":47591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9850997329,"difficulty":0.0149002671}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnulfo's card is shown to Ethel. Ethel's card is shown to David. David's card is shown to David. 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:3 Agentb:1,2 Agentc: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:3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Arnulfo can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ethel","David","Arnulfo","Richard"],"index":26254,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994058609,"difficulty":0.0005941391}
-{"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 Martin. Martin's card is shown to Donna. Paul's card is shown to Donna. 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 Martin 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 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":"Donna can now know whether Paul can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martin","Donna","Paul"],"index":9392,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9670968652,"difficulty":0.0329031348}
-{"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 James. Jason's card is shown to Sean. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Sean does not know whether James 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) ] (Agenta knows whether 1)","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":"James can now know whether James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Sean","Jason"],"index":63459,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6852491498,"difficulty":0.3147508502}
-{"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 Carolina. Emily's card is shown to Carolina. Israel's card is shown to Geraldine. Emily's card is shown to Geraldine. Carolina's card is shown to Israel. Israel's card is shown to Israel. Emily's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Emily does not know whether Geraldine picked a red card. It is publicly announced that Israel does not know whether Geraldine 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) ] (Agentb knows that (1&2&3&4))","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":"Geraldine can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carolina","Geraldine","Israel","Emily"],"index":54568,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989507198,"difficulty":0.0010492802}
-{"premise":"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 (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":"Larry can now know that Samuel can know that Lucia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucia","Ester","Larry","Samuel"],"index":41913,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903880954,"difficulty":0.0096119046}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clara 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 4) ] 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) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Clara can now know whether Mary can know that Rhonda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Clara","Donald","Rhonda","Mary"],"index":53808,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9933871627,"difficulty":0.0066128373}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Modesta'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 (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":"Modesta can now know that Barbara can know that Rudolph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rudolph","Modesta","Barbara","Robert"],"index":15818,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977472425,"difficulty":0.0022527575}
-{"premise":"There are 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 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":"James can now know that Sharon can know that Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sharon","Danny","Mary","James"],"index":33732,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976555109,"difficulty":0.0023444891}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maurine knows whether Elmer's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elmer does not know whether Elmer's forehead 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 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 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Maurine can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maurine","David","Elmer"],"index":41538,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994220734,"difficulty":0.0005779266}
-{"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 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 (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":"Rebecca can now know whether Jessica can know that Crystal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebecca","Jessica","Crystal"],"index":1627,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9950963855,"difficulty":0.0049036145}
-{"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 Deborah. Jack's card is shown to Deborah. Deborah'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:1,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know whether Jack picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Jonathan","Jack"],"index":55242,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9205588102,"difficulty":1.9205588102}
-{"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. Elizabeth's card is shown to Helen. Elizabeth's card is shown to Sharon. Helen's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Elizabeth 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 ] Agentb knows that (Agenta knows that (1&2&3))","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":"Sharon can now know that Helen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Sharon","Elizabeth"],"index":19123,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985297918,"difficulty":0.0014702082}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patsy knows whether Patsy's forehead is muddy.","smcdel_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 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":"Phillip can now know whether Patsy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Allen","Patsy","Phillip"],"index":55776,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994463325,"difficulty":0.0005536675}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Dennis can now know that Letitia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Letitia","Dennis","Leon"],"index":36999,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990544915,"difficulty":0.0009455085}
-{"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. Carl's card is shown to Linda. Mary's card is shown to Linda. Carl's card is shown to Elmer. Carl's card is shown to Carl. Carl's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Elmer 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 (Agentd 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":"Elmer can now know that Mary can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Elmer","Carl","Mary"],"index":45621,"s-l":"explicit-0","deberta_pred":0,"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). Nicole's card is shown to Joyce. John's card is shown to Joyce. Joyce's card is shown to Emmanuel. John's card is shown to Emmanuel. Emmanuel'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:2,4 Agentb:1,4 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:2,4 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know whether Emmanuel can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joyce","Nicole","Emmanuel","John"],"index":41031,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9576574564,"difficulty":0.0423425436}
-{"premise":"There are four persons. Everyone is visible 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)) ] 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":"Michel can now know that James can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Yasmine","Michel","James","Mary"],"index":14557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987627268,"difficulty":0.0012372732}
-{"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. Christine's card is shown to Nadia. Nadia's card is shown to Christine. 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.","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)) ] (Agentc knows whether 2)","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":"Nadia can now know whether Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Brian","Nadia","Christine"],"index":50276,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9686134458,"difficulty":0.0313865542}
-{"premise":"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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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 or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erika","Tracy","Robert","Gail"],"index":48287,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6020358801,"difficulty":1.6020358801}
-{"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 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 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":"Michael can now know that Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Robert"],"index":32483,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977152348,"difficulty":0.0022847652}
-{"premise":"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 not 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) ] [ ! ~(2) ] [ ! (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) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Timothy can now know whether Lois's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Timothy","Lois"],"index":26523,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993031025,"difficulty":0.0006968975}
-{"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 Monica. Joyce's card is shown to Lori. Lori's card is shown to Lori. Kari's card is shown to Lori. Monica's card is shown to Kari. 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. It is publicly announced that Joyce 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) ] Agentb knows whether (Agentc knows whether 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":"Joyce can now know whether Lori can know whether Kari picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Joyce","Lori","Kari"],"index":63836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981927276,"difficulty":0.0018072724}
-{"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 Bernard is thirsty. It is publicly announced that Albert 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 (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":"Albert can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Albert","Bernard"],"index":59362,"s-l":"internal-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 Joseph knows whether Mariano's forehead is muddy.","smcdel_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 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":"Mariano can now know that Betty can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Mariano","Joseph"],"index":67503,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991163611,"difficulty":0.0008836389}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Constance's card is shown to Constance. Constance's card is shown to Michelle. Steven's card is shown to Matthew. 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:1 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 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michelle can now know that Steven can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Constance","Michelle","Steven","Matthew"],"index":21988,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990332127,"difficulty":0.0009667873}
-{"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 Margaret. Margaret'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 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:1,2 VALID? [ ! (1|2) ] [ ! 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:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (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":["Margaret","John"],"index":47684,"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). Rex'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 Kenneth 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))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kenneth","Rex"],"index":63242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9899140596,"difficulty":0.0100859404}
-{"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 Michael. Richard's card is shown to Darrell. Michael's card is shown to Richard. Darrell'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. It is publicly announced that Michael 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)) ] Agentc knows whether (Agenta knows whether (1&2&3))","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":"Richard can now know whether Michael can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Darrell","Richard"],"index":34163,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9493461847,"difficulty":0.0506538153}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alec's card is shown to Alec. Alec'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 Alec 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 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":"Alec can now know that Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alec","Robert"],"index":35411,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988805652,"difficulty":0.0011194348}
-{"premise":"There are four persons. Everyone is visible 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) ] (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":"James can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Mary","Milton","Olive"],"index":8536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9988738894,"difficulty":0.0011261106}
-{"premise":"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 knows whether 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) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Valerie can now know that Margaret can know that Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jim","Maggie","Valerie","Margaret"],"index":67624,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994297564,"difficulty":0.005702436}
-{"premise":"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's forehead is muddy. It is publicly announced that Earl knows whether 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) ] [ ! 1 ] [ ! (Agentc 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: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":"Thomas can now know whether Carolyn can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Carolyn","Earl"],"index":59775,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994158745,"difficulty":0.0005841255}
-{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jim can now know that Howard can know that Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jim","Carmella","Howard"],"index":2942,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975281358,"difficulty":0.0024718642}
-{"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 thirsty. It is publicly announced that Carol 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":"Carol can now know that Tanya can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carol","Roger","Tanya"],"index":53747,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973795414,"difficulty":0.0026204586}
-{"premise":"There are three 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 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"George can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betsy","Robert","George"],"index":48839,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980290532,"difficulty":0.0019709468}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelvin does not know whether Ernest is thirsty. It is publicly announced that Sharon 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)) ] Agenta 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) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ernest can now know whether Kelvin can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Sharon","James","Kelvin"],"index":49923,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992625117,"difficulty":0.0007374883}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darnell's card is shown to Darnell. Johnnie's card is shown to Darnell. Nicole's card is shown to Holly. Darnell's card is shown to Johnnie. Nicole's card is shown to Johnnie. Holly's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Darnell picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Johnnie 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) ] 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 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":"Darnell can now know that Johnnie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darnell","Holly","Johnnie","Nicole"],"index":31534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993408322,"difficulty":0.0006591678}
-{"premise":"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 (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":"Sharon can now know that Lora can know that Lora's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carmelina","Jesse","Lora","Sharon"],"index":26624,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931806326,"difficulty":0.0068193674}
-{"premise":"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 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":"Richard can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Elaine","Megan"],"index":32601,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989566803,"difficulty":0.0010433197}
-{"premise":"There are four persons. Everyone is visible 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'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 (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":"Juanita can now know that Johnny can know that Grace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Johnny","Juanita","Grace"],"index":30236,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974977374,"difficulty":0.0025022626}
-{"premise":"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 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 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":"Audrey can now know whether Anne can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audrey","Sarah","Maria","Anne"],"index":53148,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990665317,"difficulty":0.0009334683}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Seth 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 (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":"Seth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Seth","Annie","Brittney"],"index":50204,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9877891541,"difficulty":0.0122108459}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thurman does not know whether Thurman'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) ] [ ! ~(Agenta 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: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":"Thurman can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thurman","Dorothy","Patrick","Milan"],"index":61950,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978495836,"difficulty":0.0021504164}
-{"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 someone is thirsty. It is publicly announced that Holly 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 (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] Agentc 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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Holly can now know whether Joseph can know that Cheryl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Cheryl","Holly","Tamika"],"index":28916,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9781256318,"difficulty":0.0218743682}
-{"premise":"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 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 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) ] 0","hypothesis":"Bryant can now know whether Kevin can know that Bryant's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Sue","Bryant"],"index":33910,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6150203347,"difficulty":0.3849796653}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kris is not thirsty. It is publicly announced that Gearldine does not know whether Madeline is 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) ] (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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Madeline can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Gearldine","Madeline","Kris"],"index":44267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989081621,"difficulty":0.0010918379}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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":"Angela can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Doris","Angela","Gerald"],"index":13560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994427562,"difficulty":0.0005572438}
-{"premise":"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 does not know whether Brian's forehead is muddy. It is publicly announced that Kenton 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 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(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":["Brian","William","Kenton","Ronald"],"index":62031,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973762035,"difficulty":0.0026237965}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mabel does not know whether Mabel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Ruth can now know whether Michael can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Michael","Ruth","Mabel"],"index":30676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967904687,"difficulty":0.0032095313}
-{"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. Colleen's card is shown to Carol. Erica's card is shown to Carol. Carol's card is shown to Delmar. Erica's card is shown to Delmar. Carol's card is shown to Erica. It is publicly announced that someone picked a red card. It is publicly announced that Delmar knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 Agentc:1 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:1,2,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Colleen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carol","Colleen","Delmar","Erica"],"index":5815,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994606376,"difficulty":0.0005393624}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucas is thirsty. It is publicly announced that James knows whether Lucas 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 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 3) ] 0","hypothesis":"Lucas can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Gerald","Lucas"],"index":52143,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994931221,"difficulty":0.0005068779}
-{"premise":"There are two 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 or not everyone's forehead is muddy. It is publicly announced that Juana 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 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)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Juana can now know whether Zachary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Zachary","Juana"],"index":36370,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9767363071,"difficulty":0.0232636929}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tatiana knows whether Robert's forehead is muddy. It is publicly announced that Tatiana'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 (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":"Robert can now know whether Tatiana can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Tatiana"],"index":37551,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994408488,"difficulty":0.0005591512}
-{"premise":"There are four persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Marie knows whether Marie's forehead is muddy. It is publicly announced that Derek's forehead is muddy. It is publicly announced that Dora 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 (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc 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) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Marie can now know whether Dora can know that Derek's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Derek","Marie","Dora","Maria"],"index":747,"s-l":"forehead_mirror-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 Gloria does not know whether Gloria's forehead is muddy. It is publicly announced that Stewart's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 ] (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 4) ] [ ! 3 ] 0","hypothesis":"Gloria can now know that Stewart's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lauri","Adrian","Stewart","Gloria"],"index":57614,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7839038968,"difficulty":1.7839038968}
-{"premise":"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 knows whether Elbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Debra can now know whether Alice can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alice","Debra","Carrie","Elbert"],"index":10140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903967381,"difficulty":0.0096032619}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alissa's card is shown to Alissa. Lisa's card is shown to Alissa. Alissa'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 Alissa picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(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 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lisa can now know that Alissa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alissa","Lisa"],"index":34485,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978938699,"difficulty":0.0021061301}
-{"premise":"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 Marina does not know whether Marina's forehead is muddy. It is publicly announced that Jack knows whether Frank's forehead is muddy. It is publicly announced that Marina does not know whether 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 (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (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 (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jack can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Jack","Barbara","Marina"],"index":34593,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990659356,"difficulty":0.0009340644}
-{"premise":"There are two persons. Everyone is visible 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 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":"Walter can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","Michael"],"index":1150,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989753962,"difficulty":0.0010246038}
-{"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. Mavis's card is shown to John. George's card is shown to Mavis. Mavis's card is shown to Mavis. It is publicly announced that someone picked a red card. It is publicly announced that George knows whether John 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) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","George","Mavis"],"index":17304,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.859649539,"difficulty":0.140350461}
-{"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 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":"Olin can now know whether Elva can know whether Elva is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olin","Rebecca","Joshua","Elva"],"index":13388,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9946920276,"difficulty":0.0053079724}
-{"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 Tracey. Thomas's card is shown to Thomas. 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 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know that Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracey","Thomas","Michael"],"index":8946,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9924701452,"difficulty":0.0075298548}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mable knows whether Mable 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 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":"Amy can now know that Angela can know that Angela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amy","Angela","Mable"],"index":7809,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9795871377,"difficulty":0.0204128623}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mamie's card is shown to Mamie. Malka's card is shown to Leonora. Leonora's card is shown to Malka. It is publicly announced that someone picked a red card. It is publicly announced that Madeline 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)) ] (Agentc 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":"Leonora can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mamie","Madeline","Leonora","Malka"],"index":66457,"s-l":"explicit-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.","smcdel_problem":"VARS 1,2,3,4 LAW Top 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 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":"Ronald can now know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Teresa","Wanda","Ronald"],"index":13852,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962190986,"difficulty":0.0037809014}
-{"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 Chris. Chris's card is shown to William. William's card is shown to Eva. Eva's card is shown to Eva. Eva's card is shown to Sherry. It is publicly announced that someone picked a red card. It is publicly announced that Sherry does not know whether Chris picked a red card. It is publicly announced that Chris does not know whether William picked a red card. It is publicly announced that Eva knows whether Eva 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 (1|2|3|4))","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":"Sherry can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Chris","William","Eva","Sherry"],"index":39104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994482398,"difficulty":0.0005517602}
-{"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 (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":"Jeremy can now know that Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denise","Robert","Jeremy","Brian"],"index":29711,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987724423,"difficulty":0.0012275577}
-{"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 Kathleen is thirsty. It is publicly announced that Theresa 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) ] (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) ] [ ! ~(3) ] 0","hypothesis":"Theresa can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Charles","Theresa"],"index":40693,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995069504,"difficulty":0.0004930496}
-{"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. Billy's card is shown to Christopher. Christopher's card is shown to Evelyn. Billy's card is shown to Evelyn. Kenneth's card is shown to Evelyn. Billy's card is shown to Billy. Billy'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 Evelyn picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,3,4 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,3,4 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Evelyn can now know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Evelyn","Billy","Kenneth"],"index":66271,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8333765268,"difficulty":0.1666234732}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rashida knows whether Rashida's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Harry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rashida","Clara","Harry","William"],"index":55089,"s-l":"forehead-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). Leonard's card is shown to Michael. Leonard's card is shown to Brian. Brian's card is shown to Brian. Brian'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:2,3 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:2 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brian can now know that Michael can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Leonard","Brian","Ronald"],"index":13054,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934802055,"difficulty":0.0065197945}
-{"premise":"There are 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":"Tonya can now know whether Gregory can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Tonya","Steven","Allen"],"index":38842,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992361069,"difficulty":0.0007638931}
-{"premise":"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 Nancy'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 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)) ] [ ! ~(2) ] 0","hypothesis":"Ethel can now know whether Nancy can know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ethel","Nancy"],"index":25663,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.989341855,"difficulty":0.010658145}
-{"premise":"There are four persons. Everyone is visible 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 Faith knows whether Faith's forehead is muddy. It is publicly announced that Michael knows whether Faith's forehead is muddy. It is publicly announced that Faith knows whether Joan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 3)","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":"Joan can now know that Fred can know that Faith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Joan","Faith","Fred"],"index":21507,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9970926046,"difficulty":0.0029073954}
-{"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. Selena's card is shown to Robert. Robert's card is shown to Richard. Robert's card is shown to Selena. 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 (Agentb knows whether 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":"Robert can now know that Richard can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Richard","Selena"],"index":44172,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9352275729,"difficulty":0.0647724271}
-{"premise":"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's forehead 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 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) ] [ ! 3 ] 0","hypothesis":"Thomas can now know that Thelma can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Thomas","Thelma"],"index":53590,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7814698219,"difficulty":0.2185301781}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_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 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":"Charles can now know that Eleanor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Eleanor","Charles"],"index":61024,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.997682929,"difficulty":0.002317071}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donovan knows whether Sherry'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: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 (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":"Donovan can now know that Sherry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Sherry","Donovan"],"index":56767,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989117384,"difficulty":0.0010882616}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adrian's card is shown to Adrian. James's card is shown to James. Armando's card is shown to Edgar. Edgar's card is shown to Edgar. 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) ] (Agentb 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":"Adrian can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Armando","Adrian","James","Edgar"],"index":49277,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989097118,"difficulty":0.0010902882}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Silvia knows whether or not everyone's forehead is muddy. It is publicly announced that 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 (1&2)) ] [ ! 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)) ] [ ! 2 ] 0","hypothesis":"Silvia can now know that Silvia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Silvia","Derrick"],"index":34107,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.980987668,"difficulty":0.019012332}
-{"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 Carlos. Carlos's card is shown to Carlos. Lisa'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:1,2 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:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Carlos can know that Carlos picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Carlos","Mark"],"index":3203,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5567389131,"difficulty":0.4432610869}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwight does not know whether Dwight's forehead is muddy. It is publicly announced that Dwight's forehead is not muddy. It is publicly announced that Dwight 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) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Wanda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dwight","Wanda"],"index":63761,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987506866,"difficulty":0.0012493134}
-{"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 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) ] [ ! ~(Agentd knows whether 3) ] 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) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Craig can now know that Corey can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alicia","Corey","Craig","William"],"index":47784,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993317723,"difficulty":0.0006682277}
-{"premise":"There are two 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 does not know whether or not everyone 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)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb 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&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Joseph can now know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kimberly","Joseph"],"index":59286,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997989893,"difficulty":0.002010107}
-{"premise":"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":"Andre can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andre","Clara"],"index":15308,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.956392467,"difficulty":0.043607533}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! 3 ] 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) ] [ ! 3 ] 0","hypothesis":"Miriam can now know that Ann can know that Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Ann","Miriam","Todd"],"index":8872,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952715039,"difficulty":0.0047284961}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sterling's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 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":"Susan can now know whether Sterling can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alisa","Steven","Sterling","Susan"],"index":59859,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9937864542,"difficulty":1.9937864542}
-{"premise":"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 does not know whether Sadie's forehead 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":"Sadie can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sadie","Thomas","Joseph"],"index":57439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994441867,"difficulty":0.0005558133}
-{"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 Lillian 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) ] [ ! (Agentb knows whether 1) ] [ ! (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) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Christine can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lillian","Christine"],"index":2615,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994198084,"difficulty":0.0005801916}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cindi's card is shown to Cindi. Liana's card is shown to Cindi. Cindi's card is shown to Liana. Liana's card is shown to Liana. It is publicly announced that someone picked a red card. It is publicly announced that Cindi knows whether Liana picked a red card. It is publicly announced that Cindi 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) ] [ ! 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) ] [ ! (Agenta knows whether 2) ] [ ! 1 ] 0","hypothesis":"Liana can now know whether Cindi picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cindi","Liana"],"index":50228,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9821692109,"difficulty":0.0178307891}
-{"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 Kimberly is thirsty. It is publicly announced that Christopher is thirsty. It is publicly announced that Kimberly is thirsty. It is publicly announced that Christopher 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 (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":"Christopher can now know whether Kimberly can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Kimberly","Mary"],"index":7332,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994831085,"difficulty":0.0005168915}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ginger is not thirsty. It is publicly announced that Jessica knows whether or not everyone is thirsty. It is publicly announced that Ginger 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 (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":"Andrew can now know whether Jessica can know whether Andrew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Andrew","Ginger","Charles"],"index":43075,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989558458,"difficulty":0.0010441542}
-{"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 Janice. David's card is shown to Janice. Arthur's card is shown to Janice. David's card is shown to David. Arthur's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Arthur 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) ] 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:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"David can now know whether Arthur can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Janice","David","Arthur"],"index":14018,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8393124938,"difficulty":0.1606875062}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne 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 (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":"Suzanne can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eryn","Beverly","Suzanne"],"index":17417,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994702935,"difficulty":0.0005297065}
-{"premise":"There are three persons. Everyone is visible 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.","smcdel_problem":"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":"Timothy can now know that Jerome can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","Jerome","Timothy"],"index":13878,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989461303,"difficulty":0.0010538697}
-{"premise":"There are three persons. Everyone is visible 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 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":"Duane can now know that Leo can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leo","Duane","Victor"],"index":21645,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989695549,"difficulty":0.0010304451}
-{"premise":"There are four persons. Everyone is visible 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 Traci's forehead is muddy. It is publicly announced that Traci knows whether Traci's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (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 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jim can now know whether James can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Traci","James","Jim"],"index":27907,"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 Dorothy 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 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) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Dorothy can now know whether Barry can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darla","Dorothy","Barry","John"],"index":8404,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993078709,"difficulty":0.0006921291}
-{"premise":"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.","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 3)","n_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":"Richard can now know that Eric can know whether Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Richard","Eric"],"index":55582,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964717627,"difficulty":0.0035282373}
-{"premise":"There are four persons. Everyone is visible 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 knows whether someone's forehead is muddy. It is publicly announced that Brandon 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentc knows whether 2) ] 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","Ronald","Brandon","Don"],"index":29025,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980546236,"difficulty":0.0019453764}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Felicia 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)) ] (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 (1&2&3&4)) ] 0","hypothesis":"Betty can now know that Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Betty","Felicia","William"],"index":57808,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9898263216,"difficulty":0.0101736784}
-{"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 Patricia 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 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":"Robert can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patricia","Robert"],"index":7469,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987395406,"difficulty":0.0012604594}
-{"premise":"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) ] [ ! 2 ] (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":"Joyce can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lola","Joyce","Yvonne","Nella"],"index":55088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994829893,"difficulty":0.0005170107}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Joshua. Joshua's card is shown to Anne. 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. It is publicly announced that Anne knows whether Anne 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 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)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joshua can now know that Anne can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joshua","Anne"],"index":17325,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975824356,"difficulty":0.0024175644}
-{"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 Carl. Emily's card is shown to Joyce. Jennie's card is shown to Joyce. Carl's card is shown to Emily. Jennie's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Carl does not know whether Jennie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Carl can now know whether Emily can know that Jennie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carl","Joyce","Emily","Jennie"],"index":51186,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8844183087,"difficulty":1.8844183087}
-{"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 Michael. Lisa's card is shown to Michael. Michael's card is shown to Angel. Donald's card is shown to Angel. Lisa's card is shown to Angel. Michael's card is shown to Donald. Angel'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:1,3,4 Agentc:1 Agentd: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:3,4 Agentb:1,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know whether Michael can know whether Donald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Angel","Donald","Lisa"],"index":50891,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976410866,"difficulty":0.0023589134}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronnie knows whether someone's forehead is muddy. It is publicly announced that Ronnie 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 (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":"Ronnie can now know that Marna can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marna","Zachary","Michelle","Ronnie"],"index":43079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9907859564,"difficulty":0.0092140436}
-{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Rita can now know that William can know that Cecelia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cecelia","William","Kenneth","Rita"],"index":30030,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996946156,"difficulty":0.003053844}
-{"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 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) ] 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) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Karl can now know whether Lawrence can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ron","Karl","Lawrence","Robert"],"index":21791,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993802309,"difficulty":0.0006197691}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Odell 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 (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) ] [ ! ~(3) ] 0","hypothesis":"Odell can now know whether Samuel can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Samuel","Darren","Odell"],"index":18799,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995110035,"difficulty":0.0004889965}
-{"premise":"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. 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 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Patrick can now know that Eric can know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ivan","Michael","Eric","Patrick"],"index":41785,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99386096,"difficulty":0.00613904}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rossie 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 (~(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":"Wendy can now know that Rossie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","Wendy","Rossie"],"index":58983,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994722009,"difficulty":0.0005277991}
-{"premise":"There are two persons. Everyone is visible 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 Tonya'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 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":"Brenda can now know that Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brenda","Tonya"],"index":2435,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928435683,"difficulty":0.0071564317}
-{"premise":"There are three persons. Everyone is visible 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 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 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":"Charles can now know that Rose can know whether Marie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","Rose","Charles"],"index":44554,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993464351,"difficulty":0.0006535649}
-{"premise":"There are four 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 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) ] [ ! 3 ] [ ! (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) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Brenda","Renee","Joseph"],"index":57334,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9523705244,"difficulty":0.0476294756}
-{"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 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) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Cheryl can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pedro","Cheryl","Gregory","Andrew"],"index":25469,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989905953,"difficulty":0.0010094047}
-{"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. Emilio's card is shown to Beverly. Tammy's card is shown to Beverly. Tammy's card is shown to Emilio. Emilio's card is shown to Tammy. Tammy'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:2,3,4 Agentb:4 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:2,3,4 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emilio can now know whether David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Beverly","Emilio","Tammy"],"index":60618,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978690147,"difficulty":0.0021309853}
-{"premise":"There are 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 (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":"Andrew can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mario","Angela","Andrew","Shanae"],"index":63041,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993638396,"difficulty":0.0006361604}
-{"premise":"There are two persons. Everyone is visible 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 Jerry'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 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":"Josephine can now know whether Jerry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Josephine","Jerry"],"index":52547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993779659,"difficulty":0.0006220341}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leanna does not know whether Leanna's forehead 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|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":"Leanna can now know whether Darlene can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Leanna","Darlene"],"index":35624,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994276166,"difficulty":0.0005723834}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daphine's card is shown to Daphine. William's card is shown to Daphine. Ellen's card is shown to Ellen. William's card is shown to Ellen. Daphine'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) ] 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:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Daphine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daphine","Ellen","William"],"index":23795,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9811378717,"difficulty":0.0188621283}
-{"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 Carin is thirsty.","smcdel_problem":"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)","n_announcements":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":"Carin can now know that Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Nellie","Carin","Louis"],"index":40291,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979972243,"difficulty":0.0020027757}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina 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 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":"Regina can now know whether Betsy can know that Regina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Regina","Thelma","Betsy"],"index":24934,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8963709474,"difficulty":0.1036290526}
-{"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. Travis's card is shown to Sandra. Travis's card is shown to Travis. Sandra's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Travis 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 (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":"Sandra can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","Travis","Anna"],"index":15376,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9501934648,"difficulty":0.0498065352}
-{"premise":"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 Monica'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 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) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Monica can now know that Megan can know that Monica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Megan","Monica","Virginia"],"index":67356,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954688549,"difficulty":0.0045311451}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terry is not thirsty. It is publicly announced that Megan 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) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 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) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Larry can now know that Terry can know that Larry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Tracy","Terry","Megan"],"index":57115,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950953722,"difficulty":0.0049046278}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kylie's card is shown to Kylie. Deanna's card is shown to Norman. Norman's card is shown to James. Kylie's card is shown to Deanna. Norman's card is shown to Deanna. 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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows whether 2)","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":"Norman can now know whether Norman picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kylie","Norman","James","Deanna"],"index":19411,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5784884095,"difficulty":0.4215115905}
-{"premise":"There are three persons. Everyone is visible 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 Ross's forehead is muddy.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Alexander can now know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Veronica","Ross","Alexander"],"index":12969,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998257935,"difficulty":0.001742065}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincenzo's card is shown to Cody. David's card is shown to David. David's card is shown to Jared. It is publicly announced that someone 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:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Vincenzo can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cody","Vincenzo","David","Jared"],"index":12436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994451404,"difficulty":0.0005548596}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregg does not know whether or not everyone is thirsty. It is publicly announced that Gregg does not know whether or not everyone is thirsty. It is publicly announced that Gregg does not know whether or not everyone is thirsty. It is publicly announced that Gregg does not know whether Nathan 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":"Gregg can now know that Nathan can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregg","Nathan"],"index":34651,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994675517,"difficulty":0.0005324483}
-{"premise":"There are three persons. Everyone is visible 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 Donald's forehead is muddy.","smcdel_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 (1|2|3))","n_announcements":1,"pbcheck":"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":"Donald can now know whether Paul can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","Donald","Brian"],"index":66619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993627667,"difficulty":0.0006372333}
-{"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. James's card is shown to Antonio. Antonio's card is shown to Michael. James'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. It is publicly announced that someone picked a red card. It is publicly announced that Antonio knows whether or not nobody picked a red card. It is publicly announced that James knows whether Michael 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)","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":"Antonio can now know that Antonio picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antonio","James","Michael"],"index":29513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.994361639,"difficulty":0.005638361}
-{"premise":"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 (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":"Luis can now know that Ralph can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Ralph","Luis","Barbara"],"index":64089,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957593083,"difficulty":0.0042406917}
-{"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 Susannah. Tessa's card is shown to Tessa. Susannah'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 Tessa 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:1,3 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:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Susannah can now know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Susannah","Tessa","Dorothy"],"index":22121,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8732469082,"difficulty":0.1267530918}
-{"premise":"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's forehead is muddy. It is publicly announced that Edward's forehead is muddy. It is publicly announced that Susie 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 (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 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Julius can now know that Susie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Edward","Julius","Susie"],"index":2347,"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'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 (~(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":"Jesse can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Colin","Jesse","Mary","Wendy"],"index":9233,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998849988,"difficulty":0.001150012}
-{"premise":"There are two persons. Everyone is visible 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 Steven 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)","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":"Steven can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Steven","Robbin"],"index":37482,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948241711,"difficulty":0.0051758289}
-{"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 Charlotte. Charlotte's card is shown to Patsy. Patsy's card is shown to Patsy. Jared's card is shown to Patsy. Charlotte's card is shown to Jared. It is publicly announced that someone picked a red card. It is publicly announced that Jared 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)) ] Agentc knows that (Agenta knows that 1)","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":"Jared can now know that Charlotte can know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlotte","Patsy","Jared"],"index":620,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6509642005,"difficulty":1.6509642005}
-{"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. Lewis's card is shown to John. Annie's card is shown to John. John's card is shown to Lewis. Lewis's card is shown to Paula. Annie'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:1,2,4 Agentb:1 Agentc:2,4 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:1,2,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Paula can now know whether Lewis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lewis","Paula","Annie"],"index":60102,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994044304,"difficulty":0.0005955696}
-{"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 Matthew. Matthew's card is shown to Sidney. Dawn's card is shown to Sidney. Sidney's card is shown to Dawn. It is publicly announced that someone picked a red card. It is publicly announced that Sidney 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 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:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Matthew can now know that Sidney can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Matthew","Sidney","Dawn"],"index":25082,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994006157,"difficulty":0.0005993843}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nydia's card is shown to Bill. Nydia's card is shown to Nydia. It is publicly announced that someone picked a red card. It is publicly announced that Bill 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 (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":"Nydia can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bill","Nydia"],"index":53371,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994243383,"difficulty":0.0005756617}
-{"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 Terry 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) ] (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) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ryan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Terry","Ryan"],"index":309,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988299012,"difficulty":0.0011700988}
-{"premise":"There are three persons. Everyone is visible 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marilyn can now know that John can know that Julie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julie","Marilyn","John"],"index":27737,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981911778,"difficulty":0.0018088222}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcia's card is shown to Ramona. Ramona's card is shown to Marcia. Jeanne's card is shown to Jeanne. It is publicly announced that someone picked a red card. It is publicly announced that Jeanne knows whether Jeanne 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 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":"Marcia can now know that Ramona picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ramona","Marcia","Jeanne"],"index":22803,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9898472428,"difficulty":0.0101527572}
-{"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 Aurora. 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 Aurora 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Richard can now know whether Aurora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Aurora","Richard"],"index":51170,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.925537467,"difficulty":0.074462533}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erica's card is shown to Erica. Estela's card is shown to Marc. Estela'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 Agentb: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:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marc can now know whether Erica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erica","Marc","Estela","Jason"],"index":33533,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7053470612,"difficulty":0.2946529388}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ashly does not know whether or not everyone is thirsty. It is publicly announced that Casey knows whether Ashly is 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 (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)) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Ashly can now know that Juanita can know that Casey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juanita","Marjorie","Ashly","Casey"],"index":22985,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9373114109,"difficulty":0.0626885891}
-{"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 Eddie. Eddie's card is shown to Jennifer. Eddie's card is shown to Jessica. 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 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jessica can now know that Jennifer can know whether Jessica picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eddie","Jennifer","Jessica"],"index":17655,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8383966684,"difficulty":1.8383966684}
-{"premise":"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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Marilyn","Joseph","Alfred"],"index":48094,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981075525,"difficulty":0.0018924475}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosemary's card is shown to Rosemary. Paula's card is shown to Doug. Doug's card is shown to Doug. 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 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":"Paula can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rosemary","Paula","Doug"],"index":3048,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994119406,"difficulty":0.0005880594}
-{"premise":"There are two persons. Everyone is visible 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 Daniel knows whether Charles'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 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Charles can now know whether Daniel can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Charles"],"index":20094,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994180202,"difficulty":0.0005819798}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharan knows whether Joseph'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: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 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":"Joseph can now know that Sharan can know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michelle","Joseph","Sharan"],"index":8006,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982395172,"difficulty":0.0017604828}
-{"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 Jeffrey 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) ] [ ! (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":"David can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Barbara","David","Ron"],"index":56572,"s-l":"internal-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 Gene 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) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Cynthia can now know whether Christopher can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Gene","Christopher","Randal"],"index":62274,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993127584,"difficulty":0.0006872416}
-{"premise":"There are 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 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":"Betty can now know that Danna can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Betty","Danna","Donna"],"index":5226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99705863,"difficulty":0.00294137}
-{"premise":"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 Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Steven can now know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Jeannette","Alice","Lisa"],"index":61153,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9914441705,"difficulty":0.0085558295}
-{"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 (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":"Lavonda can now know whether Wilhelmina can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wilhelmina","Donald","Lavonda"],"index":47342,"s-l":"internal-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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd: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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know whether Jamie can know whether Laura is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Lynnette","Jamie","Daniel"],"index":23324,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989413619,"difficulty":0.0010586381}
-{"premise":"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 everyone's forehead is muddy. It is publicly announced that Gene 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 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)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anita","Gene","Laura"],"index":39937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990544915,"difficulty":0.0009455085}
-{"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 Ruby. James's card is shown to Keith. Isaiah'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:1 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:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruby can now know whether Isaiah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Isaiah","Ruby","Keith","James"],"index":10113,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8450246453,"difficulty":0.1549753547}
-{"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 Charles. Charles's card is shown to Charles. Erin's card is shown to Fred. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether Fred picked a red card. It is publicly announced that Erin 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 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb 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:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! 4 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Fred can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephen","Charles","Fred","Erin"],"index":13302,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9267155528,"difficulty":0.0732844472}
-{"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 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":"Ron can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ron","Melba","Michael","Leonard"],"index":23702,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997151196,"difficulty":0.002848804}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver knows whether or not nobody's forehead is muddy. It is publicly announced that Oliver 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 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))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Oliver can now know that Mae can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Miguel","Mae","Oliver"],"index":16747,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9475747347,"difficulty":0.0524252653}
-{"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 Walter knows whether Walter is thirsty. It is publicly announced that Walter 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 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&2&3)) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Walter can now know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Milton","Anthony","Walter"],"index":34307,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978402853,"difficulty":0.0021597147}
-{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reyes 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 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":"Angel can now know that Ronald can know that Reyes's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Reyes","Ronald","Angel"],"index":3064,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981173277,"difficulty":0.0018826723}
-{"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. Charles's card is shown to Dorothy. Charles's card is shown to Charles. Bryan's card is shown to Charles. Dorothy's card is shown to Bryan. Charles's card is shown to Bryan. Bryan'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 Agentb:2,3 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:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Charles","Bryan"],"index":40961,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9931045175,"difficulty":0.0068954825}
-{"premise":"There are four persons. Everyone is visible 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 Rita 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 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)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Maria can now know whether Rita can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Maria","Mark","Rita"],"index":29291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992726445,"difficulty":0.0007273555}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mathew's card is shown to Robert. Glenda's card is shown to Mathew. Robert's card is shown to Glenda. Mathew's card is shown to Glenda. 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) ] (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":"Robert can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Mathew","Glenda"],"index":4955,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993822575,"difficulty":0.0006177425}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelton does not know whether Shelton's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Shelton's forehead 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 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) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Robert can now know whether Shelton can know whether Shelton's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelton","Duane","Robert"],"index":13816,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9735352993,"difficulty":0.0264647007}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Artie knows whether Jose'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: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 ] 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) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Diane can now know that Jose can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Artie","Pete","Diane","Jose"],"index":6188,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986073375,"difficulty":0.0013926625}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanne 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 (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":"Mark can now know whether Kathleen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Mark","Jeanne"],"index":55007,"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'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.","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 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":"Robert can now know that Nicola can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicola","Richard","Robert"],"index":48603,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962259531,"difficulty":0.0037740469}
-{"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. It is publicly announced that David knows whether Debra 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 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) ] [ ! (1|2) ] 0","hypothesis":"David can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Debra","David"],"index":31347,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999045074,"difficulty":0.000954926}
-{"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 Brandon. Brandon'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 Ray picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ray can now know that Brandon can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brandon","Ray"],"index":30172,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989859462,"difficulty":0.0010140538}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Rebecca's forehead 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))","n_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 everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Betty","Elizabeth"],"index":41111,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9643954635,"difficulty":0.0356045365}
-{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edmund's card is shown to Edmund. Gwendolyn's card is shown to Timothy. Edmund's card is shown to Timothy. Timothy'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:1,2 Agentc: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:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gwendolyn can now know that Edmund can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gwendolyn","Edmund","Timothy","Robert"],"index":884,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980956912,"difficulty":0.0019043088}
-{"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 Marcy is thirsty. It is publicly announced that Laura does not know whether Marcy 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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Laura can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Marcy","Leslie","Laura"],"index":15815,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9755345583,"difficulty":0.0244654417}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melody knows whether Melody is thirsty. It is publicly announced that Joel is thirsty. It is publicly announced that Joel 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 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 ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Joel can now know that Melody can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Melody","Joel"],"index":53802,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984455705,"difficulty":0.0015544295}
-{"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 (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":"Alfred can now know that Heather can know that Alfred is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denise","James","Alfred","Heather"],"index":42270,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969049096,"difficulty":0.0030950904}
-{"premise":"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 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) ] (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) ] 0","hypothesis":"Michelle can now know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michelle","Joseph","Tony"],"index":48513,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742434025,"difficulty":0.0257565975}
-{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 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:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Eric can now know whether Robert can know whether Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Eric"],"index":3899,"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 is thirsty. It is publicly announced that Michael 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 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":"Evelyn can now know whether Chris is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Michael","Chris"],"index":12532,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9967071414,"difficulty":0.0032928586}
-{"premise":"There are three persons. Everyone is visible 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 someone'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:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agenta 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) ] [ ! ~(1) ] [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Donna can now know whether Jose can know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","Donna","Alex"],"index":12024,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994606376,"difficulty":0.0005393624}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hector 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) ] 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Steven can now know that Hector can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Hector","Steven"],"index":19542,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994140863,"difficulty":0.0005859137}
-{"premise":"There are 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 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":"Ashlee can now know whether Stanley can know that Ashlee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eleanor","Jennifer","Stanley","Ashlee"],"index":19936,"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. 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 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":"Harold can now know that Sheila can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Sheila","John"],"index":56310,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975239635,"difficulty":0.0024760365}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick'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":"Sandra can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frederick","Sandra"],"index":39605,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988842607,"difficulty":0.0011157393}
-{"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. Lori's card is shown to Dale. Lori's card is shown to Lori. Michael's card is shown to Lori. 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:1,2 Agentb: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 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Dale can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Lori","Michael"],"index":17517,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994797111,"difficulty":0.0005202889}
-{"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 Nikki does not know whether Robert is thirsty. It is publicly announced that Tammy knows whether or not everyone is thirsty. It is publicly announced that Tammy does not know whether Nikki 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 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) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Tammy can now know whether Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Nikki","Tammy"],"index":61112,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994749427,"difficulty":0.0005250573}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Olive's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (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":"Olive can now know that Olive's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Delbert","Olive"],"index":48280,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969153404,"difficulty":0.0030846596}
-{"premise":"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) ] [ ! ~(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:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Stephen can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Cynthia","Stephen","Novella"],"index":23941,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989677668,"difficulty":0.0010322332}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samual knows whether Melissa'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:1,2,3,4 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) ] 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) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Melissa can now know whether Mathew can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Melissa","Samual","Mathew"],"index":10522,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993504882,"difficulty":0.0006495118}
-{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gaylord's card is shown to Lois. Lois's card is shown to Gaylord. It is publicly announced that someone picked a red card. It is publicly announced that Gaylord 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 (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":"Gaylord can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lois","Gaylord"],"index":14264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994084835,"difficulty":0.0005915165}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether Ralph's forehead is muddy. It is publicly announced that Ralph 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":"Ralph can now know that Ann can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ralph","Ann"],"index":20880,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990347624,"difficulty":0.0009652376}
-{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agenta knows whether 1) ] [ ! ~(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) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Elizabeth can now know that William can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Lloyd","William","Elizabeth"],"index":22227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986681938,"difficulty":0.0013318062}
-{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilbur knows whether Wilbur's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Elton can now know whether Wilbur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Wilbur","Ruth","Elton","Roland"],"index":56597,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994481206,"difficulty":0.0005518794}
-{"premise":"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 Gary'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 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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gary can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anita","Gary","Martha"],"index":16215,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994558692,"difficulty":0.0005441308}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone 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) ] [ ! ~(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) ] [ ! ~(1) ] 0","hypothesis":"Kim can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Jerry","Kim","Andrew"],"index":9504,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990371466,"difficulty":0.0009628534}
-{"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 Sue. Sue's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Sue 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 (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":"Luis can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sue","Luis"],"index":48877,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981595874,"difficulty":0.0018404126}
-{"premise":"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 knows whether Thomas's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy. It is publicly announced that Geneva knows whether Jeannette's forehead is muddy. It is publicly announced that Geneva knows whether Austin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jeannette can now know whether Austin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Geneva","Jeannette","Austin","Thomas"],"index":22327,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991718531,"difficulty":0.0008281469}
-{"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.","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":"Daniel can now know that Jack is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Adam","Jack","Daniel"],"index":22996,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8648807406,"difficulty":1.8648807406}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregg knows whether someone's forehead is muddy. It is publicly announced that Juanita knows whether Gregg'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 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) ] 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Juanita can now know that Gregg can know that Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juanita","Steven","Gregg"],"index":56277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967761636,"difficulty":0.0032238364}
-{"premise":"There are two persons. Everyone is visible 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 Madie'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 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":"Thomas can now know that Madie can know whether Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Madie","Thomas"],"index":18297,"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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael 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) ] [ ! (Agentd knows whether 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: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":"Danielle can now know that Courtney can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danielle","Linda","Courtney","Michael"],"index":33685,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988473654,"difficulty":0.0011526346}
-{"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. Yu's card is shown to Chris. Michael's card is shown to Yu. Chris'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 Agentb:3 Agentc:4 Agentd:2 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:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Yu can now know that Michael can know whether Yu picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Chris","Yu","Michael"],"index":37578,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5018200278,"difficulty":0.4981799722}
-{"premise":"There are three persons. Everyone is visible 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 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":"Vanessa can now know that Robert can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arthur","Vanessa","Robert"],"index":27304,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978628755,"difficulty":0.0021371245}
-{"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 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) ] [ ! ~(Agenta knows whether 3) ] Agentc 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 3) ] 0","hypothesis":"Chad can now know that Daniel can know whether Wallace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Wallace","Chad","Adam"],"index":50949,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980831146,"difficulty":0.0019168854}
-{"premise":"There are four 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 muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that 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) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentd knows that (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) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Nicholas can now know that Colleen can know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Colleen","Laura","John","Nicholas"],"index":43310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988705516,"difficulty":0.0011294484}
-{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sally knows whether Sally'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 (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 2) ] 0","hypothesis":"Sally can now know that Danielle can know whether Danielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Danielle","Sally"],"index":20655,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993408322,"difficulty":0.0006591678}
-{"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 Heather. Christine's card is shown to Christine. 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 Heather 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 that 1)","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":"Heather can now know that Heather picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Heather","Christine"],"index":48476,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9148827195,"difficulty":0.0851172805}
-{"premise":"There are three persons. Everyone is visible 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 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) ] (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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Barbara can now know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","John","Gregory"],"index":28862,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9958723187,"difficulty":0.0041276813}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeremiah's card is shown to Jeremiah. William's card is shown to William. Jeremiah's card is shown to Manuel. It is publicly announced that someone picked a red card. It is publicly announced that Manuel does not know whether Manuel 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":"William can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremiah","William","Manuel"],"index":65410,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990455508,"difficulty":0.0009544492}
-{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Rene 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|2|3|4)) ] [ ! (Agentc knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Edward can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lester","Edward","Rene","Elsie"],"index":56272,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989842772,"difficulty":0.0010157228}
-{"premise":"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 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":"Reba can now know whether David can know whether Enrique's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Reba","Enrique"],"index":33355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992769361,"difficulty":0.0007230639}
-{"premise":"There are four persons. Everyone is visible 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) ] [ ! 2 ] 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) ] [ ! 2 ] 0","hypothesis":"Paula can now know that Charles can know that Paula's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marquita","Charles","Bruce","Paula"],"index":40546,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952142239,"difficulty":0.0047857761}
-{"premise":"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 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 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":"Daniel can now know whether Angie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Natalie","Daniel","Angie"],"index":52360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8874572515,"difficulty":0.1125427485}
-{"premise":"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 does not know whether Gloria's forehead 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 3)","n_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 Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Michael","Gloria"],"index":61642,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931609631,"difficulty":0.0068390369}
-{"premise":"There are four persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Virgil can now know whether Phillip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Phillip","Susan","Wayne","Virgil"],"index":30888,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993779659,"difficulty":0.0006220341}
-{"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 Micaela. Micaela's card is shown to Brigette. James's card is shown to Brigette. Brigette'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 Brigette knows whether or not everyone picked a red card. It is publicly announced that Brigette knows whether James picked a red card. It is publicly announced that Brigette 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)) ] Agentb knows whether (Agentc knows that 2)","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":"Brigette can now know whether James can know that Brigette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Micaela","Brigette","James"],"index":59412,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9565897584,"difficulty":1.9565897584}
-{"premise":"There are two persons. Everyone is visible 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. 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 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|2) ] 0","hypothesis":"Susan can now know whether Amy can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susan","Amy"],"index":57525,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993276596,"difficulty":0.0006723404}
-{"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.","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)","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":"Roy can now know that Linda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linda","Roy","Thelma"],"index":7550,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9343008399,"difficulty":0.0656991601}
-{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fae's card is shown to Cara. Cara's card is shown to Susan. Fae's card is shown to Susan. Cara's card is shown to Fae. Susan's card is shown to Fae. Fae's card is shown to Fae. 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) ] Agenta knows that (Agentc knows whether 2)","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":"Cara can now know that Fae can know whether Susan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cara","Susan","Fae"],"index":40590,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6333019137,"difficulty":0.3666980863}
-{"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 Olga. Norbert's card is shown to Lorraine. Margaret's card is shown to Norbert. Norbert's card is shown to Norbert. 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 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":"Lorraine can now know that Norbert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Olga","Margaret","Lorraine","Norbert"],"index":44587,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957585931,"difficulty":0.0042414069}