diff --git "a/data/validation-all.jsonl" "b/data/validation-all.jsonl"
new file mode 100644--- /dev/null
+++ "b/data/validation-all.jsonl"
@@ -0,0 +1,3725 @@
+{"premise":"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 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) ] [ ! (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) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Christopher","Timothy"],"index":13728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998221457,"difficulty":0.001778543}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Manuel. Betty's card is shown to Jose. Manuel's card is shown to Betty. Jose's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card. It is publicly announced that Manuel knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows that (~(1|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 3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Manuel can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Manuel","Jose","Betty"],"index":40829,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998513639,"difficulty":0.001486361}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Inez's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] 0","hypothesis":"Crystal can now know that Inez can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Crystal","Inez"],"index":23982,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972608089,"difficulty":0.0027391911}
+{"premise":"There are four persons. Everyone is visible 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 Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Robert can now know that Wanda can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Wanda","Loralee","Robert"],"index":63331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997463822,"difficulty":0.0002536178}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie does not know whether Marjorie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carl can now know whether David can know whether Marjorie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","David","Carl"],"index":52927,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995366335,"difficulty":0.0004633665}
+{"premise":"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's forehead is not muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Annie can now know whether Sylvester can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sylvester","Patricia","Annie"],"index":26283,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954330921,"difficulty":0.0045669079}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Judie does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Angela can now know whether Judie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Brian","Judie"],"index":41683,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Bonnie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonnie","Matthew","John","Lawrence"],"index":2950,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9942783117,"difficulty":0.0057216883}
+{"premise":"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. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Maria knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ronald can now know whether Maria can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Ronald","Maria"],"index":59799,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.951094389,"difficulty":0.048905611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether Dennis's forehead is muddy. It is publicly announced that Louis's forehead is muddy. It is publicly announced that Rochelle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Louis can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Louis","Rochelle","Lawrence","Dennis"],"index":26765,"s-l":"forehead-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 Monica's forehead is not muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Donald can now know whether Monica can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Jennifer","Monica"],"index":36724,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly is not thirsty. It is publicly announced that Maureen does not know whether Jim is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] Agentd knows whether (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) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Maureen can now know whether Jim can know that Maureen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jim","Marian","Kimberly","Maureen"],"index":60956,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9912533164,"difficulty":0.0087466836}
+{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Christopher knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd 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:1,2,3,4 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":"Carmen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Charles","Christopher","Lester"],"index":48384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998494029,"difficulty":0.001505971}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany does not know whether Tiffany's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows whether (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":"Tiffany can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ebony","Gregory","Tiffany","Terry"],"index":30831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Susan","Gary","Don"],"index":8433,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982314706,"difficulty":0.0017685294}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether or not everyone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] Agentd knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Kenneth can now know that Sheldon can know that Sheldon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sheldon","Jennifer","Harold","Kenneth"],"index":24756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9268339276,"difficulty":0.0731660724}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brooke's card is shown to Brooke. Clara's card is shown to Brooke. Ronald's card is shown to Clara. Brooke's card is shown to Ronald. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Ronald does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 1)","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":"Clara can now know that Ronald can know that Brooke picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brooke","Clara","Ronald"],"index":43711,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5308222771,"difficulty":1.5308222771}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bart knows whether Randy's forehead is muddy. It is publicly announced that Randy knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (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) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Bart can now know whether Randy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Randy","Bart"],"index":44377,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9770485759,"difficulty":0.0229514241}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carol does not know whether Jordan is thirsty. It is publicly announced that Andrew 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) ] [ ! ~(Agentc knows whether 2) ] (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 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mary can now know that Carol is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Mary","Andrew","Jordan"],"index":154,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997612834,"difficulty":0.002387166}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanna knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Bradley can now know that Joanna can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Bradley","Joanna"],"index":31025,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997602105,"difficulty":0.0002397895}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Paul knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Harley can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Harley","Deborah","Paul","Everett"],"index":47363,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996805191,"difficulty":0.0003194809}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Emily's card is shown to Ethel. Leslie's card is shown to Leslie. Ethel's card is shown to Emily. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:2 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:1 Agentb:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know whether Joan can know that Ethel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joan","Ethel","Leslie","Emily"],"index":61139,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9331834316,"difficulty":0.0668165684}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcella'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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Paul can now know that Jessica can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Jessica","Marcella","Paul"],"index":36098,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.819228828,"difficulty":1.819228828}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether Mable is thirsty. It is publicly announced that William knows whether Mable is thirsty. It is publicly announced that Mable knows whether William is thirsty. It is publicly announced that William knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows 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 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mable can now know whether William can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Mable"],"index":64004,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976104498,"difficulty":0.0023895502}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leon's card is shown to Teresia. Leon's card is shown to Robert. Robert's card is shown to Leon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 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:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresia can now know whether Teresia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Teresia","Robert","Leon"],"index":8457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9344807863,"difficulty":0.0655192137}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Victoria can now know that Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victoria","Robert"],"index":53349,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997810721,"difficulty":0.0002189279}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip does not know whether or not everyone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Dewayne can now know whether Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heidi","Dewayne","Richard","Philip"],"index":45970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991273284,"difficulty":0.0008726716}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elmer's card is shown to Elmer. Elmer's card is shown to Mattie. Robert's card is shown to Mattie. Mattie's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Mattie 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)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Mattie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elmer","Mattie","Robert"],"index":26370,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.626519084,"difficulty":0.373480916}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Helen can now know that Joyce can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Joyce","Helen"],"index":34668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998423934,"difficulty":0.001576066}
+{"premise":"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 Kenneth knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Angela can now know whether Kenneth can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Angela"],"index":36914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997592568,"difficulty":0.0002407432}
+{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Joyce can now know whether Vicky can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Vicky","Joyce"],"index":35107,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996953011,"difficulty":0.0003046989}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wesley is not thirsty. It is publicly announced that Wesley does not know whether Tony is thirsty. It is publicly announced that Wesley knows whether Wesley 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 whether 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":"Lana can now know whether Lana is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tony","Lana","Wesley"],"index":28602,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9921910167,"difficulty":0.0078089833}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Florence is thirsty. It is publicly announced that Florence knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Florence can now know whether Daisy can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daisy","Florence"],"index":58933,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994612336,"difficulty":0.0005387664}
+{"premise":"There are two persons. Everyone is visible 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 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)","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":"Bobby can now know that Bobby's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bobby","Catherine"],"index":63152,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975998998,"difficulty":0.0024001002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeannine does not know whether Linda is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Linda can now know that Jeannine can know that Jeannine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Jeannine","Louise"],"index":12434,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.698356092,"difficulty":0.301643908}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janeth 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 (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Janet can now know that Jerry can know that Janeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Jerry","Janeth","Janet"],"index":42030,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6597003937,"difficulty":1.6597003937}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wanda's card is shown to Lyle. Lyle's card is shown to Wanda. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria knows whether Maria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Maria can now know whether Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lyle","Wanda","Maria"],"index":12761,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9688028097,"difficulty":0.0311971903}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan does not know whether Joan's forehead is muddy. It is publicly announced that Charlotte's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows that (Agentb knows whether 1)","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":"Charlotte can now know that Joan can know whether Charlotte's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Charlotte","Joan"],"index":12327,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994263649,"difficulty":0.0005736351}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris does not know whether or not everyone's forehead is muddy. It is publicly announced that Chris 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 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":"Chris can now know that Chris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gregory","Chris"],"index":36346,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8114206791,"difficulty":1.8114206791}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve knows whether Steve is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Steve can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Alberto","Steve"],"index":58617,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985681772,"difficulty":0.0014318228}
+{"premise":"There are four persons. Everyone is visible 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 Roy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Roy can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Jesse","Roy","Mary"],"index":2457,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985148311,"difficulty":0.0014851689}
+{"premise":"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's forehead is not muddy. It is publicly announced that Herbert 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)) ] (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) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dennis can now know that Herbert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Catherine","Dennis","Herbert"],"index":53390,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8422586322,"difficulty":0.1577413678}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 (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":"Sidney can now know whether Brenda can know that Brenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sidney","Brenda","Warren"],"index":59706,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996783733,"difficulty":0.0003216267}
+{"premise":"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's forehead is muddy. It is publicly announced that Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agenta knows that (Agentb knows whether 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 ] [ ! 3 ] 0","hypothesis":"David can now know that Joseph can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Joseph","Irene","Jody"],"index":19967,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999168396,"difficulty":0.000831604}
+{"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 Anna. Anna's card is shown to David. Anna's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether or not everyone picked a red card. It is publicly announced that Steven does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta 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:4 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Steven can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anna","David","Steven","Patricia"],"index":34641,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999779284,"difficulty":0.000220716}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sylvia 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Rita can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","James","Rita","Sylvia"],"index":6949,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997654557,"difficulty":0.0002345443}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy knows whether Edith is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Edith knows whether Edith is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (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) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Roy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Roy","Edith"],"index":32976,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984145164,"difficulty":0.0015854836}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Norman. Jeffrey's card is shown to Norman. Edith's card is shown to Edith. Jeffrey's card is shown to Edwin. Norman's card is shown to Jeffrey. Edith's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 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:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know whether Edwin can know whether Edith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norman","Edith","Edwin","Jeffrey"],"index":36534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986781478,"difficulty":0.0013218522}
+{"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 Jeffery is thirsty. It is publicly announced that Jose does not know whether Rose is thirsty. It is publicly announced that Rose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] Agentc knows whether (Agenta 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 2) ] [ ! ~(Agentc knows whether 4) ] [ ! 4 ] 0","hypothesis":"Jose can now know whether Deborah can know that Jeffery is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Jeffery","Jose","Rose"],"index":2095,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9864539504,"difficulty":0.0135460496}
+{"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 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":"Cynthia can now know that Cheryl can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nathan","Cheryl","Cynthia"],"index":66100,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930141568,"difficulty":0.0069858432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melody knows whether someone's forehead is muddy. It is publicly announced that Austin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Janice can now know that Austin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Debra","Austin","Melody"],"index":43254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9723722935,"difficulty":0.0276277065}
+{"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 Addie knows whether Phyllis is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","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":"Addie can now know that Phyllis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Phyllis","Addie"],"index":57191,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948091507,"difficulty":0.0051908493}
+{"premise":"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 Dana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Paul can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dana","Paul","Roland"],"index":42713,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977637529,"difficulty":0.0022362471}
+{"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 Martha is thirsty. It is publicly announced that Douglas knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Dewey can now know whether Douglas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Douglas","Scott","Dewey","Martha"],"index":4999,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8081713319,"difficulty":1.8081713319}
+{"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. Winston's card is shown to Sharon. Winston's card is shown to Winston. Meredith's card is shown to Meredith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (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":"Meredith can now know whether Winston can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Winston","Meredith"],"index":57213,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997728467,"difficulty":0.0002271533}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathaniel's card is shown to Henry. Vernon's card is shown to Vernon. Henry's card is shown to Carol. Henry's card is shown to Nathaniel. Vernon'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:4 Agentb:2 Agentc:1 Agentd:1,2 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:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathaniel can now know that Carol can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Vernon","Carol","Nathaniel"],"index":38056,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984462857,"difficulty":0.0015537143}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows 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":"Sally can now know whether Elsie can know that Elsie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elsie","Sally","Vera","Maggie"],"index":49408,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9847615957,"difficulty":0.0152384043}
+{"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. Joe's card is shown to William. Sara's card is shown to Jeremiah. William's card is shown to Joe. Jeremiah's card is shown to Sara. Joe's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeremiah can now know whether William can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jeremiah","Joe","Sara"],"index":45356,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8421244621,"difficulty":0.1578755379}
+{"premise":"There are three persons. Everyone is visible 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 Rachel knows whether Migdalia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 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":"Rachel can now know that Migdalia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Migdalia","Rachel","Melissa"],"index":33757,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9934878349,"difficulty":0.0065121651}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether or not everyone is thirsty. It is publicly announced that Dawn knows whether Dorothy is thirsty. It is publicly announced that Dawn does not know whether Sharon is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Dorothy can now know whether Sharon can know whether Dorothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Megan","Dorothy","Dawn","Sharon"],"index":8257,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977629185,"difficulty":0.0022370815}
+{"premise":"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. It is publicly announced that Fernando's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 that (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Angela can now know that Fernando can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Angela","Richard","Fernando"],"index":26005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985021353,"difficulty":0.0014978647}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dianna does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"James can now know that Dianna can know whether James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","James","Dianna"],"index":11920,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971886277,"difficulty":0.0028113723}
+{"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. Jorge's card is shown to Paul. Tommy's card is shown to Jorge. Paul's card is shown to Tommy. 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)) ] (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 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jorge can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Jorge","Tommy"],"index":25649,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984759688,"difficulty":0.0015240312}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cathleen's card is shown to Phillip. Phillip's card is shown to Cathleen. Charles's card is shown to Cathleen. Charles's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether Phillip 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 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:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Charles can now know that Cathleen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phillip","Cathleen","Charles"],"index":42150,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977940321,"difficulty":0.0022059679}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ike's card is shown to Laurie. Linda's card is shown to Charles. Ike's card is shown to Ike. 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 (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:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laurie can now know that Charles can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laurie","Charles","Ike","Linda"],"index":42332,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9866583943,"difficulty":0.0133416057}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmie does not know whether Mary is thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] 0","hypothesis":"Mary can now know whether John can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Donna","Mary","Jimmie"],"index":7568,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5174188614,"difficulty":0.4825811386}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roberto's card is shown to Roberto. John's card is shown to Roberto. John's card is shown to John. Roberto's card is shown to Evelyn. 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 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":"John can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roberto","John","Evelyn"],"index":45423,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.839566648,"difficulty":0.160433352}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Steven can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Allison","Margaret","Steven","Stephen"],"index":6751,"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 Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (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":"James can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Armando","Donald","James"],"index":67049,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984135628,"difficulty":0.0015864372}
+{"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 Teresa. Karen's card is shown to Teresa. Mary's card is shown to Teresa. Teresa's card is shown to Karen. Karen's card is shown to Karen. Linda's card is shown to Karen. Mary's card is shown to Karen. Teresa's card is shown to Linda. Mary's card is shown to Linda. Teresa's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Karen picked a red card. It is publicly announced that Mary does not know whether Linda picked a red card. It is publicly announced that Teresa does not know whether Linda 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 (Agenta knows whether (1&2&3&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":"Karen can now know that Teresa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Teresa","Karen","Linda","Mary"],"index":63343,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8555288315,"difficulty":0.1444711685}
+{"premise":"There are four persons. Everyone is visible 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 Stacy knows whether Stacy's forehead is muddy. It is publicly announced that Salina knows whether Salina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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) ] (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) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jesus can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stacy","Salina","Jesus","Randy"],"index":26441,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9839292765,"difficulty":0.0160707235}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 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":"Maria can now know that Corey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephanie","Maria","Corey","Jessica"],"index":25070,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983345866,"difficulty":0.0016654134}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not nobody's forehead is muddy. It is publicly announced that Myrtle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] (Agentd knows that 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":"Myrtle can now know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorna","Betty","Raymond","Myrtle"],"index":38631,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9895688891,"difficulty":0.0104311109}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yvette's card is shown to Yvette. Jessica's card is shown to Yvette. Faye's card is shown to Yvette. Faye's card is shown to Jessica. Yvette's card is shown to Faye. Yvette's card is shown to Luis. Jessica's card is shown to Luis. Faye's card is shown to Luis. It is publicly announced that someone picked a red card. It is publicly announced that Yvette knows whether Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jessica can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Yvette","Jessica","Faye","Luis"],"index":54074,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Stephany can now know whether Patricia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Frank","Andrew","Stephany"],"index":48748,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997512698,"difficulty":0.0002487302}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 3)","n_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":"John can now know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","John","Mark"],"index":11819,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999597609,"difficulty":0.000402391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawn does not know whether Trina is thirsty. It is publicly announced that Trina 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Trina can now know that William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawn","William","Trina","Dorothy"],"index":37619,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969870448,"difficulty":0.0030129552}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Cheryl. Robert's card is shown to Cheryl. Mathew's card is shown to Mathew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Mathew","Robert"],"index":8567,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960761666,"difficulty":0.0039238334}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether or not everyone is thirsty.","smcdel_problem":"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 (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Aurora can know that Sharon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aurora","Sharon","Frank","Robert"],"index":52669,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9900614023,"difficulty":0.0099385977}
+{"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 Ruby 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 (1&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":"Ruby can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stephanie","Margaret","Ruby"],"index":15255,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985827208,"difficulty":0.0014172792}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terri does not know whether Terri's forehead is muddy. It is publicly announced that Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agenta knows whether (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) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Mary can now know whether Cheryl can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Terri","Cheryl","Timothy"],"index":43798,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999207437,"difficulty":0.000792563}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth does not know whether Neil is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Luther can now know whether Ruth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Priscilla","Luther","Ruth","Neil"],"index":6213,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9899116158,"difficulty":0.0100883842}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma knows whether Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Ashley can now know that Alma can know whether Ashley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Alma","William","Michael"],"index":45425,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997430444,"difficulty":0.0002569556}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alane's card is shown to Alane. Janice's card is shown to Alane. Alane's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Janice does not know whether or not everyone picked a red card. It is publicly announced that Janice picked a black card. It is publicly announced that Janice knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Alane can now know that Alane picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alane","Janice"],"index":30383,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.71362257,"difficulty":0.28637743}
+{"premise":"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 Doreen's forehead is muddy. It is publicly announced that Earnest knows whether Doreen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know whether Mark can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Earnest","Mark","Doreen","Robert"],"index":38209,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.575820744,"difficulty":1.575820744}
+{"premise":"There are three persons. Everyone is visible 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 Joyce's forehead is muddy. It is publicly announced that Lori knows whether or not nobody's forehead is muddy. It is publicly announced that Joyce knows whether Lori's forehead is muddy.","smcdel_problem":"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 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":"Thomas can now know whether Joyce's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Lori","Joyce"],"index":16992,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997000694,"difficulty":0.0002999306}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Joseph's card is shown to Maria. Maria's card is shown to Joseph. Louis's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Louis can now know whether Maria can know that Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Maria","Louis","Joseph"],"index":28883,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9067435265,"difficulty":0.0932564735}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clifton 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 (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Clifton can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Matthew","Galen","Clifton","Robert"],"index":65244,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998496294,"difficulty":0.001503706}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marjorie does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Leonard can now know whether Mary can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leonard","Mary","Marjorie"],"index":46481,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999417901,"difficulty":0.000582099}
+{"premise":"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 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. It is publicly announced that Bobby 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) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Timothy can now know that Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Charles","Bobby"],"index":2997,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9884310961,"difficulty":1.9884310961}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to James. James's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card. It is publicly announced that Larry knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (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 (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"James can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Larry"],"index":32237,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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)) ] (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":"Martin can now know whether Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Martin","Guy","Jennifer"],"index":49468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99646312,"difficulty":0.00353688}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frances is thirsty. It is publicly announced that Frances knows whether or not nobody is thirsty. It is publicly announced that Frances does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Roberta can now know whether Roberta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frances","Ramon","Roberta","Gloria"],"index":15136,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976868629,"difficulty":0.0023131371}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kristin's card is shown to Kristin. Kristin's card is shown to Don. Kristin's card is shown to Bernice. It is publicly announced that someone picked a red card. It is publicly announced that Bernice does not know whether Don 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) ] (Agentb 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":"Don can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristin","Don","Bernice"],"index":50800,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9824464321,"difficulty":0.0175535679}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawrence knows whether someone is thirsty. It is publicly announced that Harvey does not know whether Gudrun is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Gudrun can now know that Harvey can know whether Lawrence is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gudrun","Lawrence","Harvey"],"index":54366,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978938699,"difficulty":0.0021061301}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentc knows whether (Agenta knows that (1|2|3))","n_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":"Sidney can now know whether Dorothy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Paul","Sidney"],"index":6847,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997865558,"difficulty":0.0002134442}
+{"premise":"There are three persons. Everyone is visible 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 3)","n_announcements":1,"pbcheck":"VARS 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":"Amy can now know that Lance's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Amy","Gwen","Lance"],"index":6423,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984067082,"difficulty":0.0015932918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vicky knows whether Mark'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) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] (Agentd knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Vanessa can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Vicky","Mark","Vanessa"],"index":55500,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","James","Dennis","Melanie"],"index":58168,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997813106,"difficulty":0.0002186894}
+{"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 Pauline. Cindi's card is shown to Pauline. Pauline's card is shown to Jose. Cindi's card is shown to Jose. Pauline's card is shown to Cindi. 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) ] (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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pauline can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pauline","Jose","Cindi"],"index":64181,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983600974,"difficulty":0.0016399026}
+{"premise":"There are four persons. Everyone is visible 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's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Michelle can now know whether Barbara can know that Barbara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Barbara","Michelle","Wayne"],"index":43675,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996758699,"difficulty":0.0003241301}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandie's forehead is muddy. 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brandie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Harry","Brandie"],"index":57162,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Don'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 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":"Marlyn can now know whether Raymond can know that Don's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Don","Marlyn","Raymond","Theresa"],"index":36587,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997020364,"difficulty":0.0002979636}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Cheryl can now know that Dorothy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Cheryl","Dorothy","Mistie"],"index":55258,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996910095,"difficulty":0.0003089905}
+{"premise":"There are two 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 Louis. Louis's card is shown to Louis. It is publicly announced that someone picked a red card. It is publicly announced that Jessie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jessie can now know whether Louis can know that Louis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jessie","Louis"],"index":62995,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9450370073,"difficulty":1.9450370073}
+{"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 Lynn. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card. It is publicly announced that Lynn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Lynn can now know whether Lynn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brenda","Lynn","Michael"],"index":18206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8966013789,"difficulty":0.1033986211}
+{"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 Lesley is thirsty. It is publicly announced that Alicia is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Jason can now know whether Russell can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alicia","Russell","Jason","Lesley"],"index":54262,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5046632886,"difficulty":1.5046632886}
+{"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 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":"Jennifer can now know that Maynard can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phyllis","Maynard","Jennifer"],"index":15078,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997600913,"difficulty":0.0002399087}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Joshua. Mary's card is shown to Joshua. Terry'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 someone picked a red card. It is publicly announced that Terry knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|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:2,3 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joshua can now know that Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Terry","Mary","Steve"],"index":53179,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971188307,"difficulty":0.0028811693}
+{"premise":"There are two persons. Everyone is visible 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 Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (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 (1&2)) ] 0","hypothesis":"Joseph can now know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Linda"],"index":52450,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 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":"Thomas can now know whether Bessie can know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Carol","Bessie","Thomas"],"index":9774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996697903,"difficulty":0.0003302097}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Buck's card is shown to Buck. Margaret's card is shown to Buck. Margaret's card is shown to Margaret. Buck's card is shown to Darryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Margaret can now know that Buck picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Buck","Margaret","Darryl"],"index":45715,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980893731,"difficulty":0.0019106269}
+{"premise":"There are four persons. Everyone is visible 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 Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Lyle can now know whether Thomas can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lyle","Reinaldo","Willie","Thomas"],"index":57470,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996731281,"difficulty":0.0003268719}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows 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":"James can now know that Lorraine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eva","Lorraine","Gail","James"],"index":38276,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984335303,"difficulty":0.0015664697}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Augusta's card is shown to Augusta. Yolanda's card is shown to Augusta. Edgardo's card is shown to Pedro. Yolanda's card is shown to Yolanda. Yolanda's card is shown to Edgardo. 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) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pedro can now know whether Yolanda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Augusta","Pedro","Yolanda","Edgardo"],"index":6259,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Kelly can now know that Terry can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kelly","Terry"],"index":53191,"s-l":"internal-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 Francisco 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) ] 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) ] 0","hypothesis":"Francisco can now know that Timothy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Albert","Francisco"],"index":59886,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9842032194,"difficulty":0.0157967806}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brian's card is shown to Walter. Brian's card is shown to Brian. It is publicly announced that someone picked a red card. It is publicly announced that Walter does not know whether Walter picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Walter can now know that Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Walter","Brian"],"index":17274,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9543434978,"difficulty":0.0456565022}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Pamela can now know that Tracy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Elizabeth","Pamela"],"index":27919,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983371496,"difficulty":0.0016628504}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Devon does not know whether Devon's forehead is muddy. It is publicly announced that Brandi knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Shirley can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brandi","Devon","Charles","Shirley"],"index":45525,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"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. Kristine's card is shown to Andrew. Gilbert's card is shown to Andrew. Andrew's card is shown to Gilbert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (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":["Andrew","Kristine","Gilbert"],"index":51898,"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 Beverly does not know whether Roberto is thirsty. It is publicly announced that Pauline does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Pauline can now know that Roberto can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberto","Amy","Beverly","Pauline"],"index":58795,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980868101,"difficulty":0.0019131899}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donnell knows whether Donnell'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 whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Donnell can now know that Joseph can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donnell","Joseph"],"index":29640,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997537732,"difficulty":0.0002462268}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Julio is thirsty. It is publicly announced that Douglas does not know whether Heather is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Heather can now know that Douglas can know whether Douglas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Heather","Julio"],"index":63410,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986727238,"difficulty":0.0013272762}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane does not know whether Diane's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Travis can now know that Joseph can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Diane","Joseph"],"index":61209,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998498559,"difficulty":0.001501441}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffry knows whether Phyllis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jorge can now know whether Phyllis can know that Jeffry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jorge","Phyllis","Jeffry"],"index":43768,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996682405,"difficulty":0.0003317595}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jenny 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Jenny can now know that Tara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tara","Jenny"],"index":44407,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9828436375,"difficulty":0.0171563625}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricardo knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (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":"Ricardo can now know whether Hector can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ricardo","Hector","Kathryn"],"index":22021,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9554798007,"difficulty":0.0445201993}
+{"premise":"There are four persons. Everyone is visible 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 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":"William can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Lilian","Stephen","Lisa"],"index":40079,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964439273,"difficulty":0.0035560727}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether Jennie is thirsty. It is publicly announced that Jennie does not know whether Larry is thirsty. It is publicly announced that Larry does not know whether Jennie is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jon can now know whether Bruce can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennie","Larry","Jon","Bruce"],"index":20009,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980987906,"difficulty":0.0019012094}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherman's card is shown to Sherman. Sherman's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Sherman does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Sherman can now know that Deborah can know whether Sherman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherman","Deborah"],"index":55362,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9679063559,"difficulty":0.0320936441}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danny is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentb knows 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":"Lien can now know that Julienne can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lien","Julienne","Betty","Danny"],"index":64133,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997825027,"difficulty":0.0002174973}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead is muddy. It is publicly announced that Anna knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (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 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bryan can now know that Reynaldo can know whether Reynaldo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bryan","Reynaldo","Anna"],"index":65448,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6611828804,"difficulty":1.6611828804}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Issac's card is shown to Lorena. Clara's card is shown to Lorena. Andria's card is shown to Lorena. Issac's card is shown to Issac. Issac's card is shown to Clara. Clara's card is shown to Clara. Clara's card is shown to Andria. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andria can now know that Lorena picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorena","Issac","Clara","Andria"],"index":2824,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978628755,"difficulty":0.0021371245}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Coral's forehead is muddy.","smcdel_problem":"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":"Alice can now know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Coral","Alice","Theron"],"index":61656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9761471152,"difficulty":0.0238528848}
+{"premise":"There are four persons. Everyone is visible 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 Fred knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Fred can now know whether Maria can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fred","Matthew","Maria","Doris"],"index":7691,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997487664,"difficulty":0.0002512336}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Brian's forehead is muddy. 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.","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 whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Brian"],"index":39029,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.94575876,"difficulty":0.05424124}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is not muddy.","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":"Donna can now know that Raymon can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Raymon","Donna"],"index":50824,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982896447,"difficulty":0.0017103553}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bruce 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) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Constance can now know that Dolores can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Constance","Bruce","Dolores"],"index":64985,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984959364,"difficulty":0.0015040636}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly's forehead is not muddy. It is publicly announced that Douglas'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":"Douglas can now know whether Angla can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Kelly","Angla"],"index":59704,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997131228,"difficulty":0.0002868772}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that William does not know whether William'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) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"George can now know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mike","William","George"],"index":51969,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6125044227,"difficulty":1.6125044227}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allison 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))","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":"Allison can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allison","Laura","Dominga"],"index":60646,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6774163842,"difficulty":1.6774163842}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Douglas can now know that Joseph can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Michael","Douglas"],"index":25495,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are four persons. Everyone is visible to others. 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 (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":"Audrey can now know whether Matthew can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","Andy","Audrey","Edwina"],"index":42720,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974588752,"difficulty":0.0025411248}
+{"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 Lula is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Linda can now know that Robert can know that Lula is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gladys","Robert","Lula","Linda"],"index":6947,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979650974,"difficulty":0.0020349026}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corey is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 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":"Arleen can now know whether Corey can know that Corey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebecca","Corey","Arleen"],"index":46194,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9758194089,"difficulty":0.0241805911}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hallie does not know whether or not everyone's forehead is muddy. It is publicly announced that Norma 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 (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Hallie can now know that Norma can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Robert","Neil","Hallie"],"index":22614,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995077848,"difficulty":0.0004922152}
+{"premise":"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 Darla'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":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Darla can now know that William can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Darla"],"index":29767,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6372277141,"difficulty":0.3627722859}
+{"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 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) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Elizabeth can now know that Sandra can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Elizabeth","Sandra","Wayne"],"index":35446,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983298182,"difficulty":0.0016701818}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Gary knows whether Gary is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Gary can now know whether Jessica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gary","Jessica"],"index":36775,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9751038551,"difficulty":1.9751038551}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know that Lisa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Albert","Mary","Lisa","Donna"],"index":64527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984349608,"difficulty":0.0015650392}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Anthony. Anthony's card is shown to Raymond. Anthony's card is shown to James. Joe's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card. It is publicly announced that Raymond 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)) ] (Agentb knows whether 2)","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":"Raymond can now know whether Raymond picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Raymond","James","Joe"],"index":1761,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9024614096,"difficulty":1.9024614096}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows whether (Agentc knows 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) ] 0","hypothesis":"Willie can now know whether Lucas can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Melissa","Willie","Lucas"],"index":498,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999540329,"difficulty":0.000459671}
+{"premise":"There are four persons. Everyone is visible 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 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":"Mark can now know whether Katerine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katerine","Candy","Mark","James"],"index":15492,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999725759,"difficulty":0.000274241}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether Felicia is thirsty. It is publicly announced that Deborah does not know whether Kenneth is thirsty. It is publicly announced that Felicia knows whether Felicia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentc knows 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 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Felicia can now know whether Kenneth can know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Deborah","Felicia"],"index":52530,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8927207589,"difficulty":1.8927207589}
+{"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. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 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":"David can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Marian"],"index":21132,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986000657,"difficulty":0.0013999343}
+{"premise":"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 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 (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":"David can now know whether Nichole can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","David","Brad","Nichole"],"index":34086,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9889290929,"difficulty":0.0110709071}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether or not 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 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|2|3|4))) ] 0","hypothesis":"David can now know that Patricia can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Patricia","Angela","David"],"index":1663,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998252213,"difficulty":0.001747787}
+{"premise":"There are four persons. Everyone is visible 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 Leonard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"David can now know whether Tyrone can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Roy","David","Leonard"],"index":7941,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995989203,"difficulty":0.0004010797}
+{"premise":"There are four persons. Everyone is visible 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))) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Stephanie can now know whether Dwayne can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Dwayne","Kenny","Stephanie"],"index":22883,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996396303,"difficulty":0.0003603697}
+{"premise":"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 (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Sheryl can now know that Bill can know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kay","Brandon","Sheryl","Bill"],"index":31808,"s-l":"forehead-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 someone is thirsty. It is publicly announced that James does not know whether Nelda is thirsty. It is publicly announced that Nelda does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Nelda can now know whether James can know whether Catherine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Catherine","James","Nelda"],"index":6322,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988620281,"difficulty":0.0011379719}
+{"premise":"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 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":"Melissa can now know whether Tyrone can know whether Tyrone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","Tyrone","Joseph"],"index":12378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9834998846,"difficulty":0.0165001154}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andre's card is shown to Andre. Andre's card is shown to Dirk. Dirk's card is shown to Dirk. 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 whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Dirk can now know whether Andre can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andre","Dirk"],"index":65709,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997016788,"difficulty":0.0002983212}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 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":"Anthony can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Anthony","John"],"index":48174,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995728135,"difficulty":0.0004271865}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristina does not know whether or not everyone is thirsty. It is publicly announced that Donna knows whether someone is thirsty. It is publicly announced that Lisa does not know whether Donna is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Donna can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Lisa","Kristina"],"index":1444,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981026053,"difficulty":0.0018973947}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony knows whether or not 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":"Andrew can now know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anthony","Andrew","Mindy"],"index":27460,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9051070213,"difficulty":0.0948929787}
+{"premise":"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 Alice's forehead is muddy. It is publicly announced that Joanna knows whether or not everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Joanna can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joanna","Ruby","Bill","Alice"],"index":42391,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Justin does not know whether Ralph is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Robert 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 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Ralph can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ralph","Justin","Rose","Robert"],"index":22735,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9706064463,"difficulty":1.9706064463}
+{"premise":"There are four persons. Everyone is visible 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 Kimberly 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) ] [ ! (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:1,2,3,4 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":"Walter can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Florence","Kimberly","Charles"],"index":16691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940165281,"difficulty":0.0059834719}
+{"premise":"There are two persons. Everyone is visible 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 Curt's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1&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":"Curt can now know that Paul can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Curt","Paul"],"index":64229,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983882904,"difficulty":0.0016117096}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ninfa 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":"Ninfa can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ninfa","Julie"],"index":4428,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980146885,"difficulty":0.0019853115}
+{"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 Gabriel. Gabriel's card is shown to John. Amber's card is shown to Derek. Derek's card is shown to Derek. It is publicly announced that someone picked a red card. It is publicly announced that Gabriel does not know whether Gabriel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows whether (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":"John can now know that Amber can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gabriel","Amber","John","Derek"],"index":20673,"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 is thirsty. It is publicly announced that Arthur knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentd knows 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)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Dennis can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Vincent","Richard","Dennis"],"index":57271,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patty's card is shown to Patty. Robin's card is shown to Patty. Patty's card is shown to Robin. Patty's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robin can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patty","Robin","John","Thomas"],"index":29519,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.924518466,"difficulty":0.075481534}
+{"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. John's card is shown to Michael. Donny'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 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donny","Michael","Teresa","John"],"index":67439,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9641411304,"difficulty":1.9641411304}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Allan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Allan","Angeline"],"index":13654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986139536,"difficulty":0.0013860464}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Alicia can now know that Sandra can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Alicia","Sandra"],"index":18006,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9832450151,"difficulty":0.0167549849}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether Taryn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agenta knows 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":"Jessica can now know whether Taryn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Taryn","Ronald","Jessica"],"index":89,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997674823,"difficulty":0.0002325177}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Helen. Sandra's card is shown to Sandra. Joseph's card is shown to Sandra. Helen's card is shown to Joseph. Sandra's card is shown to Joseph. Joseph's card is shown to Joseph. Sandra's card is shown to Teddy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Teddy can now know that Sandra can know that Helen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Sandra","Joseph","Teddy"],"index":912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970978498,"difficulty":0.0029021502}
+{"premise":"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 does not know 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) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Jere can now know whether Marty can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marty","Jere","Mark","Juan"],"index":25604,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9090505242,"difficulty":0.0909494758}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Robert. Sherry's card is shown to Thomas. Robert's card is shown to Sherry. Thomas's card is shown to Sherry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sherry can now know that Robert can know whether Sherry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Thomas","Sherry"],"index":11924,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5948124528,"difficulty":0.4051875472}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lettie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Lettie","Tara","Michael"],"index":51715,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marjorie's card is shown to Marjorie. Shawn's card is shown to Marjorie. Shawn's card is shown to Shawn. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Marjorie can now know that Shawn can know whether Marjorie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marjorie","Shawn"],"index":28910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8531727791,"difficulty":0.1468272209}
+{"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 Hazel. Virginia's card is shown to Virginia. Hazel's card is shown to Curtis. Judith's card is shown to Judith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Hazel can now know whether Curtis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hazel","Virginia","Curtis","Judith"],"index":40992,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9488701224,"difficulty":0.0511298776}
+{"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))) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Don can now know that Sonya can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Sonya","Julius","Don"],"index":19007,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9020254016,"difficulty":0.0979745984}
+{"premise":"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 (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christopher can now know whether Ray can know that Ruby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Christopher","Ray"],"index":6662,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986159801,"difficulty":0.0013840199}
+{"premise":"There are 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 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":"Rosie can now know that Raul can know that Raul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosie","Christopher","Raul"],"index":11143,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998555243,"difficulty":0.001444757}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Melody is thirsty. It is publicly announced that Melody does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Amy can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Melody","Amy","Steven"],"index":37590,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Christina can now know that Jan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jan","Christina"],"index":45091,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944100976,"difficulty":0.0055899024}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mercedes knows whether or not nobody's forehead is muddy. It is publicly announced that Larry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (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":"Sandra can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mercedes","Sandra","Larry"],"index":20455,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984388947,"difficulty":0.0015611053}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeff does not know whether Alice is thirsty. It is publicly announced that Cory 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Cory can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Cory","Jeff"],"index":7172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985926747,"difficulty":0.0014073253}
+{"premise":"There are four persons. Everyone is visible 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 Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Glenda can now know whether Eric can know whether Glenda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Glenda","Eric","Ron","Laura"],"index":16735,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996929169,"difficulty":0.0003070831}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that June does not know whether Irene is thirsty. It is publicly announced that June does not know whether Irene is thirsty.","smcdel_problem":"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) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Ronald can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Irene","Luis","June"],"index":37138,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997217059,"difficulty":0.0002782941}
+{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Nathaniel does not know whether Nathaniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows 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)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathaniel can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Jake","Nathaniel"],"index":41106,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991748929,"difficulty":0.0008251071}
+{"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 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 2) ] 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) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Raymond can now know that Bonnie can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonnie","Joseph","Raymond","Michael"],"index":65624,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9882869124,"difficulty":0.0117130876}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tuyet's card is shown to Richard. William's card is shown to Richard. Tuyet's card is shown to Tuyet. William's card is shown to Tuyet. William's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that William knows whether or not nobody picked a red card. It is publicly announced that William does not know whether Tuyet picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Richard can now know that William can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Tuyet","William"],"index":14842,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8587175012,"difficulty":0.1412824988}
+{"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 Deborah. Deborah's card is shown to Terry. Terry's card is shown to Terry. Deborah's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether Terry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Terry can now know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deborah","Terry","Mark"],"index":61443,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.994046092,"difficulty":0.005953908}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether or not everyone's forehead is muddy. It is publicly announced that Jennifer'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) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 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) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Gloria can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Gloria","Maria"],"index":60536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jennifer's card is shown to Jennifer. Danny's card is shown to Jennifer. Barbara's card is shown to Barbara. Danny's card is shown to Dale. Jennifer's card is shown to Danny. Barbara's card is shown to Danny. Danny's card is shown to Danny. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 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:1,4 Agentb:2 Agentc:4 Agentd:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jennifer can now know that Dale can know whether Danny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Barbara","Dale","Danny"],"index":16007,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9916152358,"difficulty":0.0083847642}
+{"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. Rhonda's card is shown to Carol. Jeffrey's card is shown to Rhonda. Carol's card is shown to Robert. Robert's card is shown to Robert. Jeffrey's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Carol can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carol","Rhonda","Robert","Jeffrey"],"index":1526,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997033477,"difficulty":0.0002966523}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Winifred's card is shown to Juan. Winifred's card is shown to Winifred. Andrew's card is shown to Kristopher. Juan'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:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Winifred can now know that Juan can know that Winifred picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Winifred","Kristopher","Andrew"],"index":36476,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972605705,"difficulty":0.0027394295}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eleanor does not know whether Randy is thirsty. It is publicly announced that Eleanor knows whether or not nobody is thirsty. It is publicly announced that Eleanor does not know whether Randy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Randy can now know whether Eleanor can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandy","Eleanor","Randy"],"index":64323,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997829795,"difficulty":0.0002170205}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bryan 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 (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":"Bryan can now know that Susie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Susie","Bryan"],"index":61376,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983332753,"difficulty":0.0016667247}
+{"premise":"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 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 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|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":"James can now know that Elizabeth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Elizabeth"],"index":48781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay does not know whether Fay's forehead is muddy. It is publicly announced that Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 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) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Pamela can now know that Fay can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Martha","Fay","Pamela","Sharon"],"index":37785,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9729511738,"difficulty":0.0270488262}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marta 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 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":"Mandy can now know whether Marta is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marta","Mandy","Victor","Lura"],"index":40130,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9495565891,"difficulty":0.0504434109}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 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) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kevin can now know that John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","John"],"index":18207,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5133118629,"difficulty":1.5133118629}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heather does not know whether Clarence is thirsty. It is publicly announced that Heather does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that (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":"Heather can now know whether Marguerite can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heather","Clarence","Marguerite"],"index":59881,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977086782,"difficulty":0.0022913218}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby does not know whether Michael is thirsty. It is publicly announced that Bruce does not know whether Ruby 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Frank can now know that Bruce can know that Bruce is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruby","Frank","Michael","Bruce"],"index":54264,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9457776546,"difficulty":1.9457776546}
+{"premise":"There are three persons. Everyone is visible 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 Betty's forehead is muddy. It is publicly announced that Alfonso knows whether or not nobody's forehead is muddy. It is publicly announced that Betty knows whether Alfonso's forehead is muddy.","smcdel_problem":"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 that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Alfonso can now know that Alfonso's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eric","Alfonso","Betty"],"index":60842,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9916743636,"difficulty":0.0083256364}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Juanita. Juanita's card is shown to Craig. Craig's card is shown to Craig. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Juanita can now know whether Craig can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Juanita","Craig"],"index":30947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999592483,"difficulty":0.000407517}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 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":"Lloyd can now know that Raymond can know that Lester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lester","Raymond","Richard","Lloyd"],"index":1459,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956976175,"difficulty":0.0043023825}
+{"premise":"There are four persons. Everyone is visible 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 Magaret knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows that 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":"Frances can now know that Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Judith","Magaret","Frances"],"index":33825,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.832944572,"difficulty":0.167055428}
+{"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 everyone is thirsty. It is publicly announced that Catherine knows whether Catherine is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Catherine","Michael"],"index":43315,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5789720416,"difficulty":1.5789720416}
+{"premise":"There are four persons. Everyone is visible 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 Anthony's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] Agentd knows whether (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! 3 ] 0","hypothesis":"George can now know whether Michael can know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Jeremy","Anthony","George"],"index":2162,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994075298,"difficulty":0.0005924702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows 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":"Rosella can now know that Julia can know that Herman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Larry","Herman","Julia","Rosella"],"index":24470,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9332294464,"difficulty":0.0667705536}
+{"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. It is publicly announced that Caleb 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 2) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Barbara can now know that Caleb can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Caleb","Jessica","Barbara"],"index":37580,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9786771536,"difficulty":0.0213228464}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 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) ] [ ! ~(2) ] 0","hypothesis":"Thomas can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Christopher","Dorotha"],"index":6536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996950626,"difficulty":0.0003049374}
+{"premise":"There are three persons. Everyone is visible 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 Venita's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 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":"Anna can now know that Venita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Venita","Anna"],"index":57870,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974250793,"difficulty":0.0025749207}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candice knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows 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":"Candice can now know that Dan can know that Candice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dan","Candice"],"index":36325,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975981116,"difficulty":0.0024018884}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leroy knows whether someone is thirsty. It is publicly announced that Fred 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)) ] (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) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know that Leroy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jerry","Leroy","Fred","Kevin"],"index":15872,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8789359927,"difficulty":0.1210640073}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeffery's card is shown to Suzanne. Suzanne's card is shown to Jeffery. Linda's card is shown to Jeffery. Jeffery's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery does not know whether Jeffery picked a red card. It is publicly announced that Jeffery knows whether or not nobody picked a red card. It is publicly announced that Suzanne picked a red card. It is publicly announced that Suzanne does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! 1 ] [ ! ~(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:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jeffery can now know that Suzanne can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Suzanne","Jeffery","Linda"],"index":22547,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971950054,"difficulty":0.0028049946}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Noah does not know whether Julie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (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":"Noah can now know that Julie can know that Raymond is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julie","Noah","Raymond","James"],"index":13804,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981122017,"difficulty":0.0018877983}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Mary can now know whether Stephen can know that Harrison's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecile","Harrison","Stephen","Mary"],"index":29758,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9932096601,"difficulty":0.0067903399}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that 1)","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":"Jacquelyn can now know that Jacquelyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jacquelyn","Samuel"],"index":66505,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982013702,"difficulty":0.0017986298}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Sharon's card is shown to Ronald. Ronald's card is shown to Darlena. Darlena's card is shown to Darlena. Sharon's card is shown to Darlena. Ronald's card is shown to Sharon. It is publicly announced that someone picked a red card. It is publicly announced that Darlena knows whether or not nobody picked a red card. It is publicly announced that Ronald does not know whether Darlena picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] (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:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ronald can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ronald","Darlena","Sharon"],"index":52209,"s-l":"explicit-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 is thirsty. It is publicly announced that Timothy does not know whether Ernesto is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Susie does not know whether Timothy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Susie can now know whether Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ernesto","Maria","Susie","Timothy"],"index":45139,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9923102856,"difficulty":0.0076897144}
+{"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 (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Isabel can now know that David can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Isabel","Stewart","Theresa","David"],"index":45727,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983250499,"difficulty":0.0016749501}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Julian can now know that Mario can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mario","Julian","Greg"],"index":31988,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983785152,"difficulty":0.0016214848}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows 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":"Pedro can now know whether Jordan can know that Jordan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jordan","Pedro","Noel"],"index":56849,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9697989821,"difficulty":0.0302010179}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Christopher can now know whether Miriam's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Miriam","James","Christopher"],"index":31049,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997250438,"difficulty":0.0002749562}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Kristen can now know that Kristen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristen","Gary","George","Thomas"],"index":24839,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5689430833,"difficulty":0.4310569167}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest does not know whether Ernest's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Freddie can now know that Ernest can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Freddie","Ernest","David"],"index":12983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891564846,"difficulty":0.0108435154}
+{"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 Chelsea. Chelsea's card is shown to George. George's card is shown to George. Michelle's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chelsea","George","Michelle"],"index":61726,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8019625545,"difficulty":0.1980374455}
+{"premise":"There are two persons. Everyone is visible 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 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 (~(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":"Beverly can now know that Daniel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Beverly","Daniel"],"index":47121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997571111,"difficulty":0.0002428889}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that 3)","n_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":"Esther can now know that Amy can know that Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Esther","Amy"],"index":15117,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978860021,"difficulty":0.0021139979}
+{"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 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":"Gerald can now know whether Derrick can know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Derrick","Jeffrey","Gerald"],"index":4416,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9873124957,"difficulty":0.0126875043}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raven knows whether someone's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffery can now know that Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raven","Mary","Jeffery","Dale"],"index":37023,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6088863611,"difficulty":1.6088863611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether William is thirsty. It is publicly announced that Amanda does not know whether Frank is thirsty. It is publicly announced that William does not know whether Amanda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"William can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Amanda","William","Frank"],"index":30569,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9876360297,"difficulty":0.0123639703}
+{"premise":"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's forehead is muddy. It is publicly announced that Joyce does not know whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that (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":"Joyce can now know whether Charles can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Charles"],"index":35963,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997822642,"difficulty":0.0002177358}
+{"premise":"There are two persons. Everyone is visible 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 Irma's forehead is muddy. It is publicly announced that Jeremy 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 whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Jeremy can now know that Irma can know whether Jeremy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeremy","Irma"],"index":55185,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997096658,"difficulty":0.0002903342}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laurie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sean can now know that Isabel can know that Isabel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sean","Isabel","Laurie"],"index":61954,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981880784,"difficulty":0.0018119216}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette'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":"Annette 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":["Clyde","Laura","Annette"],"index":14345,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997219443,"difficulty":0.0002780557}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether Herman's forehead is muddy. It is publicly announced that Melissa knows whether Herman's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows 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) ] [ ! (Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Melissa can now know that Virginia can know whether Herman's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virginia","Herman","Melissa"],"index":57542,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997432828,"difficulty":0.0002567172}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgiann knows whether Georgiann's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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":"Carrie can now know that Carrie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Georgiann","Carrie"],"index":60467,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981473684,"difficulty":0.0018526316}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether Betty can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","John","Betty"],"index":56452,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99966681,"difficulty":0.00033319}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia does not know whether or not everyone is thirsty.","smcdel_problem":"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 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":"Virginia can now know that John can know that Norman is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Virginia","Norman","John"],"index":17395,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9047992229,"difficulty":0.0952007771}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jaime's card is shown to Willie. Willie's card is shown to Allison. Jaime's card is shown to Allison. Willie's card is shown to Jaime. Jaime's card is shown to Jaime. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jaime can now know that Allison can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Allison","Jaime"],"index":58407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984475374,"difficulty":0.0015524626}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Vivian can now know whether Leslie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Myles","Jeanette","Leslie","Vivian"],"index":9434,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995989203,"difficulty":0.0004010797}
+{"premise":"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 Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(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":"Linda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Mary","Linda"],"index":13161,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9813010693,"difficulty":0.0186989307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Vanessa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Vanessa","John"],"index":65166,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985497594,"difficulty":0.0014502406}
+{"premise":"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's forehead is not 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) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"April can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["April","Lydia","Sara"],"index":58878,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985260367,"difficulty":0.0014739633}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Betsy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Betsy can now know that Betsy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dianne","Otto","Gerald","Betsy"],"index":57122,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973753691,"difficulty":0.0026246309}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Quentin knows whether Dan'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)","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":"Dan can now know that Quentin can know whether Dan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dan","Quentin"],"index":40780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997444749,"difficulty":0.0002555251}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Lawrence can now know that George can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mandy","Lawrence","George"],"index":38368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997848868,"difficulty":0.0002151132}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"James can now know that Melony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Melony","Edmund"],"index":3560,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9851629138,"difficulty":0.0148370862}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Judy. Judy's card is shown to Darci. Douglas's card is shown to Darci. Douglas's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Judy does not know whether Darci picked a red card. It is publicly announced that Douglas does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc 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:3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Douglas can now know whether Darci can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Judy","Darci","Douglas"],"index":50400,"s-l":"explicit-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 Neil does not know whether Christopher is thirsty. It is publicly announced that Christopher knows whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Christopher can now know that Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Neil","James","Christopher"],"index":30267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9726499915,"difficulty":0.0273500085}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy. It is publicly announced that Jane knows whether or not nobody's forehead is muddy. It is publicly announced that Jane knows whether Linda's forehead is muddy. It is publicly announced that Farah knows whether Farah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (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)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Farah can now know that Jane can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Linda","Farah","Jane"],"index":21316,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969099164,"difficulty":0.0030900836}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rocio does not know whether or not everyone's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy. It is publicly announced that Rocio does not know whether Rocio's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Rocio can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rocio","Kimberly"],"index":2014,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952782393,"difficulty":0.0047217607}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jared does not know whether Mary is thirsty. It is publicly announced that Mona does not know whether Robert is thirsty. It is publicly announced that Mona does not know whether Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mary can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mona","Mary","Robert","Jared"],"index":17440,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989228845,"difficulty":0.0010771155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gina does not know whether Gina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Vicki can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vicki","Terrell","Gina","Crystal"],"index":46287,"s-l":"forehead-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). Ophelia's card is shown to Ophelia. Russell's card is shown to Russell. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Ophelia picked a red card. It is publicly announced that Timothy does not know whether Timothy picked a red card. It is publicly announced that Ophelia does not know whether Timothy 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ophelia can now know that Russell picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ophelia","Russell","Timothy","Richard"],"index":25767,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.981323123,"difficulty":0.018676877}
+{"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 Leroy. Rebecca's card is shown to Leroy. Leroy's card is shown to John. John's card is shown to John. Rebecca's card is shown to John. Leroy's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Leroy does not know whether Leroy 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 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) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know that Leroy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leroy","John","Rebecca"],"index":19019,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9899166226,"difficulty":0.0100833774}
+{"premise":"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's forehead 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))","n_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":"Paul can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marie","Paul","Arianna"],"index":3467,"s-l":"forehead-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). David's card is shown to David. Bruce's card is shown to David. David's card is shown to Bruce. Donald's card is shown to Bruce. David's card is shown to Donald. Bruce's card is shown to Donald. Mark's card is shown to Donald. David's card is shown to Mark. Bruce's card is shown to Mark. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether Mark picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:1,2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Donald can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Bruce","Donald","Mark"],"index":8731,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"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 Alice'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: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 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) ] [ ! 4 ] 0","hypothesis":"Alice can now know whether Marilyn can know that Marilyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Alice","Heidy","Marilyn"],"index":33967,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9054900408,"difficulty":0.0945099592}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco does not know whether Francisco'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) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Kenneth can now know that Francisco's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eugene","Kenneth","Francisco","Julia"],"index":18912,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9690589309,"difficulty":0.0309410691}
+{"premise":"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 Adam'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 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Charlene can now know whether Charlene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charlene","Adam"],"index":44463,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9601352811,"difficulty":0.0398647189}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann does not know whether or not everyone's forehead is muddy. It is publicly announced that Francis knows whether or not everyone's forehead is muddy. It is publicly announced that Ann does not know whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentb 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":"Francis can now know that Michael can know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Francis","Sandra","Ann"],"index":38488,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8863900304,"difficulty":1.8863900304}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nadine's forehead is muddy. It is publicly announced that Nadine knows whether Jerry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentb knows 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) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ruben can now know that Jerry can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Ruben","Nadine"],"index":62295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984186888,"difficulty":0.0015813112}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Blanca can now know whether Jim's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kenneth","Blanca","Shawn","Jim"],"index":13971,"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). Randy's card is shown to Robert. Frances's card is shown to Randy. Randy's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Frances 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 whether (~(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":"Frances can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Frances","Robert","Randy"],"index":25292,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997043014,"difficulty":0.0002956986}
+{"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 Ronald. Madeleine's card is shown to Madeleine. Ronald's card is shown to Clara. Madeleine's card is shown to Clara. Clara's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Madeleine picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Madeleine","Ralph","Clara"],"index":6976,"s-l":"explicit-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 Mary is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows that (1&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":"Tommy can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tommy","Mary","Janice"],"index":8349,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985402822,"difficulty":0.0014597178}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Latoya. Marcus's card is shown to Latoya. Latoya's card is shown to Eva. Latoya's card is shown to Marcus. Eva's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Eva does not know whether Eva picked a red card.","smcdel_problem":"VARS 1,2,3,4 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":"Latoya can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Latoya","Eva","Marcus","George"],"index":6803,"s-l":"explicit-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 Doris does not know whether Jonathan is thirsty. It is publicly announced that Elmer knows whether Elmer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] Agenta knows that (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Doris can now know that Elmer can know that Doris is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Jonathan","John","Elmer"],"index":60433,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9939348102,"difficulty":0.0060651898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sheldon does not know whether Rachel is thirsty. It is publicly announced that William does not know whether Sheldon is thirsty. It is publicly announced that Sheldon does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Mavis can know that Rachel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sheldon","Mavis","Rachel","William"],"index":33475,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8521407247,"difficulty":0.1478592753}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Kenneth can now know that Monte can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Monte","Bryan"],"index":66919,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960545301,"difficulty":0.0039454699}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Belinda's card is shown to Janina. Ann's card is shown to Janina. Belinda's card is shown to Belinda. Ann's card is shown to Belinda. Ann's card is shown to Ann. It is publicly announced that someone picked a red card. It is publicly announced that Ann knows whether or not nobody picked a red card. It is publicly announced that Ann does not know whether Belinda picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Belinda can now know that Janina can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janina","Belinda","Ann"],"index":50295,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
+{"premise":"There are two persons. Everyone is visible 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 Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|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":"Victoria can now know that Terry can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victoria","Terry"],"index":35366,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997605681,"difficulty":0.0002394319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know that Kimberly can know that Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Kimberly","Katherine","Benjamin"],"index":62003,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984419942,"difficulty":0.0015580058}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Joan does not know whether Elaine 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) ] (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Joan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Basil","Joan","Elaine"],"index":9388,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985029697,"difficulty":0.0014970303}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernie knows whether Keith's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows 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 2) ] 0","hypothesis":"Ernie can now know that Irene can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irene","Keith","Ernie","Rosemary"],"index":30907,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997032285,"difficulty":0.0002967715}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luisa knows whether someone's forehead is muddy. It is publicly announced that Luisa 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) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb 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|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"James can now know whether Angela can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","James","Jeremy","Luisa"],"index":18146,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997059703,"difficulty":0.0002940297}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelvin does not know whether Valerie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that 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":"Kelvin can now know that Valerie can know that Charles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelvin","Valerie","Charles"],"index":58015,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980929494,"difficulty":0.0019070506}
+{"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 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) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Charlotte can now know that Derrick can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lois","Charlotte","Derrick","Mark"],"index":14970,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998436749,"difficulty":0.001563251}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carole knows whether Steven's forehead is muddy. It is publicly announced that Carlos knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 (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 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Carole can now know that Carlos can know whether Carole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carlos","Steven","Carole"],"index":7073,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997311234,"difficulty":0.0002688766}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cleveland's card is shown to Cleveland. Jonathan's card is shown to Cleveland. Cleveland's card is shown to Jonathan. Jonathan's card is shown to Linda. Harry's card is shown to Linda. Linda's card is shown to Harry. It is publicly announced that someone picked a red card. It is publicly announced that Jonathan 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 whether (Agentc knows whether 1)","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":"Jonathan can now know whether Linda can know whether Cleveland picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cleveland","Jonathan","Linda","Harry"],"index":3680,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981533885,"difficulty":0.0018466115}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia does not know whether Olive is thirsty. It is publicly announced that Olive does not know whether Maria is thirsty. It is publicly announced that Maria is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Maria can now know that Melody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melody","Olive","Maria","Marcia"],"index":37115,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9084642529,"difficulty":0.0915357471}
+{"premise":"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 Christopher's forehead is not muddy. It is publicly announced that Angel knows whether Christopher's forehead is muddy. It is publicly announced that Christopher knows whether Angel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Angel can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angel","John","Christopher"],"index":64494,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9493365288,"difficulty":0.0506634712}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Robert. Janette's card is shown to Janette. Robert's card is shown to Kristin. It is publicly announced that someone picked a red card. It is publicly announced that Janette picked a red card. It is publicly announced that Henry knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that Henry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Henry","Robert","Janette","Kristin"],"index":20216,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9161271453,"difficulty":0.0838728547}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentd knows that 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":"Stewart can now know that Melanie can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stewart","Kendra","John","Melanie"],"index":60764,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944264889,"difficulty":0.0055735111}
+{"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 Sheree does not know whether Harriet is 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) ] Agentd 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) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"John can now know whether Harriet can know that Sheree is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juanita","Sheree","Harriet","John"],"index":4114,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9786971211,"difficulty":0.0213028789}
+{"premise":"There are four persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that Elmira knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know that Samuel can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harry","Samuel","Colleen","Elmira"],"index":15032,"s-l":"forehead_mirror-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). Carol's card is shown to Carol. Amy's card is shown to Amy. Amy'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:1 Agentb:2 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 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carol can now know that Amy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Amy","Thelma"],"index":20895,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9852012992,"difficulty":0.0147987008}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Earl 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))","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":"Earl can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Meta","Earl","Gladys"],"index":27007,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7033029795,"difficulty":0.2966970205}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Antonio can now know whether Antonio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Antonio","John","Kimberly","Angelo"],"index":55285,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988052845,"difficulty":0.0011947155}
+{"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 Martha. Ronald's card is shown to Martha. Dana's card is shown to Dana. Dana's card is shown to Edmund. Edmund's card is shown to Edmund. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Edmund knows whether Edmund picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ronald can now know that Ronald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martha","Dana","Edmund","Ronald"],"index":37245,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.991778791,"difficulty":0.008221209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edgar does not know whether Ray is thirsty. It is publicly announced that Isabella knows whether someone is thirsty. It is publicly announced that Isabella does not know whether Edgar is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (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) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Isabella can now know whether Edgar can know that Ray is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edgar","Isabella","Ray","Joshua"],"index":49965,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9903261065,"difficulty":0.0096738935}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Edward can now know whether Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["David","Edward"],"index":56192,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7015801072,"difficulty":1.7015801072}
+{"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 (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":"Jane can now know whether Charlotte can know whether Charlotte is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Charlotte","Diana"],"index":22824,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982838035,"difficulty":0.0017161965}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not everyone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Dennis can now know whether Marguerite can know whether Marguerite's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marguerite","Dennis","Eduardo"],"index":44533,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8887568712,"difficulty":1.8887568712}
+{"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 Eugene 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 whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Maria can now know whether Sharon can know whether Eugene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Eugene","Sharon","Clarence"],"index":60946,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991681576,"difficulty":0.0008318424}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blanche knows whether 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))) ] 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joseph can now know whether Lawrence can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Callie","Joseph","Blanche"],"index":11546,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9955258965,"difficulty":0.0044741035}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frederick does not know whether Christopher is thirsty. It is publicly announced that Frederick does not know whether Rocky is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Frederick can now know whether Rocky is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rocky","Christopher","Frederick"],"index":30629,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.987188518,"difficulty":0.012811482}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 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":"Stuart can now know whether Eugene can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","Stuart","Cynthia","Duncan"],"index":23583,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995054007,"difficulty":0.0004945993}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janelle's card is shown to George. Janelle's card is shown to Janelle. It is publicly announced that someone picked a red card. It is publicly announced that Janelle picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Janelle can now know that George can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["George","Janelle"],"index":63102,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7517800331,"difficulty":0.2482199669}
+{"premise":"There are two persons. Everyone is visible 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 Cedric's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows 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":"Sean can now know that Cedric can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sean","Cedric"],"index":14973,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999545753,"difficulty":0.000454247}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corina knows whether someone's forehead is muddy. It is publicly announced that Howard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentd knows that (~(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":"Corina can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Fern","Howard","Corina"],"index":61854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982414246,"difficulty":0.0017585754}
+{"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 George. Rhonda's card is shown to George. Rhonda's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda knows whether or not everyone picked a red card. It is publicly announced that Rhonda knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Rhonda can now know whether George can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Rhonda"],"index":55641,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9856907725,"difficulty":0.0143092275}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":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":"Lauren can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruby","Odell","Harold","Lauren"],"index":16487,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982563853,"difficulty":0.0017436147}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 2 ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Stephanie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Leslie","Adam","Lee"],"index":2186,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983816147,"difficulty":0.0016183853}
+{"premise":"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 Keith's forehead is muddy. It is publicly announced that Carmela does not know whether Carmela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Irma can now know whether Keith can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keith","Irma","Carmela"],"index":10955,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9962792993,"difficulty":0.0037207007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows 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":"Jane can now know whether Anthony can know whether Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Jane","Terri"],"index":12428,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965571165,"difficulty":0.0034428835}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Neville does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows 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":"Neville can now know that Eric can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eric","Neville","Glen"],"index":57397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976875782,"difficulty":0.0023124218}
+{"premise":"There are four persons. Everyone is visible 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 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 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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Mary can now know that Elizabeth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eduardo","Amy","Elizabeth","Mary"],"index":64768,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983974099,"difficulty":0.0016025901}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Michael. Michael's card is shown to Jamie. Samuel's card is shown to Jamie. Reva's card is shown to Jamie. Michael's card is shown to Reva. Samuel's card is shown to Reva. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Jamie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Jamie","Samuel","Reva"],"index":17195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8879345655,"difficulty":0.1120654345}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ida does not know whether Jay is thirsty. It is publicly announced that Ida does not know whether Jay is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Frederick can now know that Frederick is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rebecca","Jay","Frederick","Ida"],"index":60888,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9920451641,"difficulty":0.0079548359}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 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":"Luanne can now know that Diana can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Luanne","Diana"],"index":26255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996279478,"difficulty":0.0003720522}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Kenneth's card is shown to Patrick. Jose's card is shown to Patrick. Patrick'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 everyone picked a red card. It is publicly announced that Jose picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,3 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:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Patrick can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Kenneth","Jose"],"index":9496,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997742772,"difficulty":0.0002257228}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole's forehead is muddy. It is publicly announced that Maria 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 (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":"Sarah can now know that Lisa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Maria","Lisa","Nicole"],"index":4496,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984804988,"difficulty":0.0015195012}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Charles. Charles's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether Ruth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Charles can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Marie","Andrew","Ruth"],"index":49899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997150302,"difficulty":0.0002849698}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Miles's card is shown to Dale. Dale's card is shown to Miles. Miles's card is shown to Miles. Pamela's card is shown to Miles. Pamela's card is shown to Pamela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Dale can now know that Pamela can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Miles","Pamela"],"index":17084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997152686,"difficulty":0.0002847314}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Chad's card is shown to Andrea. Martha's card is shown to Andrea. Andrea's card is shown to Chad. Chad's card is shown to Chad. Andrea's card is shown to Martha. 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 Martha knows whether Martha 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) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentc knows whether 3) ] [ ! (1&2&3) ] 0","hypothesis":"Martha can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrea","Chad","Martha"],"index":10369,"s-l":"explicit-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 is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Octavio knows whether Juan 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":"Juan can now know whether Octavio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Juan","Octavio"],"index":27365,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8469623327,"difficulty":1.8469623327}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tyesha's card is shown to Tyesha. Tyesha's card is shown to Jay. 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 Tyesha does not know whether Jay picked a red card. It is publicly announced that Tyesha does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jay can now know that Tyesha can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tyesha","Jay"],"index":14542,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerard's card is shown to Victoria. Gerard's card is shown to Gerard. It is publicly announced that someone 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 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Victoria can now know whether Victoria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Victoria","Gerard"],"index":56945,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9549604058,"difficulty":1.9549604058}
+{"premise":"There are two persons. Everyone is visible 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 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":"Nancy can now know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Estella","Nancy"],"index":58635,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9939134717,"difficulty":0.0060865283}
+{"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 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":"Brian can now know whether Lucille's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brian","Lucille","Bridgett","Keely"],"index":65375,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995377064,"difficulty":0.0004622936}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carla's card is shown to Carla. Johnathan's card is shown to Carla. Carla's card is shown to Colleen. Johnathan's card is shown to Colleen. Colleen's card is shown to Mickey. Mickey's card is shown to Mickey. Colleen's card is shown to Johnathan. It is publicly announced that someone picked a red card. It is publicly announced that Colleen knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,4 Agentc:2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows that (~(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":"Johnathan can now know whether Carla can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carla","Colleen","Mickey","Johnathan"],"index":46598,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995494485,"difficulty":0.0004505515}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derrick knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows that 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":"Derrick can now know that Derrick is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Derrick"],"index":3236,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977157116,"difficulty":0.0022842884}
+{"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 or not everyone is thirsty.","smcdel_problem":"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":"Michael can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roger","Chad","Michael","Arthur"],"index":1778,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970759153,"difficulty":0.0029240847}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janet's card is shown to Dorothy. Suzanne's card is shown to Dorothy. Dorothy's card is shown to Janet. Janet's card is shown to Janet. Janet's card is shown to Suzanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janet can now know whether Dorothy can know that Suzanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Janet","Suzanne"],"index":30601,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8985098004,"difficulty":1.8985098004}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorrie's card is shown to Lorrie. Andrea's card is shown to Lorrie. 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 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lorrie can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lorrie","Andrea"],"index":8575,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997205138,"difficulty":0.0002794862}
+{"premise":"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) ] [ ! ~(Agentd 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:2,3,4 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":"Nina can now know that Jose can know that Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Grace","Nina","Jose"],"index":9463,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6757603288,"difficulty":0.3242396712}
+{"premise":"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 knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (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":"Jesus can now know whether Donald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesus","Mary","Donald"],"index":15769,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9719337821,"difficulty":1.9719337821}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Susan can now know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Susan","William"],"index":24895,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8423573971,"difficulty":0.1576426029}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nickie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows whether (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) ] [ ! ~(4) ] 0","hypothesis":"Dianne can now know whether Anthony can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","David","Dianne","Nickie"],"index":408,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995177984,"difficulty":0.0004822016}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bud knows whether Curtis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Shawna can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bud","Curtis","Shawna","Julia"],"index":6332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9880852699,"difficulty":0.0119147301}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ardelia's card is shown to Winnie. Winnie's card is shown to Tina. Ardelia's card is shown to Tina. Winnie's card is shown to Ardelia. Ardelia's card is shown to Ardelia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tina can now know whether Ardelia can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Winnie","Tina","Ardelia"],"index":52326,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tricia does not know whether Wendy is thirsty. It is publicly announced that Wendy knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":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":"Wendy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tricia","Jean","Wendy","Cindy"],"index":22214,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983483553,"difficulty":0.0016516447}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Viola's card is shown to Robert. Robert's card is shown to Viola. Viola's card is shown to Viola. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Viola can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Viola"],"index":4552,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9859825969,"difficulty":1.9859825969}
+{"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 Evelyn. Amy's card is shown to Amy. David's card is shown to Amy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Evelyn can now know that Amy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evelyn","Amy","David"],"index":33208,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983691573,"difficulty":0.0016308427}
+{"premise":"There are three persons. Everyone is visible 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 Lance's forehead is muddy.","smcdel_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":"Lance can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeanette","Scott","Lance"],"index":27106,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985018969,"difficulty":0.0014981031}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith's forehead is not muddy. It is publicly announced that Kristopher's forehead is muddy. It is publicly announced that Edith knows whether Edith's forehead 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 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 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kristopher can now know that Thuy can know whether Edith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edith","Kristopher","Thuy"],"index":25579,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995604157,"difficulty":0.0004395843}
+{"premise":"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 Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Sheryl","Greg"],"index":67429,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936007857,"difficulty":0.0063992143}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether or not everyone'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 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Melissa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melissa","Freddie","Stephanie"],"index":33044,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921340942,"difficulty":0.0078659058}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Alan's card is shown to Alan. Alan's card is shown to Michael. Michael's card is shown to Michael. Michael'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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Alan can now know that Kenneth can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alan","Michael","Kenneth"],"index":61134,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983085394,"difficulty":0.0016914606}
+{"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 Carol does not know whether Kathryn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Mamie can now know that Kathryn can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Emily","Mamie","Carol"],"index":54486,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy does not know whether 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) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Erin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katherine","Jimmy","Jeanne","Erin"],"index":46923,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997475743,"difficulty":0.0002524257}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Constance's card is shown to Constance. Jean's card is shown to Jean. Tracy's card is shown to Jean. Constance's card is shown to Tracy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jean can now know that Tracy can know that Jean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Constance","Jean","Tracy"],"index":40772,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966057539,"difficulty":0.0033942461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that David knows whether Joseph'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 not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"David can now know whether Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Brenda","Joseph","Edna","David"],"index":4600,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995070696,"difficulty":0.0004929304}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Megan knows whether 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)","n_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":"Austin can now know that Paula can know whether Paula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paula","Austin","Megan"],"index":6285,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966689944,"difficulty":0.0033310056}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacy knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Stacy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Stacy","Nancy","Anthony"],"index":60811,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982460737,"difficulty":0.0017539263}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Jacquelyn can now know that Christine can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Charles","Jacquelyn","James"],"index":36917,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981284738,"difficulty":0.0018715262}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lydia knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Ronald can now know whether Staci can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Staci","Lydia","Ronald"],"index":35514,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995769858,"difficulty":0.0004230142}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannette'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) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Mike can now know whether Gary can know whether Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mike","Jeannette","Gary"],"index":14305,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978819489,"difficulty":0.0021180511}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wilfred does not know whether or not everyone is thirsty. It is publicly announced that Terri does not know whether Lucy is thirsty. It is publicly announced that Terri does not know whether Lucy is thirsty. It is publicly announced that Lucy 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)) ] (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Wilfred can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Terri","Wilfred","Lucy"],"index":53471,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7254763842,"difficulty":0.2745236158}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wallace can now know whether Michael can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geneva","Wallace","Michael","Theresa"],"index":50380,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999771297,"difficulty":0.000228703}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Annemarie's card is shown to Annemarie. Stacy's card is shown to Stacy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Annemarie can now know whether Stacy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annemarie","Stacy","Susan"],"index":50924,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7172392607,"difficulty":0.2827607393}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jared knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jared can now know that Jeffrey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Jared","Jeffrey"],"index":7748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983170033,"difficulty":0.0016829967}
+{"premise":"There are two persons. Everyone is visible 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 Kimberly'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 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":"Ralph can now know whether Kimberly can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberly","Ralph"],"index":47052,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997857213,"difficulty":0.0002142787}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorthey 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) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jacqueline can now know that James can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorthey","Jacqueline","James"],"index":20864,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995955825,"difficulty":0.0004044175}
+{"premise":"There are four persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Clara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Norma","April","Clara"],"index":35978,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984278679,"difficulty":0.0015721321}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether Milton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"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":"Milton can now know that Shana can know that Milton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Julio","Shana","Milton"],"index":4692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974611998,"difficulty":0.0025388002}
+{"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. Louis's card is shown to Faye. Louis's card is shown to Jeremiah. Faye's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Jeremiah does not know whether Jeremiah picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jeremiah can now know whether Louis can know that Jeremiah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Faye","Jeremiah","Elizabeth"],"index":399,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8739686608,"difficulty":0.1260313392}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randa knows whether or not everyone's forehead is muddy. It is publicly announced that Randa does not know whether Randa's forehead is muddy.","smcdel_problem":"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 (~(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":"Peggy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Randa","Jimmy","Peggy"],"index":12216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981841445,"difficulty":0.0018158555}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jack does not know whether Adam is thirsty. It is publicly announced that Tamara does not know whether Adam is thirsty. It is publicly announced that Tamara does not know whether Adam is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jack can now know whether Adam is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jack","Adam","Tamara"],"index":54854,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9674314857,"difficulty":0.0325685143}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether Florence's forehead is muddy. 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) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Florence can now know whether Robert can know that Freda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Freda","Florence","Vincent","Robert"],"index":41019,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9900333285,"difficulty":0.0099666715}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether or not nobody is thirsty. It is publicly announced that Paula does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (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":"Frederick can now know whether Paula can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paula","Richard","Frederick"],"index":9711,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9916811585,"difficulty":0.0083188415}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Myrtice can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alvin","David","Myrtice"],"index":14469,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997550845,"difficulty":0.0002449155}
+{"premise":"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 (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Glen can now know whether Meagan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Meagan","Wade","Glen"],"index":19091,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9964482784,"difficulty":0.0035517216}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sue does not know whether Gwendolyn is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Gwendolyn can now know whether William can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sue","Gwendolyn","William"],"index":14207,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997826219,"difficulty":0.0002173781}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darlene knows whether someone is thirsty. It is publicly announced that George 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)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Don can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hope","Darlene","George","Don"],"index":18131,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978654981,"difficulty":0.0021345019}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest knows whether or not nobody's forehead is muddy. It is publicly announced that Michael'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 that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(4) ] 0","hypothesis":"Ernest can now know that Ernest's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brittney","Bethany","Ernest","Michael"],"index":57658,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937018156,"difficulty":0.0062981844}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know that Norma can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Norma","Jesse"],"index":55409,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984179735,"difficulty":0.0015820265}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danielle's card is shown to Scott. Donald's card is shown to Donald. Danielle's card is shown to Danielle. 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 Agentc:3 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:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Danielle can now know whether Donald can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Donald","Danielle","Julia"],"index":57357,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8656083345,"difficulty":0.1343916655}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irma's card is shown to Mable. Maria's card is shown to Maria. Mable's card is shown to Gary. Irma's card is shown to Gary. Mable's card is shown to Irma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 1)","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":"Maria can now know whether Mable picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mable","Maria","Gary","Irma"],"index":20956,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6251083016,"difficulty":0.3748916984}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether 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 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Liane can now know whether Robert can know whether Liane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Maria","Liane"],"index":8548,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985557199,"difficulty":0.0014442801}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (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":"Jay can now know whether Jody can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Regina","Albert","Jody","Jay"],"index":44183,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974730611,"difficulty":0.0025269389}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis's forehead is muddy.","smcdel_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 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":"Bennett can now know that William can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bennett","William","Dennis"],"index":45860,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9841819406,"difficulty":0.0158180594}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that 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":"Tony can now know that Tony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marlene","Tony","Scott"],"index":20874,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9647946954,"difficulty":0.0352053046}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emmanuel does not know whether or not everyone is thirsty. It is publicly announced that Judith knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Thomas can now know whether Judith can know whether Emmanuel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emmanuel","Stephen","Thomas","Judith"],"index":13815,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988656044,"difficulty":0.0011343956}
+{"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. Charlie's card is shown to Marion. Mark's card is shown to Charlie. Marion's card is shown to Mark. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:2 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:1 Agentb:3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know whether Gregory can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Marion","Charlie","Mark"],"index":52717,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980310798,"difficulty":0.0019689202}
+{"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (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) ] [ ! ~(4) ] 0","hypothesis":"Samatha can now know that James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maureen","Samatha","Sandy","James"],"index":22677,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997840524,"difficulty":0.0002159476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcellus knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows whether (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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jean can now know whether Marcellus can know that Marcellus is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Russell","Stephen","Marcellus"],"index":42981,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8394451141,"difficulty":1.8394451141}
+{"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 Josephine. Christopher's card is shown to Lynn. Lynn's card is shown to Lynn. It is publicly announced that someone picked a red card. It is publicly announced that Josephine does not know whether Josephine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Josephine can now know that Lynn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Josephine","Dawn","Christopher","Lynn"],"index":18832,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9953373671,"difficulty":0.0046626329}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows that 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":"Keith can now know that Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Francis","Matthew","Lori","Keith"],"index":33425,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939773083,"difficulty":0.0060226917}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hope does not know whether or not everyone is thirsty. It is publicly announced that Antoinette 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)) ] (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)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Hope can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Antoinette","Charlene","Hope"],"index":18882,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows that (Agenta knows that 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":"Mabel can now know that Jennie can know that Mabel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennie","Michael","Mabel","Rosalie"],"index":19995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9784299135,"difficulty":0.0215700865}
+{"premise":"There are four persons. Everyone is visible 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 Sandra knows whether Sandra's forehead is muddy. It is publicly announced that Kyle knows whether Kyle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kyle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","Kyle","James","Laura"],"index":18696,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9910384417,"difficulty":0.0089615583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Talia's forehead is muddy. It is publicly announced that Floyd does not know whether Floyd's forehead is muddy. It is publicly announced that Floyd knows whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Floyd can now know whether Ralph can know whether Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Talia","Ralph","Jeffrey","Floyd"],"index":61564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989338517,"difficulty":0.0010661483}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Krista knows whether Krista's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 3)","n_announcements":1,"pbcheck":"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":"Krista can now know that Sarah can know that Krista's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sarah","Stanley","Krista"],"index":13007,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976298809,"difficulty":0.0023701191}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Pamela can now know that James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Pamela","James"],"index":36234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983849525,"difficulty":0.0016150475}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Amy. Amy's card is shown to Valerie. Valerie's card is shown to Valerie. Tracy's card is shown to Valerie. It is publicly announced that someone picked a red card. It is publicly announced that Amy 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 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:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Amy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amy","Valerie","Tracy"],"index":66282,"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 Lewis does not know whether Gloria is thirsty. It is publicly announced that William does not know whether Gloria 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that Lewis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","John","Gloria","Lewis"],"index":66895,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9340484738,"difficulty":0.0659515262}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Douglas. Wanda's card is shown to Jerome. Douglas's card is shown to Wanda. Wanda's card is shown to Wanda. It is publicly announced that someone picked a red card. It is publicly announced that Jerome picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Wanda can now know that Douglas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Douglas","Jerome","Wanda"],"index":65016,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.947609067,"difficulty":0.052390933}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Patricia can now know whether Stephanie can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Stephanie","Patricia"],"index":57844,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997113347,"difficulty":0.0002886653}
+{"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 Lee is thirsty. It is publicly announced that Deanna does not know whether John 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 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Lee can now know that John can know that John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Harry","Lee","Deanna"],"index":66444,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9915748239,"difficulty":0.0084251761}
+{"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 Diana. Elizabeth's card is shown to Diana. Karen's card is shown to Karen. Elizabeth's card is shown to Karen. Diana's card is shown to Elizabeth. Karen's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Diana 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 (1&2&3&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":"Karen can now know whether Elizabeth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Karen","Elizabeth","Mary"],"index":64114,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9591677785,"difficulty":1.9591677785}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlo's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 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":"Marlo can now know that Julie can know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marlo","Julie","Scott"],"index":7491,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957060218,"difficulty":0.0042939782}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Magda knows whether Magda's forehead is muddy. It is publicly announced that Roxanne knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Magda can now know that Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Magda","Adam","Roxanne"],"index":65670,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977667332,"difficulty":0.0022332668}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexandra's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Alexandra knows whether Chae's forehead 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 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 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Chae can now know that Alice can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexandra","Chae","Alice"],"index":36478,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"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 Marlene does not know whether Dell is thirsty. It is publicly announced that Doris knows whether or not everyone is thirsty. It is publicly announced that Doris 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) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Marlene can now know that Doris can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dell","Marlene","Doris"],"index":53627,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gabriel knows whether Dannielle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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 4) ] 0","hypothesis":"Dannielle can now know that Gabriel can know that Dannielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gabriel","Timothy","Janet","Dannielle"],"index":36508,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973996878,"difficulty":0.0026003122}
+{"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. It is publicly announced that Robert knows whether Robert is thirsty. It is publicly announced that Jennifer does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Blanch can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Jennifer","Carlos","Blanch"],"index":5600,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6664562821,"difficulty":1.6664562821}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Vernon's card is shown to Pauline. Vernon's card is shown to Stephanie. Vernon's card is shown to Todd. Pauline's card is shown to Vernon. It is publicly announced that someone picked a red card. It is publicly announced that Pauline knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Pauline can now know that Todd can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Stephanie","Todd","Vernon"],"index":27002,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carmen knows whether someone is thirsty. It is publicly announced that Christopher does not know whether Frank is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Christopher can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carmen","Christopher","Frank"],"index":63323,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997158647,"difficulty":0.0002841353}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leandra's card is shown to Leandra. Leandra's card is shown to Dale. Dale's card is shown to Dale. Joyce's card is shown to Dale. Dale's card is shown to Joyce. Joyce's card is shown to Joyce. Janice's card is shown to Joyce. Janice's card is shown to Janice. It is publicly announced that someone picked a red card. It is publicly announced that Dale knows whether Joyce picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:2,3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Joyce can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leandra","Dale","Joyce","Janice"],"index":51365,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997205138,"difficulty":0.0002794862}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francisco is thirsty. It is publicly announced that Nathaniel 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)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Francisco","Nathaniel","Mary","Michael"],"index":53176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Shawn does not know whether Shawn's forehead is muddy.","smcdel_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 (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Shawn can now know whether Eun can know that Shawn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eun","Linda","Shawn"],"index":50964,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5265455246,"difficulty":0.4734544754}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roland knows whether someone's forehead is muddy. It is publicly announced that Joseph knows whether Roland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] (Agenta knows 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)) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Doris can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Doris","Joseph","Irene","Roland"],"index":59636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984890223,"difficulty":0.0015109777}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mark can now know that Ramon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Ramon","Mark","Melinda"],"index":44509,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983677268,"difficulty":0.0016322732}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maddie's forehead is not muddy. It is publicly announced that Maddie knows whether Nancy's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Nancy can now know that Maddie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nancy","Maddie"],"index":27085,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984916449,"difficulty":0.0015083551}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dewayne knows whether or not nobody is thirsty. It is publicly announced that Carla does not know whether Dewayne is thirsty. It is publicly announced that Dewayne is thirsty. It is publicly announced that Douglas does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 4) ] [ ! 4 ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Carla can now know that Douglas can know that Douglas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carla","Michael","Douglas","Dewayne"],"index":48449,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.985250175,"difficulty":0.014749825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Georgette 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 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":"Elnora can now know that Georgette can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Georgette","Elnora","Donna","Jean"],"index":45480,"s-l":"internal-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 is thirsty. It is publicly announced that Lila does not know whether Frank is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Frank can now know whether Aaron is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Frank","David","Lila"],"index":41776,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969595671,"difficulty":0.0030404329}
+{"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 Edwina. Edwina's card is shown to Mary. Mary's card is shown to Mary. Mary's card is shown to William. William's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Edwina can know whether Edwina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edwina","Mary","William"],"index":3701,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8919342756,"difficulty":0.1080657244}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brenda's card is shown to Brenda. Brenda's card is shown to Tricia. Brenda's card is shown to Becky. Tricia's card is shown to Becky. Becky's card is shown to Becky. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Becky can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brenda","Tricia","Becky"],"index":36884,"s-l":"explicit-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 Rocky does not know whether Rocky's forehead is muddy. It is publicly announced that Bradley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know that Wilma can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rocky","Bradley","Wilma"],"index":6031,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9490939975,"difficulty":0.0509060025}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kara's card is shown to Irving. Kara's card is shown to Donna. Donna's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Irving does not know whether Irving picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Irving can now know whether Kara can know that Kara picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Irving","Kara","Donna"],"index":49512,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8672891259,"difficulty":0.1327108741}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (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":"Eric can now know that Amy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teresa","Eric","Amy"],"index":16125,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983975291,"difficulty":0.0016024709}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfredo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Rhonda can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Alfredo","Jeremy","Rhonda"],"index":22027,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9427281618,"difficulty":0.0572718382}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 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":"Joyce can now know that David can know that Jan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joyce","David","Jan"],"index":20756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984745383,"difficulty":0.0015254617}
+{"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 Jason is thirsty. It is publicly announced that Edward knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that (1|2|3|4))","n_announcements":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":"Crystal can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Beth","Crystal","Jason"],"index":16182,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not nobody's forehead is muddy. It is publicly announced that Darrell does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 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":"Bruce can now know that Bruce's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bruce","Patrick","Darrell"],"index":46456,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5440402031,"difficulty":0.4559597969}
+{"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 Beverly. Phyllis's card is shown to Beverly. Gladys's card is shown to Elizabeth. Elizabeth's card is shown to Elizabeth. Elizabeth's card is shown to Phyllis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows 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:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beverly can now know whether Gladys can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Gladys","Elizabeth","Phyllis"],"index":59464,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen knows whether Glen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Terry can now know that Glen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Glen","Elijah","Leora","Terry"],"index":34490,"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. It is publicly announced that someone is thirsty. It is publicly announced that Melissa knows whether Melissa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Melissa can now know that Shannon can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Constance","Shannon","Melissa"],"index":28844,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9563267231,"difficulty":0.0436732769}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy. 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 Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Gregory can now know that Matthew can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gregory","Matthew","Martha"],"index":41133,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996908903,"difficulty":0.0003091097}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darell does not know whether Darell's forehead is muddy. It is publicly announced that Ollie knows whether Darell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 4) ] Agenta knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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 4) ] 0","hypothesis":"Ollie can now know that Darell can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ollie","Elisa","Jose","Darell"],"index":61943,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997157454,"difficulty":0.0002842546}
+{"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 Vincent. Vincent's card is shown to Robert. Robert's card is shown to Robert. Vincent's card is shown to Bert. Robert's card is shown to Bert. Bert's card is shown to Sharon. Sharon's card is shown to Sharon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vincent","Robert","Bert","Sharon"],"index":7478,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998500824,"difficulty":0.001499176}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Alice's card is shown to Alice. Bernice's card is shown to Alice. Alice's card is shown to Bernice. 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 Bernice does not know whether Bernice 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) ] (Agentb knows that 2)","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":"Alice can now know that Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Alice","Bernice"],"index":26690,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9630122185,"difficulty":0.0369877815}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Veronica's card is shown to Ronald. Helene's card is shown to Ronald. Ronald's card is shown to Veronica. Helene's card is shown to Veronica. Helene's card is shown to Sally. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know whether Veronica can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Veronica","Helene","Sally"],"index":4260,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999565661,"difficulty":0.000434339}
+{"premise":"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) ] [ ! (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: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":"Jeffrey can now know whether Cassie can know whether Karen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Mary","Karen","Cassie"],"index":11617,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995340109,"difficulty":0.0004659891}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daisy's card is shown to Daisy. Mavis's card is shown to Daisy. Lee's card is shown to Mavis. Daisy's card is shown to Lee. It is publicly announced that someone picked a red card. It is publicly announced that Lee does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mavis can now know whether Daisy can know whether Lee picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daisy","Mavis","Lee"],"index":39116,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979871511,"difficulty":0.0020128489}
+{"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 Mandy. Mandy's card is shown to Steven. Steven's card is shown to Steven. Minnie's card is shown to Steven. Mandy's card is shown to Minnie. It is publicly announced that someone picked a red card. It is publicly announced that Minnie does not know whether or not everyone picked a red card. It is publicly announced that Steven knows whether Minnie 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) ] Agentc knows that (Agenta knows whether (1&2&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":"Minnie can now know that Mandy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mandy","Steven","Minnie"],"index":52454,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7805024981,"difficulty":1.7805024981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luther does not know whether Luther's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agenta knows that (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) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Brian can now know that Leo can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Luther","Leo"],"index":2183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984735847,"difficulty":0.0015264153}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that Dennis knows whether someone's forehead is muddy. It is publicly announced that Louis 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|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Louis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louis","Dennis"],"index":6914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lela's card is shown to Jessie. Sandra's card is shown to Lela. Jessie's card is shown to Sandra. Neil's card is shown to Sandra. Jessie's card is shown to Neil. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know that Lela can know whether Lela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessie","Lela","Sandra","Neil"],"index":49084,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8495640159,"difficulty":0.1504359841}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandy does not know whether Melissa is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Melissa can now know that Brandy can know whether Brandy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brandy","Melissa"],"index":39173,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988135099,"difficulty":0.0011864901}
+{"premise":"There are three persons. Everyone is visible 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 Margie 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) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Margie can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margie","Frank","David"],"index":64787,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997611642,"difficulty":0.0002388358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that (1|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":"Rudolph can now know whether Apolonia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Apolonia","Rudolph","Joseph","Woodrow"],"index":38345,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997664094,"difficulty":0.0002335906}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Tamara knows 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) ] [ ! (1&2&3&4) ] [ ! (Agenta 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Tamara can now know whether Clark can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tamara","Daniel","Clark","Melvin"],"index":55831,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know whether Arthur can know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Arthur","Timothy"],"index":23291,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990122318,"difficulty":0.0009877682}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen does not know whether Mary is thirsty. It is publicly announced that Helen does not know whether Mary 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 (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Mary can now know whether Helen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Mary"],"index":30245,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994644523,"difficulty":0.0005355477}
+{"premise":"There are three persons. Everyone is visible 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 Stewart's forehead is muddy. It is publicly announced that Jimmie's forehead is not muddy. It is publicly announced that Jimmie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that (1|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":"Mary can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Jimmie","Stewart"],"index":42320,"s-l":"forehead_mirror-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 Maria does not know whether or not everyone is thirsty. It is publicly announced that Bruce does not know whether Vincent is thirsty. It is publicly announced that Maria does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Bruce can now know that Maria can know whether Bruce is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Vincent","Bruce"],"index":45811,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7449011803,"difficulty":1.7449011803}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Antoinette's card is shown to Ricky. Antoinette's card is shown to Virginia. Virginia's card is shown to Antoinette. Ricky's card is shown to Jordan. It is publicly announced that someone picked a red card. It is publicly announced that Ricky picked a black card. It is publicly announced that Ricky does not know whether Jordan picked a red card. It is publicly announced that Ricky does not know whether Jordan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Antoinette can now know that Jordan can know whether Antoinette picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ricky","Virginia","Antoinette","Jordan"],"index":11369,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6426513791,"difficulty":0.3573486209}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Xavier does not know whether Judith is thirsty. It is publicly announced that Judith is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Judith can now know that Aaron can know that Judith is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Aaron","Gregory","Judith","Xavier"],"index":54835,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9193585515,"difficulty":0.0806414485}
+{"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 Ramona knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Leigh can now know that Ramona can know whether Crystal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ramona","Crystal","Leigh"],"index":14403,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9824135303,"difficulty":0.0175864697}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lessie does not know whether James is thirsty. It is publicly announced that David does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Lessie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Lessie","David","James"],"index":30429,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986374974,"difficulty":0.0013625026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene does not know whether Rene's forehead is muddy. It is publicly announced that Diana 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))) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"George can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rene","Linda","Diana","George"],"index":52211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996106029,"difficulty":0.0003893971}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows 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":"Tammy can now know that Steve can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tammy","Steve"],"index":63601,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996311665,"difficulty":0.0003688335}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sherrie does not know whether Al is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Crystal can now know whether Al can know whether Sherrie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sherrie","Crystal","Al"],"index":65393,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987990856,"difficulty":0.0012009144}
+{"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 Steve is thirsty. It is publicly announced that Joanie is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] (Agentb knows that 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) ] [ ! ~(2) ] 0","hypothesis":"Joanie can now know that Joanie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Joanie","Steve"],"index":26608,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6170182824,"difficulty":1.6170182824}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby knows whether or not everyone is thirsty. It is publicly announced that Darlene is not thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] [ ! (1|2|3) ] 0","hypothesis":"Ruby can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Darlene","Ruby","Lawrence"],"index":52125,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are four persons. Everyone is visible 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 Christopher'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) ] 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) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Stewart can now know that Christopher can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Lourdes","Jeremy","Stewart"],"index":10456,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9964630008,"difficulty":0.0035369992}
+{"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 Richard. Carolyn's card is shown to Carolyn. Jean's card is shown to Carolyn. 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:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carolyn can now know that Lorene can know that Jean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Carolyn","Lorene","Jean"],"index":27195,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976602793,"difficulty":0.0023397207}
+{"premise":"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 does not know whether Jessie's forehead is muddy. It is publicly announced that Frederick does not know whether Frederick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 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) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Randy can now know that Jessie can know whether Randy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frederick","Alicia","Randy","Jessie"],"index":60881,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992811084,"difficulty":0.0007188916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Calvin does not know whether or not everyone is thirsty. It is publicly announced that Barbara knows whether someone is thirsty. It is publicly announced that Mattie does not know whether Barbara is thirsty. It is publicly announced that Mattie does not know whether Maurice is thirsty.","smcdel_problem":"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 whether (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Mattie can now know whether Maurice can know that Mattie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Maurice","Mattie","Calvin"],"index":150,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.993449986,"difficulty":0.006550014}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dawn 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 (~(1|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":"David can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dawn","Jerry","David"],"index":37391,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997079968,"difficulty":0.0002920032}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether or not everyone is thirsty. It is publicly announced that Walter is thirsty. It is publicly announced that Walter is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Mary can now know that Walter can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Charles","Walter","Thomas"],"index":28622,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9323219657,"difficulty":1.9323219657}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gordon's card is shown to Sandra. Beata's card is shown to Beata. Gordon's card is shown to Beata. Sandra's card is shown to Gordon. 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) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beata can now know whether Sandra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","Janet","Beata","Gordon"],"index":27626,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5510857701,"difficulty":0.4489142299}
+{"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 Viola. Nancy's card is shown to Viola. Chris's card is shown to Chris. Nancy's card is shown to Chris. Viola's card is shown to Anne. Chris's card is shown to Anne. Nancy's card is shown to Anne. Anne's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1,2,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1,2,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nancy can now know that Nancy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Viola","Chris","Anne","Nancy"],"index":20870,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9913593531,"difficulty":0.0086406469}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stefanie does not know whether Bonnie is thirsty. It is publicly announced that Mary does not know whether Stefanie is thirsty. It is publicly announced that Bonnie does not know whether or not everyone is thirsty. It is publicly announced that Harold does not know whether Stefanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mary can now know whether Bonnie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stefanie","Mary","Harold","Bonnie"],"index":10440,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996937513,"difficulty":0.0003062487}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Socorro's card is shown to Johnnie. Karyn's card is shown to Johnnie. Johnnie's card is shown to Constance. Socorro's card is shown to Constance. Socorro's card is shown to Socorro. Constance's card is shown to Karyn. It is publicly announced that someone picked a red card. It is publicly announced that Karyn picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Johnnie can now know whether Johnnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnnie","Constance","Socorro","Karyn"],"index":19917,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9880892634,"difficulty":1.9880892634}
+{"premise":"There are three persons. Everyone is visible 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 Eleanor 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 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":"Elizabeth can now know that Eleanor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlie","Elizabeth","Eleanor"],"index":65737,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8399729133,"difficulty":0.1600270867}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agentb knows that 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":"Sylvia can now know that Robert can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Libby","Robert","Sylvia"],"index":40889,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978216887,"difficulty":0.0021783113}
+{"premise":"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 Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Joseph can know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Joseph","Julian"],"index":2948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725578427,"difficulty":0.0274421573}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to 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)","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 Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Mary"],"index":40697,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9669574499,"difficulty":0.0330425501}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows 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) ] [ ! (~(1&2)) ] 0","hypothesis":"Robert can now know that Joyce can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Joyce"],"index":35071,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995751977,"difficulty":0.0004248023}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lenora knows whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 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":"Lenora can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Mary","Lenora","Katie"],"index":44477,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998172164,"difficulty":0.001827836}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether or not 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 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":"Martha can now know whether Andrew can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","Andrew","Christopher"],"index":10857,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999453485,"difficulty":0.000546515}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Rebecca. Henry's card is shown to Rebecca. Richard's card is shown to Rebecca. Rebecca's card is shown to Henry. Henry'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:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rebecca can now know whether Henry can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebecca","Henry","Richard"],"index":37739,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8911633492,"difficulty":1.8911633492}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Lester can now know that Lester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kathy","Lester"],"index":39484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.955119133,"difficulty":0.044880867}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gary's card is shown to Gary. Gary's card is shown to Kevin. Delores's card is shown to Kevin. Jennifer's card is shown to Kevin. Kevin's card is shown to Jennifer. Delores's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Delores can now know that Kevin can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Kevin","Delores","Jennifer"],"index":24536,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974691868,"difficulty":0.0025308132}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Grace. Charles's card is shown to Charles. Richard's card is shown to Richard. Grace's card is shown to Michelle. Richard's card is shown to Michelle. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:1,3 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:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know that Michelle can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Grace","Charles","Richard","Michelle"],"index":34931,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9365061522,"difficulty":0.0634938478}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Venessa 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)","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":"Ignacio can now know whether Ignacio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ignacio","Venessa","William"],"index":65529,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9982168078,"difficulty":0.0017831922}
+{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that Nathaniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Nathaniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Kelly knows whether Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Judson can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Judson","Kelly","Nathaniel"],"index":37847,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.988483727,"difficulty":0.011516273}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyson 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 3) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Erika can now know that Tyson can know that Charlene is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Erika","Charlene","Monica","Tyson"],"index":62206,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981672764,"difficulty":0.0018327236}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emilia's card is shown to Phyllis. Marcia's card is shown to Phyllis. Phyllis's card is shown to Emilia. Joseph's card is shown to Emilia. Phyllis's card is shown to Joseph. Emilia's card is shown to Joseph. Joseph's card is shown to Joseph. Phyllis's card is shown to Marcia. Marcia's card is shown to Marcia. 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 Agentc:1,2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3 Agentc:1,2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emilia can now know that Phyllis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phyllis","Emilia","Joseph","Marcia"],"index":2092,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984639883,"difficulty":0.0015360117}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anna does not know whether Marylou is thirsty. It is publicly announced that Joshua does not know whether Marylou is thirsty. It is publicly announced that Anna 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) ] (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 4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(1) ] 0","hypothesis":"Joshua can now know whether Marylou is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Mary","Joshua","Marylou"],"index":55595,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.868981421,"difficulty":0.131018579}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Phillip's card is shown to Phillip. John's card is shown to George. Ryan's card is shown to John. George's card is shown to Ryan. 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) ] Agentb knows that (Agenta knows that 1)","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":"George can now know that Phillip can know that Phillip picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Phillip","George","John","Ryan"],"index":64815,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976670742,"difficulty":0.0023329258}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty. It is publicly announced that James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! 3 ] 0","hypothesis":"Diane can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dorothy","Diane","James"],"index":34445,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985386133,"difficulty":0.0014613867}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 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 (1&2&3&4)) ] 0","hypothesis":"Linda can now know that Suzanne can know that Julio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julio","Linda","Judith","Suzanne"],"index":9851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9362828135,"difficulty":0.0637171865}
+{"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 Frances. Frances's card is shown to Judith. Amy's card is shown to Judith. 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 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amy can now know whether Frances picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Frances","Amy","Judith"],"index":17754,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8626035452,"difficulty":1.8626035452}
+{"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 Virginia. Lisa's card is shown to Virginia. Virginia's card is shown to Steven. Virginia's card is shown to Lisa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know whether Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Steven","Lisa"],"index":5838,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9660279751,"difficulty":1.9660279751}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether (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":"Hazel can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Hazel","Charlotte"],"index":60725,"s-l":"internal-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). Rachel's card is shown to Samuel. Anthony's card is shown to Anthony. Victor's card is shown to Rachel. Rachel's card is shown to Victor. Victor's card is shown to Victor. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether Rachel 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) ] 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:2 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Anthony can now know whether Samuel can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Anthony","Rachel","Victor"],"index":65847,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9964700937,"difficulty":0.0035299063}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lan's card is shown to Raymond. Gary's card is shown to Gary. Gary's card is shown to Lan. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (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) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Gary can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Raymond","Gary","Lan"],"index":42696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997722507,"difficulty":0.0002277493}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows 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":"Chelsey can now know that Elida can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jamie","Chelsey","Elida"],"index":26580,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982631803,"difficulty":0.0017368197}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arnold's forehead is muddy. It is publicly announced that Jo does not know whether or not everyone's forehead is muddy. It is publicly announced that Jo does not know whether Jo'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|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":"Jo can now know whether Arnold can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Arnold","Jo"],"index":38365,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (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) ] [ ! ~(2) ] 0","hypothesis":"George can now know whether Robert can know that Linda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Linda","Robert"],"index":29380,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9877370596,"difficulty":0.0122629404}
+{"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 Adrian. Paul's card is shown to Adrian. Michael's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether Paul picked a red card. It is publicly announced that Adrian knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Michael can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Adrian","Paul"],"index":14728,"s-l":"explicit-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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gordon can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Justine","Gordon","Christopher","Carolina"],"index":25610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982891679,"difficulty":0.0017108321}
+{"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 Lorene. Juan's card is shown to Lorene. Lorene's card is shown to Billy. Juan's card is shown to Billy. Juan's card is shown to Juan. It is publicly announced that someone picked a red card. It is publicly announced that Lorene does not know whether Lorene picked a red card. It is publicly announced that Billy picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Billy can know whether Juan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lorene","Billy","Mary","Juan"],"index":31979,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6766723394,"difficulty":0.3233276606}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jill's card is shown to Alton. Alton's card is shown to Jill. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Sarah can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","John","Alton","Jill"],"index":254,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984810948,"difficulty":0.0015189052}
+{"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 Betty is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Freddie knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Betty can now know that Freddie can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Betty","Freddie"],"index":19991,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9888644218,"difficulty":0.0111355782}
+{"premise":"There are four persons. Everyone is visible 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 Andrea knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentb knows 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)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christopher can now know that Klara can know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrea","Klara","Christopher","Samantha"],"index":55462,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965535402,"difficulty":0.0034464598}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erin's card is shown to Erin. Erin's card is shown to Martin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Martin can now know whether Whitney picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Erin","Martin","Whitney"],"index":39210,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.964279294,"difficulty":0.035720706}
+{"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 Aubrey is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] 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) ] [ ! ~(Agentd knows whether 3) ] [ ! 1 ] 0","hypothesis":"Mark can now know whether Nellie can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Nellie","Aubrey","Mark"],"index":61289,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997863173,"difficulty":0.0002136827}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Mary can now know that George can know that Joann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Judy","George","Joann","Mary"],"index":4633,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925664663,"difficulty":0.0074335337}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lisa can now know that Kisha can know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Lisa","Julia","Kisha"],"index":35492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9822385311,"difficulty":0.0177614689}
+{"premise":"There are 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)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Marjorie can know that Lourdes's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lourdes","William","Willie","Marjorie"],"index":545,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986203909,"difficulty":0.0013796091}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether or not everyone's forehead is muddy.","smcdel_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":"John can now know that Raymond can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Lucille","John"],"index":62991,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983154535,"difficulty":0.0016845465}
+{"premise":"There are four persons. Everyone is visible 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) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Natividad can now know that Cathleen can know that Natividad's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Natividad","Kay","Cathleen"],"index":34998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9776135683,"difficulty":0.0223864317}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecka's card is shown to Megan. Rosemary's card is shown to Megan. Wai's card is shown to Rebecka. Rebecka's card is shown to Rosemary. Megan's card is shown to Wai. It is publicly announced that someone picked a red card. It is publicly announced that Rebecka 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)) ] (Agenta knows that 3)","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":"Megan can now know that Rosemary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Megan","Rebecka","Rosemary","Wai"],"index":17931,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7503600121,"difficulty":0.2496399879}
+{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Russell knows whether someone's forehead is muddy. It is publicly announced that Russell knows whether someone's forehead is muddy. It is publicly announced that Russell knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Russell can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Russell","Timothy","Jasmine"],"index":10012,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996802807,"difficulty":0.0003197193}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is muddy. It is publicly announced that Monica knows whether Monica's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that (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":"Karla can now know that Monica can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jonas","Karla","Monica"],"index":23319,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982963204,"difficulty":0.0017036796}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chelsey knows whether Chelsey's forehead is muddy. It is publicly announced that Arthur knows whether Anita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Nicole can now know whether Nicole's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anita","Nicole","Chelsey","Arthur"],"index":34494,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9989537001,"difficulty":0.0010462999}
+{"premise":"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 Vicki's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Wayne can now know that Vicki can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stephen","Hugh","Wayne","Vicki"],"index":28481,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984048009,"difficulty":0.0015951991}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Syble's card is shown to Syble. William's card is shown to Syble. Syble'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 William picked a red card. It is publicly announced that Syble knows whether William picked a red card. It is publicly announced that Syble knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"William can now know whether Syble can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Syble","William"],"index":48432,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Otto's forehead is muddy.","smcdel_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 whether (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Matthew can now know whether Jason can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Otto","Matthew","Jason"],"index":26947,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995954633,"difficulty":0.0004045367}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruben does not know whether 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 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":"Freddie can now know that Amanda can know whether Freddie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Ruben","Freddie"],"index":27552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992764592,"difficulty":0.0007235408}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michelle can now know that Mollie can know whether Mollie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mollie","Craig","Michelle"],"index":30529,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978405237,"difficulty":0.0021594763}
+{"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. Theresa's card is shown to Dennis. Lucille's card is shown to Theresa. Lucille's card is shown to Lucille. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lucille can now know that Dennis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dennis","Theresa","Lucille"],"index":38886,"s-l":"explicit-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). Frieda's card is shown to Frieda. Rosemarie's card is shown to Kassandra. Frieda's card is shown to Nathaniel. Nathaniel's card is shown to Nathaniel. Frieda's card is shown to Rosemarie. Rosemarie's card is shown to Rosemarie. It is publicly announced that someone picked a red card. It is publicly announced that Kassandra does not know whether Nathaniel picked a red card. It is publicly announced that Rosemarie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! 4 ] 0","hypothesis":"Kassandra can now know whether Rosemarie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frieda","Kassandra","Nathaniel","Rosemarie"],"index":20136,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8630918264,"difficulty":0.1369081736}
+{"premise":"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 not muddy. It is publicly announced that Mikki does not know whether Mikki's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know that Shirley can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shirley","Mikki","James"],"index":20706,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984691739,"difficulty":0.0015308261}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerald's card is shown to Gerald. Emily's card is shown to Emily. Barbara's card is shown to Emily. Emily's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Emily can know that Gerald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gerald","Emily","Barbara"],"index":12689,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978551269,"difficulty":0.0021448731}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy.","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":"Joseph can now know that Thomas can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joseph","Thomas"],"index":47978,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984285235,"difficulty":0.0015714765}
+{"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 Andrea is thirsty. It is publicly announced that Andrea does not know whether Jonathan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Andrea can now know whether Mary can know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrea","Mary","Faith","Jonathan"],"index":9254,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985022545,"difficulty":0.0014977455}
+{"premise":"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 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":"Loraine can now know that Patrick can know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Patrick","Loraine","Beverly"],"index":21056,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956634641,"difficulty":0.0043365359}
+{"premise":"There are two 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 Terry 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&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":"Terry can now know whether Jeremy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jeremy","Terry"],"index":21285,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9722246528,"difficulty":0.0277753472}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. John's card is shown to Joseph. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 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:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Joseph can now know whether John can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","John"],"index":1865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
+{"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 Michael does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Bernard can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Bernard"],"index":54014,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997144341,"difficulty":0.0002855659}
+{"premise":"There are four persons. Everyone is visible 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 Fredrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 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":"Fredrick can now know whether Pauline can know whether Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pauline","Gary","Fredrick","Ruby"],"index":22674,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997195601,"difficulty":0.0002804399}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (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":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Barney","Christine","Mary","Jason"],"index":44052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9809282422,"difficulty":0.0190717578}
+{"premise":"There are three persons. Everyone is visible 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) ] [ ! ~(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) ] [ ! ~(2) ] 0","hypothesis":"George can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","George","John"],"index":3872,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997820258,"difficulty":0.0002179742}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cristal does not know whether Cristal'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 (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":"Cristal can now know whether Mary can know that Cristal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eileen","Cristal","Mary"],"index":37460,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6429062486,"difficulty":0.3570937514}
+{"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 Tanisha. Tanisha's card is shown to William. William's card is shown to William. William's card is shown to Kate. 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 (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":"William can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tanisha","William","Kate"],"index":12694,"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's forehead is muddy. It is publicly announced that Carolyn does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows 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)) ] [ ! (1|2|3) ] 0","hypothesis":"Dora can now know whether Carolyn can know whether Becky's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Becky","Dora","Carolyn"],"index":64467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994137287,"difficulty":0.0005862713}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elaine's card is shown to Elaine. Janice's card is shown to Elaine. Susana's card is shown to Janice. Katherine's card is shown to Susana. Susana's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 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:1,2 Agentb:3 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Katherine can now know that Susana can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elaine","Janice","Susana","Katherine"],"index":35892,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9788283706,"difficulty":0.0211716294}
+{"premise":"There are four persons. Everyone is visible 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 Amy's forehead is muddy. It is publicly announced that Joseph knows whether Carroll's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Ronnie can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carroll","Ronnie","Amy","Joseph"],"index":27103,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998013854,"difficulty":0.001986146}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Penny knows whether Penny's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Penny can now know that Edith can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edith","James","Robert","Penny"],"index":63746,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984768033,"difficulty":0.0015231967}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Heriberto is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows 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":"Martin can now know whether Lorraine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorraine","Heriberto","Martin","Martha"],"index":63513,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9950048327,"difficulty":0.0049951673}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mia's card is shown to Nina. Nina's card is shown to Joseph. Mia's card is shown to Joseph. Nina's card is shown to Mia. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Nina can now know that Joseph can know whether Nina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nina","Joseph","Mia"],"index":61864,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9724622369,"difficulty":0.0275377631}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Freda is not thirsty. It is publicly announced that Irene is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Freda can now know whether Freda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Irene","Freda","Harriet","Patricia"],"index":50864,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991944432,"difficulty":0.0008055568}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara does not know whether Tamara's forehead is muddy. It is publicly announced that Tamara does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Tamara can now know that Charles can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamara","Charles","Darla","Christine"],"index":52018,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9845522642,"difficulty":0.0154477358}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan does not know whether Guy is thirsty. It is publicly announced that Guy 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) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Joan can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Guy","David","Joan"],"index":33681,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997220635,"difficulty":0.0002779365}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth'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 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":"Henry can now know that Albert can know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Albert","Ruth"],"index":24553,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963536263,"difficulty":0.0036463737}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Elaine can now know that Joseph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Joseph","Barbara","Elaine"],"index":16297,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9867905974,"difficulty":0.0132094026}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ben knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agentb knows 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":"Danny can now know whether Ben can know whether Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michele","Ben","Danny","Harley"],"index":28806,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996886253,"difficulty":0.0003113747}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether Gladys is thirsty. It is publicly announced that Julia 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 (~(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":"Gladys can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gladys","Julia"],"index":43669,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981344342,"difficulty":0.0018655658}
+{"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":"Linda can now know whether Keith can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Keith","Linda","Ernest"],"index":27058,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997846484,"difficulty":0.0002153516}
+{"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 knows whether or not nobody is thirsty. It is publicly announced that Stephanie does not know whether Rose is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Stephanie can now know whether Robert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Rose","Stephanie"],"index":3104,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996989965,"difficulty":0.0003010035}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Corey can now know whether Corey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Corey","Gloria"],"index":30981,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9847390652,"difficulty":0.0152609348}
+{"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 Sheila. Helen's card is shown to Stuart. Alice's card is shown to Helen. Sheila's card is shown to Alice. Helen's card is shown to Alice. It is publicly announced that someone picked a red card. It is publicly announced that Stuart 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)) ] Agentb knows that (Agentd knows whether 1)","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":"Stuart can now know that Alice can know whether Sheila picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheila","Stuart","Helen","Alice"],"index":18376,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6304622293,"difficulty":0.3695377707}
+{"premise":"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 3)","n_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":"Sheila can now know whether Roxanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Son","Sheila","Roxanne"],"index":9823,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994878769,"difficulty":0.0005121231}
+{"premise":"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.","smcdel_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 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":"Milton can now know whether Tiffany can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Milton","Tiffany","Laura"],"index":15422,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9836560488,"difficulty":0.0163439512}
+{"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 Drew. Drew's card is shown to Mary. Mary's card is shown to Ross. Ross's card is shown to Ross. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Drew can now know that Mary can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Drew","Mary","Ross"],"index":46925,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9910176992,"difficulty":0.0089823008}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harriet's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 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":"Laureen can now know that Frank can know that Harriet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laureen","Harriet","Frank"],"index":4412,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9824192524,"difficulty":0.0175807476}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice does not know whether Nathan is thirsty. It is publicly announced that Alice does not know whether Arthur is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that 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) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Alice can now know that Nathan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nathan","Timothy","Arthur","Alice"],"index":27831,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970995188,"difficulty":0.0029004812}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Micheal's card is shown to Micheal. Micheal's card is shown to Debbie. Micheal's card is shown to Joshua. Debbie's card is shown to Joshua. It is publicly announced that someone picked a red card. It is publicly announced that Debbie does not know whether Vernie picked a red card. It is publicly announced that Debbie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Debbie can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Micheal","Vernie","Debbie","Joshua"],"index":17387,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8300135732,"difficulty":1.8300135732}
+{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that 3)","n_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":"Tracey can now know that Harold's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracey","Elizabeth","Harold"],"index":3344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982489347,"difficulty":0.0017510653}
+{"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 Jamie is thirsty. It is publicly announced that 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) ] [ ! ~(Agentd knows whether 1) ] [ ! 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) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Elizabeth can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jamie","Elizabeth","Donna","William"],"index":34751,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9711272717,"difficulty":0.0288727283}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Rocky can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Patricia","Anna","Rocky"],"index":63961,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983596206,"difficulty":0.0016403794}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Larry is thirsty. It is publicly announced that Kelly 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Joshua can now know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Kevin","Kelly","Larry"],"index":6543,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8929063678,"difficulty":0.1070936322}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Micheal 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 whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Eva can now know whether Micheal can know whether Eva is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Eva","Micheal"],"index":21590,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9981158972,"difficulty":1.9981158972}
+{"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. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] Agenta knows 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))) ] [ ! (1|2) ] 0","hypothesis":"Michael can now know whether Deborah can know that Deborah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Deborah"],"index":56388,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8926244378,"difficulty":0.1073755622}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antone knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether 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":"Antone can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Michael","Antone"],"index":57143,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980605245,"difficulty":0.0019394755}
+{"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 Gloria. Cynthia's card is shown to Edward. Michael's card is shown to Edward. Gloria's card is shown to Cynthia. Michael's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Gloria does not know whether Michael 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) ] Agentc knows that (Agenta knows whether 2)","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":"Cynthia can now know that Gloria can know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Edward","Cynthia","Michael"],"index":15634,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8997974396,"difficulty":1.8997974396}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terrance's card is shown to Terrance. Terrance's card is shown to Ola. It is publicly announced that someone picked a red card. It is publicly announced that Ola knows whether Terrance 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 whether 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":"Ola can now know whether Ola picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Terrance","Ola"],"index":50117,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9791584611,"difficulty":1.9791584611}
+{"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 Patricia. Claudia's card is shown to Walter. Curtis's card is shown to Walter. Curtis's card is shown to Claudia. Patricia's card is shown to Curtis. Walter's card is shown to Curtis. Claudia's card is shown to Curtis. Curtis's card is shown to Curtis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Curtis can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Walter","Claudia","Curtis"],"index":2085,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997227788,"difficulty":0.0002772212}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cameron knows whether or not nobody's forehead is muddy. It is publicly announced that Cameron 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 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":"Cameron can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Kenneth","John","Cameron"],"index":31338,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981617332,"difficulty":0.0018382668}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricardo knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Margery can now know that Ricardo can know that Margery's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margery","Ricardo","Charles","Keith"],"index":6584,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8987367153,"difficulty":0.1012632847}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annette does not know whether Annette's forehead is muddy. It is publicly announced that Wendy does not know whether Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Wendy can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annette","Wendy","Patricia"],"index":5673,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9506411552,"difficulty":0.0493588448}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley knows whether or not nobody's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bradley","Robert","Linda","Claudia"],"index":52149,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952284098,"difficulty":0.0047715902}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Becky's card is shown to Brian. Brian's card is shown to Brian. Becky's card is shown to Vernon. Brian's card is shown to Vernon. Vernon's card is shown to Vernon. It is publicly announced that someone picked a red card. It is publicly announced that Brian knows whether or not nobody picked a red card. It is publicly announced that Becky knows whether Brian 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) ] (Agenta knows that (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":"Becky can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Becky","Brian","Vernon"],"index":67090,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997734427,"difficulty":0.0002265573}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hazel's card is shown to Betty. Betty's card is shown to Hazel. Hazel's card is shown to Hazel. Betty's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Betty picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Betty can now know that Hazel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Hazel","Michael"],"index":32385,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9903401732,"difficulty":0.0096598268}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebekah does not know whether or not everyone's forehead is muddy. It is publicly announced that Kiley knows whether someone's forehead is muddy. It is publicly announced that Rebekah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows 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 (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kathleen can now know that Leona can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kathleen","Rebekah","Kiley","Leona"],"index":44937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9599503875,"difficulty":0.0400496125}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dena does not know whether Lena is thirsty. It is publicly announced that Brook does not know whether Dena is thirsty. It is publicly announced that Lena does not know whether Philip is thirsty. It is publicly announced that Philip does not know whether Brook is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Philip can now know that Dena is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brook","Dena","Philip","Lena"],"index":29699,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9936042428,"difficulty":0.0063957572}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luis 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 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":"Luis can now know whether Tomas can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tomas","Gudrun","Luis"],"index":19482,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.5051339269,"difficulty":1.5051339269}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alejandro knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 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":"Alejandro can now know whether Doris can know whether Doris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alejandro","Doris","Pat"],"index":5390,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996345043,"difficulty":0.0003654957}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emilio knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentc knows whether (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":"Joseph can now know whether Emilio can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emilio","Michael","Joseph"],"index":64816,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995773435,"difficulty":0.0004226565}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marcos knows whether Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Marcos can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Janet","Marcos"],"index":17302,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998273015,"difficulty":0.001726985}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Jennifer's card is shown to Daniel. Daniel'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 Daniel knows whether Jennifer picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","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":"Jennifer can now know that Daniel can know that Daniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daniel","Jennifer"],"index":17779,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9673267007,"difficulty":0.0326732993}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(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":"Patricia can now know whether Jordan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Jordan","Timothy"],"index":57622,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997202754,"difficulty":0.0002797246}
+{"premise":"There are three persons. Everyone is visible 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":"Joseph can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Deborah","Donald"],"index":20554,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985126853,"difficulty":0.0014873147}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenny's forehead is not muddy.","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":"Kenny can now know whether Kirk can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenny","Kirk"],"index":25951,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995478988,"difficulty":0.0004521012}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Robert. Robert's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 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":"Robert can now know that Tracy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Tracy"],"index":4962,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8455287218,"difficulty":1.8455287218}
+{"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 Steve is thirsty. It is publicly announced that Casey knows whether someone is thirsty. It is publicly announced that Casey does not know whether Anthony is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Casey can now know that Steve can know whether Steve is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Casey","Steve","Delores"],"index":50151,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9901294112,"difficulty":0.0098705888}
+{"premise":"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 Susan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Susan can now know whether Howard can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Susan","Howard"],"index":62667,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9942193031,"difficulty":0.0057806969}
+{"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 Robert. Michael's card is shown to Robert. Linda's card is shown to Linda. Linda's card is shown to Werner. Robert's card is shown to Michael. Werner's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Werner picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Werner knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Werner can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Linda","Werner","Michael"],"index":49246,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9849446416,"difficulty":0.0150553584}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Leroy can now know that Richard can know that Leroy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Stacey","Leroy"],"index":43661,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9420685768,"difficulty":0.0579314232}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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":"Karen can now know whether John can know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","John","Kenneth"],"index":36036,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997060895,"difficulty":0.0002939105}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 1)","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":"Elizabeth can now know that Ramon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ramon","Elizabeth"],"index":26962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984360337,"difficulty":0.0015639663}
+{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Howard can now know whether Howard's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Michael","Howard"],"index":34532,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993106127,"difficulty":0.0006893873}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Matthew is thirsty. It is publicly announced that Matthew knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"James can now know that Matthew can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Matthew"],"index":59008,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997814298,"difficulty":0.0002185702}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether or not everyone's forehead is muddy. It is publicly announced that Tony does not know whether Tony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Tony can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Tony","Vera","Steven"],"index":16045,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are two persons. Everyone is visible 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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 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":"James can now know whether John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","John"],"index":9807,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996689558,"difficulty":0.0003310442}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Emmitt is not thirsty. It is publicly announced that Emmitt does not know whether Edward is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Emmitt can now know that Edward can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Kirsten","Emmitt"],"index":15926,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984814525,"difficulty":0.0015185475}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether 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 Shannon can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","James","Jean","Shannon"],"index":26309,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997403026,"difficulty":0.0002596974}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Raymond's card is shown to Raymond. Raymond's card is shown to Matthew. Robert's card is shown to Matthew. Raymond's card is shown to Brooke. Raymond's card is shown to Robert. Matthew's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Raymond does not know whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Robert can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Raymond","Matthew","Brooke","Robert"],"index":31082,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997212291,"difficulty":0.0002787709}
+{"premise":"There are two persons. Everyone is visible 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 Brice's forehead is muddy. It is publicly announced that Brice knows whether Maria's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Brice can now know that Maria can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brice","Maria"],"index":62716,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99581182,"difficulty":0.00418818}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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 Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Cynthia","Linda","Alma"],"index":57097,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977610111,"difficulty":0.0022389889}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Beatrice. Grace's card is shown to Grace. Grace's card is shown to Douglas. Douglas's card is shown to Douglas. Douglas's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Beatrice 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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Beatrice can now know that Grace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beatrice","Grace","Douglas","Alan"],"index":66886,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99732095,"difficulty":0.00267905}
+{"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 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|2)) ] [ ! (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|2)) ] [ ! (1|2) ] 0","hypothesis":"Phyllis can now know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Phyllis","Kimberly"],"index":53587,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9566267133,"difficulty":0.0433732867}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agentb knows that 1)","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":"Charles can now know that Crystal's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Crystal","Charles","Robert"],"index":63407,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9951686859,"difficulty":0.0048313141}
+{"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 James. Doris's card is shown to Doris. Doris's card is shown to Jessie. 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 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 (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Jessie can now know whether James can know that Jessie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Doris","Jessie"],"index":56104,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9455159307,"difficulty":1.9455159307}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Kathryn knows whether 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) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Stanley can now know that Kathryn can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathryn","Anthony","Stanley"],"index":52801,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997575879,"difficulty":0.0002424121}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phillip does not know whether John is thirsty. It is publicly announced that Phillip does not know whether John is thirsty. It is publicly announced that Phillip knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows 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 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"John can now know that Phillip is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adam","John","Phillip"],"index":39176,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.991540134,"difficulty":0.008459866}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin does not know whether Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 (~(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":"Jennifer can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Justin","Latosha","Jennifer"],"index":2331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997010827,"difficulty":0.0002989173}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Kevin. Kevin's card is shown to Rosa. Rosa's card is shown to Rosa. Kevin's card is shown to Jeffrey. 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 everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Rosa can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kevin","Rosa","Jeffrey"],"index":46671,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966663718,"difficulty":0.0033336282}
+{"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 Kathy. Kathy's card is shown to Richard. Richard's card is shown to Richard. Frankie's card is shown to Richard. Richard's card is shown to Frankie. It is publicly announced that someone picked a red card. It is publicly announced that Frankie knows whether someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Richard picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] [ ! ~(2) ] (Agenta knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Kathy can now know whether Frankie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathy","Richard","Frankie"],"index":19104,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8715184331,"difficulty":1.8715184331}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tanya knows whether Thomas is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows 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":"Thomas can now know that Tanya can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tanya","Thomas"],"index":12680,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983801842,"difficulty":0.0016198158}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luke's card is shown to Michael. Joanne's card is shown to Sandra. Michael's card is shown to Luke. Michael's card is shown to Joanne. 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 whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Luke can now know whether Sandra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Sandra","Luke","Joanne"],"index":67469,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9399021864,"difficulty":0.0600978136}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Myra can now know whether Brenda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Myra","Brenda"],"index":57306,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9964334965,"difficulty":0.0035665035}
+{"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. Mary's card is shown to Johnny. John's card is shown to Mary. Karen'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) ] (Agentb knows whether 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":"Karen can now know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Karen","Johnny","Mary"],"index":1819,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7365050316,"difficulty":1.7365050316}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Royce's card is shown to Katherine. Katherine's card is shown to Royce. It is publicly announced that someone picked a red card. It is publicly announced that Royce knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Katherine can now know whether Royce can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Katherine","Royce"],"index":50853,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7293658853,"difficulty":1.7293658853}
+{"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 James. Mary's card is shown to Dianna. Mary's card is shown to Mary. 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:3 Agentb:3 Agentc:3 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:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Dianna","Mary"],"index":54009,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985131621,"difficulty":0.0014868379}
+{"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 Betty. Mack's card is shown to Betty. Betty's card is shown to Betty. Jason'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:1,2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jason can now know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Mack","Betty","Mark"],"index":1997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.927899003,"difficulty":0.072100997}
+{"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 Donna is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether (1|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":"Helen can now know whether Donna can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Robert","Donna"],"index":24823,"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 Melody'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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Melody can now know that Paula can know that Paula's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paula","James","Melody","Mary"],"index":49687,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945645332,"difficulty":0.0054354668}
+{"premise":"There are four persons. Everyone is visible 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 Emmanuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Carmen can now know whether Francis can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Francis","Carmen","Mildred","Emmanuel"],"index":36549,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995815158,"difficulty":0.0004184842}
+{"premise":"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 knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows whether 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":"Mike can now know whether Richard can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mike","Richard"],"index":59234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9923154116,"difficulty":0.0076845884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred's forehead is not muddy. It is publicly announced that Ismael does not know whether Ismael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Ismael can now know whether Fred can know that Ismael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ismael","Fred","William"],"index":22786,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5091009736,"difficulty":1.5091009736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence's forehead is muddy. It is publicly announced that Ray'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 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) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Andrea can now know that Zachary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ray","Andrea","Zachary","Lawrence"],"index":25094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9316990376,"difficulty":0.0683009624}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows that 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":"Maria can now know that Wesley can know that Wesley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Bryan","Wesley"],"index":53700,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9203915596,"difficulty":0.0796084404}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eileen is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know that Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eileen","Melvin","Mary"],"index":852,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9937273264,"difficulty":0.0062726736}
+{"premise":"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'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 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":"Roy can now know that Stephanie can know that Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Roy","Stephanie"],"index":12747,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937291145,"difficulty":0.0062708855}
+{"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. Levi's card is shown to Levi. James's card is shown to Melissa. Levi's card is shown to Melissa. Melissa's card is shown to Melissa. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Levi can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Levi","Melissa"],"index":31636,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930558801,"difficulty":0.0069441199}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether or not everyone's forehead is muddy.","smcdel_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":"Allen can now know that Junior can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Junior","Allen","Susan"],"index":3154,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Albert's card is shown to Richard. Cathy's card is shown to Richard. Albert's card is shown to Albert. Albert's card is shown to Cathy. It is publicly announced that someone picked a red card. It is publicly announced that Richard picked a black card. It is publicly announced that Albert knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Cathy can now know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Albert","Cathy"],"index":34624,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7182793021,"difficulty":0.2817206979}
+{"premise":"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 Sue knows whether or not everyone's forehead is muddy. It is publicly announced that Duane 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 Lucas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sue","William","Duane","Lucas"],"index":29631,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996139586,"difficulty":0.003860414}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luann knows whether someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy. It is publicly announced that Lori 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)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Luann can now know whether Gary can know that Luann's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Luann","Lori","Gary"],"index":66584,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5647748113,"difficulty":0.4352251887}
+{"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. Dwight's card is shown to James. Lela's card is shown to Dwight. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Dwight can know that James picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Dwight","Lela"],"index":28408,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7470138073,"difficulty":0.2529861927}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elijah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Elijah can now know whether Cherrie can know whether Vivian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elijah","Cherrie","Armando","Vivian"],"index":21138,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994450212,"difficulty":0.0005549788}
+{"premise":"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 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":"Jamar can now know whether Jamar's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Jamar","Stephen"],"index":5401,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9680637121,"difficulty":0.0319362879}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lidia knows whether Lidia'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) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Lidia can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lidia","Nina","James","Betty"],"index":17303,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9422448277,"difficulty":0.0577551723}
+{"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 Eleanor. Eleanor's card is shown to Emily. Charles's card is shown to Emily. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know that Rita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","Rita","Emily","Charles"],"index":66790,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982572198,"difficulty":0.0017427802}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samuel is not thirsty. It is publicly announced that Carmen 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) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 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) ] [ ! ~(3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jessica can now know that Carmen can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","Jessica","Samuel","Edward"],"index":15217,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9462533593,"difficulty":1.9462533593}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Tora's card is shown to Tora. Brandie's card is shown to Tora. Tora's card is shown to Brandie. Brandie's card is shown to Brandie. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Tora picked a red card. It is publicly announced that Brandie knows whether Tora picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Mary can now know whether Brandie can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Tora","Brandie"],"index":44775,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9975428581,"difficulty":1.9975428581}
+{"premise":"There are four 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. It is publicly announced that James does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Kevin","Nieves","Kathy"],"index":9483,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999769032,"difficulty":0.000230968}
+{"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 Pamela. Pamela's card is shown to Sarah. Sarah'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:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Pamela can know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Sarah","William"],"index":43450,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9966154695,"difficulty":0.0033845305}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steve does not know whether Charles 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 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":"Steve can now know that Steve is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Charles","Steve"],"index":35512,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9171075225,"difficulty":1.9171075225}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 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":"James can now know that Joshua can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","James","Joshua","Annette"],"index":11593,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983022213,"difficulty":0.0016977787}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harold is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Andrew can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Andrew","Harold"],"index":43309,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
+{"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 Jason. Melinda's card is shown to Jason. Jarrod's card is shown to Jarrod. Melinda's card is shown to Jarrod. Jarrod's card is shown to Jeffrey. Melinda's card is shown to Jeffrey. Jarrod's card is shown to Melinda. Melinda's card is shown to Melinda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:2,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:2,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jarrod can now know that Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Jarrod","Jeffrey","Melinda"],"index":16763,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977298379,"difficulty":0.0022701621}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monica does not know whether Alexander is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alexander can now know that Jake can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alexander","Monica","Jake","Dolores"],"index":49380,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.977964282,"difficulty":0.022035718}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willa's card is shown to Willa. Donald's card is shown to Donald. Jennie's card is shown to Jennie. It is publicly announced that someone picked a red card. It is publicly announced that Willa does not know whether Jennie 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 Donald does not know whether Jennie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Willa can now know that Donald can know whether Willa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willa","Donald","Jennie"],"index":17905,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8175765276,"difficulty":0.1824234724}
+{"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. Leah's card is shown to Dorothy. Dorothy's card is shown to William. William's card is shown to William. Dorothy's card is shown to Nicholas. Dorothy's card is shown to Leah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Leah can know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","William","Nicholas","Leah"],"index":61352,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972739816,"difficulty":0.0027260184}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynne knows whether someone's forehead is muddy. It is publicly announced that Lynne knows whether Ingrid's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Lynne can now know that Ingrid can know that Ingrid's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Darius","Ingrid","Jennifer","Lynne"],"index":41466,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971254468,"difficulty":0.0028745532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 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":"Justin can now know that Donald can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","Donald","Ronald","Holly"],"index":1446,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5069487691,"difficulty":1.5069487691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica does not know whether Jessica's forehead is muddy. It is publicly announced that Dessie 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)) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Carlos can now know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dessie","Harry","Jessica","Carlos"],"index":13942,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6971794367,"difficulty":1.6971794367}
+{"premise":"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 Gary knows whether April's forehead is muddy. It is publicly announced that Jonathan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows whether 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":"Gary can now know whether Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gary","Michelle","April","Jonathan"],"index":56034,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995006323,"difficulty":0.0004993677}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kristen does not know whether Tony is thirsty. It is publicly announced that Kristen knows whether Kristen is thirsty. It is publicly announced that Tony does not know whether Kristen is thirsty. It is publicly announced that Tina does not know whether Kristen 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 (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Tony can now know that Kristen can know that Kristen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tony","Kristen","Tina"],"index":15541,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5922492743,"difficulty":0.4077507257}
+{"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. Robert's card is shown to Daniel. James's card is shown to James. Nicole's card is shown to James. Nicole's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether someone picked a red card. It is publicly announced that James does not know whether Robert picked a red card. It is publicly announced that Daniel does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta 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 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Robert","James","Nicole"],"index":43648,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986376166,"difficulty":0.0013623834}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Sarah can now know that Jeffrey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norma","Sarah","Carolyn","Jeffrey"],"index":63639,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984458089,"difficulty":0.0015541911}
+{"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 Mary. Mary's card is shown to Stephanie. Stephanie's card is shown to Stephanie. Elisha's card is shown to Stephanie. Edna's card is shown to Stephanie. Mary's card is shown to Edna. Edna's card is shown to Edna. It is publicly announced that someone picked a red card. It is publicly announced that Elisha does not know whether or not everyone picked a red card. It is publicly announced that Elisha does not know whether Elisha picked a red card. It is publicly announced that Stephanie knows whether Stephanie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 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 Agentb:1,2,3,4 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mary can now know that Stephanie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Stephanie","Elisha","Edna"],"index":55467,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983383417,"difficulty":0.0016616583}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Todd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Refugio can now know that Duane can know whether Duane's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Todd","Virgie","Refugio","Duane"],"index":54203,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996305704,"difficulty":0.0003694296}
+{"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. Donna's card is shown to John. John's card is shown to Ralph. Ralph's card is shown to Ralph. Donna's card is shown to Ralph. Charles's card is shown to Ralph. Ralph's card is shown to Donna. Charles's card is shown to Donna. John's card is shown to Charles. Donna's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Charles does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,3,4 Agentc:2,4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Donna can now know whether Ralph can know whether Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Ralph","Donna","Charles"],"index":31387,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9978154898,"difficulty":0.0021845102}
+{"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 Heather is thirsty. It is publicly announced that Heather does not know whether Benjamin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Benjamin can now know whether John can know whether Douglas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","John","Douglas","Benjamin"],"index":3165,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989603758,"difficulty":0.0010396242}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","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 whether Crystal is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Crystal","Alexandra","Richard","Clyde"],"index":13975,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980341792,"difficulty":0.0019658208}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalie's forehead is not muddy. It is publicly announced that Amy knows whether Natalie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Rita can now know whether Natalie can know that Natalie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Natalie","Amy","Rita"],"index":16346,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9865495563,"difficulty":0.0134504437}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Herbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know whether Lewis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","Mario","Herbert","Lewis"],"index":65314,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997329116,"difficulty":0.0002670884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Suzanne is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether 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":"Arthur can now know whether Suzanne can know whether Josephine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arthur","Suzanne","Josephine"],"index":3647,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988817573,"difficulty":0.0011182427}
+{"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 (1|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":"Roger can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["William","Roger","James"],"index":41216,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997423291,"difficulty":0.0002576709}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tiffany's card is shown to Berta. Tiffany's card is shown to Tiffany. Derick's card is shown to Tiffany. Tiffany's card is shown to Derick. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","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":"Tiffany can now know that Berta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Berta","Tiffany","Derick"],"index":9592,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982916713,"difficulty":0.0017083287}
+{"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 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) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"John can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicholas","John","Curtis","Louis"],"index":45416,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997701049,"difficulty":0.0002298951}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara does not know whether Earl is thirsty. It is publicly announced that Tricia does not know whether Earl is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Taylor can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Taylor","Tara","Tricia","Earl"],"index":11461,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983716607,"difficulty":0.0016283393}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sharon is thirsty. It is publicly announced that Irene does not know whether or not everyone is thirsty. It is publicly announced that Sharon does not know whether Brandon is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Irene can now know that Sharon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Irene","Sharon","Brandon"],"index":22439,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6632897258,"difficulty":0.3367102742}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Fernando can now know whether Francis can know that Fernando's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Francis","Fernando"],"index":50426,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9905208349,"difficulty":0.0094791651}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Diane can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Barbara","Sandra","Diane"],"index":46152,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997672439,"difficulty":0.0002327561}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Devin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows 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":"Devin can now know that Lianne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lianne","Devin","Charles"],"index":58321,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.987788856,"difficulty":0.012211144}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla's forehead is muddy. It is publicly announced that Charles's forehead is not 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) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Carla can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carla","Joe","Charles"],"index":51164,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980040193,"difficulty":0.0019959807}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gabriel's card is shown to Lillian. Raymond's card is shown to Gabriel. Shelia's card is shown to Shelia. Raymond's card is shown to Shelia. Shelia'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:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gabriel can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lillian","Gabriel","Shelia","Raymond"],"index":47598,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
+{"premise":"There are three persons. Everyone is visible 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 Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kathleen can now know whether Manuel can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Manuel","Donald"],"index":43163,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996591806,"difficulty":0.0003408194}
+{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Cynthia knows whether Cynthia's forehead is muddy. It is publicly announced that Joshua knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cynthia can now know whether Joshua can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joshua","Cynthia"],"index":52781,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9656608701,"difficulty":0.0343391299}
+{"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 Dwayne. William's card is shown to William. Dwayne'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 Kenneth knows whether Dwayne picked a red card. It is publicly announced that William does not know whether Dwayne 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 that 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":"Kenneth can now know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwayne","William","Kenneth"],"index":47271,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9393619895,"difficulty":0.0606380105}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ida does not know whether Lawrence is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Ida can now know whether Lawrence can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ida","Matthew","Lawrence","Shirley"],"index":11086,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997743964,"difficulty":0.0002256036}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether or not nobody's forehead is muddy. It is publicly announced that Anne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 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":"Anne can now know whether Lloyd can know that Anne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anne","Lloyd"],"index":27804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999102354,"difficulty":0.000897646}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gaye's card is shown to Gaye. Gary's card is shown to Gary. Gaye's card is shown to Albert. It is publicly announced that someone picked a red card. It is publicly announced that Albert does not know whether Albert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (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":"Albert can now know that Gary can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gaye","Gary","Albert"],"index":43283,"s-l":"explicit-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.","smcdel_problem":"VARS 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 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":"Lavada can now know that William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lavada","William","Alex"],"index":45625,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997708201,"difficulty":0.0002291799}
+{"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 Doris is thirsty. It is publicly announced that Kevin does not know whether or not everyone is thirsty. It is publicly announced that Kevin does not know whether Doris 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 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":"Brenda can now know that Kevin can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Doris","David","Kevin"],"index":25475,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980118275,"difficulty":0.0019881725}
+{"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 (~(1|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":"Georgia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carrie","Jessica","Georgia"],"index":1443,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997363687,"difficulty":0.0002636313}
+{"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. Gregory's card is shown to Gregory. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lisa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lisa","Gregory"],"index":48321,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"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 Margaret is thirsty. It is publicly announced that Derrick does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Nicholas can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Nicholas","James","Derrick"],"index":55337,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9254587293,"difficulty":0.0745412707}
+{"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 Robert. Ralph's card is shown to Mable. Joseph's card is shown to Ralph. Mable'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:4 Agentb:4 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:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mable can now know whether Robert can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Robert","Mable","Ralph"],"index":14586,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995946288,"difficulty":0.0004053712}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Tomas can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Tomas","Peggy"],"index":49575,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997422099,"difficulty":0.0002577901}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorenzo's card is shown to Arnold. Arnold's card is shown to Arnold. It is publicly announced that someone picked a red card. It is publicly announced that Arnold picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Lorenzo can now know whether Arnold picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lorenzo","Arnold"],"index":18084,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.732229948,"difficulty":0.267770052}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amy does not know whether Lottie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Amy can now know whether Lottie can know that Howard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lottie","Michael","Amy","Howard"],"index":59641,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9923606515,"difficulty":0.0076393485}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Reginald's card is shown to Reginald. Kristine's card is shown to Sheila. Sheila's card is shown to Daphne. Kristine's card is shown to Daphne. Daphne's card is shown to Daphne. It is publicly announced that someone picked a red card. It is publicly announced that Reginald picked a red card. It is publicly announced that Kristine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 3 ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Kristine can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Reginald","Sheila","Kristine","Daphne"],"index":4271,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997141957,"difficulty":0.0002858043}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether or not everyone's forehead is muddy. It is publicly announced that Maria knows whether Suzanne's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Maria can now know whether Suzanne can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Suzanne","Maria"],"index":20547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Raymond can now know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Todd","Karen","Raymond","Patricia"],"index":47248,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9120535254,"difficulty":0.0879464746}
+{"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 Victor. Rebecca's card is shown to Victor. Rebecca's card is shown to Rebecca. 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:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Victor can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Victor","Rebecca","James"],"index":42167,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9942381382,"difficulty":0.0057618618}
+{"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 Carmen is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd 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) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Carmen can now know that Cleta can know whether Freddie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cleta","Freddie","Carmen","Charles"],"index":10075,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982353449,"difficulty":0.0017646551}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Patrick can now know whether Kimberly can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patrick","Kimberly","Sarah"],"index":6519,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989356399,"difficulty":0.0010643601}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tabitha does not know whether Adele is thirsty. It is publicly announced that Adele does not know whether Tabitha is thirsty. It is publicly announced that Tabitha does not know whether Adele is thirsty.","smcdel_problem":"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) ] Agentd knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Janie can now know whether Tabitha can know that Janie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adele","Tabitha","Silvia","Janie"],"index":49823,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9350741506,"difficulty":0.0649258494}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Takisha's card is shown to Takisha. Steven's card is shown to Takisha. Jennifer's card is shown to Jennifer. Steven's card is shown to Jennifer. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 2)","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&2&3)) ] 0","hypothesis":"Takisha can now know that Jennifer can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Takisha","Jennifer","Steven"],"index":26347,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.911283493,"difficulty":1.911283493}
+{"premise":"There are four persons. Everyone is visible 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 Kim knows whether Clarice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ashley can now know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Clarice","Kim","Ashley"],"index":51100,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9974675179,"difficulty":0.0025324821}
+{"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 Allan. Allan's card is shown to Joyce. Allan's card is shown to John. Carmen's card is shown to John. Joyce's card is shown to Carmen. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card. It is publicly announced that Joyce does not know whether Joyce picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Allan","Joyce","John","Carmen"],"index":63212,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9923977256,"difficulty":0.0076022744}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lester does not know whether Jennifer is thirsty. It is publicly announced that Desiree does not know whether Margaret is thirsty. It is publicly announced that Margaret does not know whether Lester is thirsty. It is publicly announced that Lester 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&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jennifer can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Desiree","Jennifer","Lester","Margaret"],"index":8407,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986554384,"difficulty":0.0013445616}
+{"premise":"There are three persons. Everyone is visible 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 Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 1 ] 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) ] [ ! 1 ] 0","hypothesis":"Geneva can now know that Albert can know whether Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Albert","Geneva","Charlotte"],"index":35427,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996782541,"difficulty":0.0003217459}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Johnny is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Karen is not thirsty. It is publicly announced that Johnny knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 1)","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":"Robert can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Karen","Johnny","Virginia"],"index":8737,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6390427351,"difficulty":0.3609572649}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Cortney can now know that Dustin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Travis","Cortney","Dustin"],"index":18839,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984742999,"difficulty":0.0015257001}
+{"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. Kenneth's card is shown to Kim. Kim's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Luther 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)) ] (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:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Helen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Luther","Kim","Kenneth"],"index":9180,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathryn's card is shown to Kathryn. Felton's card is shown to Kathryn. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Felton picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Robert","Felton"],"index":26857,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9150643349,"difficulty":0.0849356651}
+{"premise":"There are three persons. Everyone is visible 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 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 3)","n_announcements":1,"pbcheck":"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":"Melanie can now know that Tom can know that Tom's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Garret","Melanie","Tom"],"index":36963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972168207,"difficulty":0.0027831793}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy.","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 (~(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":"David can now know whether Jacqueline can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Jacqueline"],"index":59182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997099042,"difficulty":0.0002900958}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby knows whether Ruby is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Spencer can now know that Spencer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ruby","Spencer"],"index":25984,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9861016273,"difficulty":0.0138983727}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derek knows whether someone is thirsty. It is publicly announced that Derek knows whether Derek 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) ] 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Darrell can now know that Robert can know that Derek is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darrell","Robert","Derek"],"index":31426,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9890666008,"difficulty":0.0109333992}
+{"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 that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Steven can now know whether Theresa can know that Theresa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Theresa"],"index":292,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7713649869,"difficulty":0.2286350131}
+{"premise":"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 Gilbert'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 2) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Judith can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Gilbert","Judith"],"index":6042,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997095466,"difficulty":0.0002904534}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lenora's card is shown to Jennifer. Jennifer's card is shown to Lenora. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer knows whether someone picked a red card. It is publicly announced that Lenora picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 2 ] (Agenta knows whether (1&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":"Jennifer can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jennifer","Lenora"],"index":7233,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5625547767,"difficulty":1.5625547767}
+{"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 Priscilla is thirsty. It is publicly announced that Priscilla is not thirsty. It is publicly announced that Jeffrey is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] Agentb knows that (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(2) ] 0","hypothesis":"Jeffrey can now know that Annmarie can know whether Priscilla is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Priscilla","Jeffrey","Wendy","Annmarie"],"index":60815,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5347875953,"difficulty":0.4652124047}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Charles's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(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) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Charles","Gerald"],"index":22143,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7169127464,"difficulty":1.7169127464}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Joshua can now know whether Joshua is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joshua","David","Steven","Terrence"],"index":63083,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984968901,"difficulty":0.0015031099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lauren does not know whether or not everyone is thirsty. It is publicly announced that Lauren does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (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":"Jack can now know whether Lauren can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lauren","Jack","John"],"index":14988,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994522929,"difficulty":0.0005477071}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris knows whether Chris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeffrey","Chris","Jerome","Thomas"],"index":66064,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982827902,"difficulty":0.0017172098}
+{"premise":"There are three persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 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":"Nicholas can now know that Ruben can know that Nicholas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicholas","Ruben","Adam"],"index":7784,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961905479,"difficulty":0.0038094521}
+{"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 Louisa. Louisa's card is shown to Louisa. It is publicly announced that someone picked a red card. It is publicly announced that Debbie does not know whether or not everyone picked a red card. It is publicly announced that Debbie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Debbie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debbie","Louisa","Jim"],"index":9078,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9745937586,"difficulty":0.0254062414}
+{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Steven can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Margaret","Steven","Thomas"],"index":25500,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8845721483,"difficulty":0.1154278517}
+{"premise":"There are four persons. Everyone is visible 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 Regina knows whether someone's forehead is muddy. It is publicly announced that Debbie knows whether Regina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows that 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":"Regina can now know that Regina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debbie","Tom","Kathryn","Regina"],"index":40433,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959890246,"difficulty":0.0040109754}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether or not everyone's forehead is muddy. It is publicly announced that Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Gladys can now know whether Gerald can know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gladys","Gerald"],"index":32357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9848662615,"difficulty":0.0151337385}
+{"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. Paula's card is shown to Frances. Paul's card is shown to Sharon. Frances's card is shown to Paula. It is publicly announced that someone picked a red card. It is publicly announced that Paul does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Paula can now know that Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paul","Frances","Sharon","Paula"],"index":58315,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8540281057,"difficulty":0.1459718943}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (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":"Marie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marie","Anthony"],"index":54477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981586337,"difficulty":0.0018413663}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roger's card is shown to Roger. Roger's card is shown to David. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Roger","David"],"index":14136,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997221828,"difficulty":0.0002778172}
+{"premise":"There are three persons. Everyone is visible 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 (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":"Daniel can now know that Harry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Harry","William"],"index":55944,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99978441,"difficulty":0.00021559}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fanny's card is shown to Martha. Andrea's card is shown to Martha. Martha's card is shown to Kathryn. Fanny's card is shown to Kathryn. Andrea's card is shown to Kathryn. Martha's card is shown to Fanny. Martha's card is shown to Andrea. 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) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3,4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Martha","Kathryn","Fanny","Andrea"],"index":32260,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983540773,"difficulty":0.0016459227}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Crystal. Michael's card is shown to Nicole. Eddie's card is shown to Eddie. Nicole'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:4 Agentc:3 Agentd:2 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:4 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicole can now know that Eddie can know that Nicole picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Crystal","Nicole","Eddie","Michael"],"index":34025,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975773692,"difficulty":0.0024226308}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy does not know whether Ruth is thirsty. It is publicly announced that Timothy does not know whether Daisy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 4) ] Agentc knows whether (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 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Timothy can now know whether Ruth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Ruth","Timothy","Daisy"],"index":18805,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997765422,"difficulty":0.0002234578}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows that (~(1|2|3)))","n_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":"Leslie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cesar","Leslie","Samuel"],"index":37071,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981749058,"difficulty":0.0018250942}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Georgia can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Jason","Georgia"],"index":63344,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994446635,"difficulty":0.0005553365}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Calandra's card is shown to Calandra. Cory's card is shown to Calandra. Calandra's card is shown to Cory. It is publicly announced that someone picked a red card. It is publicly announced that Calandra knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Cory can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Calandra","Cory"],"index":10800,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985664487,"difficulty":0.0014335513}
+{"premise":"There are three persons. Everyone is visible 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 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 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":"Darrell can now know that Reginald can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darrell","Reginald","Priscilla"],"index":43539,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997541308,"difficulty":0.0002458692}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tempie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agenta knows that 3)","n_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":"Tempie can now know whether Robert can know that Tempie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Benjamin","Tempie"],"index":11832,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6458292007,"difficulty":1.6458292007}
+{"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 Robert is thirsty. It is publicly announced that Evelynn does not know whether Clayton is thirsty. It is publicly announced that Robert does not know whether Willie is thirsty. It is publicly announced that Willie does not know whether Evelynn is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Evelynn can now know whether Clayton is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelynn","Clayton","Willie","Robert"],"index":4362,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9802712202,"difficulty":0.0197287798}
+{"premise":"There are four persons. Everyone is visible 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 ] Agentd knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Marcos can now know that John can know that Marcos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shane","James","John","Marcos"],"index":47846,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9572719932,"difficulty":0.0427280068}
+{"premise":"There are three persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that Mark knows whether Bonnie's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agenta knows 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 (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Bonnie can now know that Mark can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Mark","Raymond"],"index":4090,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997535348,"difficulty":0.0002464652}
+{"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 Donald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Donald can now know that David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","John","Donald"],"index":34226,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983661771,"difficulty":0.0016338229}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leland knows whether Curtis's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Curtis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Eugene can now know that Dennis can know whether Leland's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Curtis","Leland","Eugene","Dennis"],"index":50497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997256398,"difficulty":0.0002743602}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc 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:1,2,3,4 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":"Lisa can now know whether Dustin can know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dustin","Gerald","Lisa","Antonio"],"index":10943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"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. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 1 ] 0","hypothesis":"Travis can now know that Barbara can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Travis","Krista"],"index":57154,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6964610219,"difficulty":1.6964610219}
+{"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 William knows whether William is thirsty. It is publicly announced that William 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 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":"William can now know that Eugene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Drew","Eugene","William"],"index":57713,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9937183857,"difficulty":0.0062816143}
+{"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 Yesenia. Barbara's card is shown to Jill. Yesenia's card is shown to Barbara. 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.","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 that (Agentc knows that (~(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":"Jill can now know that Barbara can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Yesenia","Jill","Barbara"],"index":21074,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985588193,"difficulty":0.0014411807}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca does not know whether Elizabeth is thirsty. It is publicly announced that Rebecca does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Elizabeth can now know that Rebecca can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rebecca","Elizabeth"],"index":64238,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984794259,"difficulty":0.0015205741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Gloria can now know that Lori can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lori","Rachel","Gloria","Mary"],"index":19458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998357594,"difficulty":0.001642406}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether Kevin's forehead is muddy. It is publicly announced that Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentc 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) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Kevin can now know whether Darin can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darin","Arthur","Kevin"],"index":12772,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996337891,"difficulty":0.0003662109}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Delores's card is shown to Delores. Donald's card is shown to Delores. John's card is shown to Donald. Donald's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Delores 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)) ] Agentc knows whether (Agentb 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":"John can now know whether Donald can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delores","Donald","John"],"index":27274,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994356036,"difficulty":0.0005643964}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Brian. Frances's card is shown to Brian. Brian's card is shown to Frances. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Randall can now know that Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Randall","Brian","Elizabeth","Frances"],"index":27759,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980480671,"difficulty":0.0019519329}
+{"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 Patricia. Manuel's card is shown to Manuel. Patricia's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 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:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jeffrey can now know whether Manuel can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Patricia","Manuel","Jeffrey"],"index":48743,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.5364099145,"difficulty":0.4635900855}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brad's card is shown to Brad. John's card is shown to Brad. John's card is shown to John. Mildred's card is shown to John. Duane'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:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Duane can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Duane","Brad","John","Mildred"],"index":48409,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997231364,"difficulty":0.0002768636}
+{"premise":"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 Adam does not know whether Adam's forehead 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 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 2) ] 0","hypothesis":"Yvonne can now know that Shawnta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shawnta","Adam","Yvonne"],"index":63414,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940000772,"difficulty":0.0059999228}
+{"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 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|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":"Julianne can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julianne","Debra","Levi"],"index":62345,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997190833,"difficulty":0.0002809167}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcus's card is shown to Marcus. Nelson's card is shown to Johnny. Laura's card is shown to Johnny. Marcus's card is shown to Nelson. Nelson's card is shown to Nelson. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nelson can now know that Marcus can know that Marcus picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marcus","Johnny","Nelson","Laura"],"index":32766,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9930603504,"difficulty":0.0069396496}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy. It is publicly announced that Fannie knows whether or not everyone's forehead is muddy. It is publicly announced that Fannie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (~(1|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":"Scott can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Scott","Fannie"],"index":14467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997237325,"difficulty":0.0002762675}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sara's card is shown to Sara. Jody's card is shown to Jody. It is publicly announced that someone picked a red card. It is publicly announced that Jody knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows 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":"Sara can now know that Jody can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sara","Jody"],"index":32845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997044206,"difficulty":0.0002955794}
+{"premise":"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 Mark does not know whether Mark's forehead is muddy. It is publicly announced that Susan 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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mark can now know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Susan","Kevin","Shaun"],"index":48019,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9113793373,"difficulty":0.0886206627}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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 Nancy can know that Joshua's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Carmen","Nancy"],"index":48024,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9275840521,"difficulty":0.0724159479}
+{"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 Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows 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":"Mary can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Mary","Thomas"],"index":9625,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985504746,"difficulty":0.0014495254}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeannette does not know whether Jeannette'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 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":"Doris can now know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Brenda","Jeannette","Doris"],"index":60357,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9908688068,"difficulty":0.0091311932}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erin does not know whether James is thirsty. It is publicly announced that James 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Erin can now know that James can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Erin","James"],"index":48811,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997058511,"difficulty":0.0002941489}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Judith's card is shown to Judith. Robert's card is shown to Judith. Judith's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Judith can now know whether Robert can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Judith","Robert"],"index":57715,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laura knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Doris can now know whether Bennie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bennie","Robert","Doris","Laura"],"index":61415,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9520111084,"difficulty":0.0479888916}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether Cole's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Cole can now know that Randall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cole","Ricardo","Susan","Randall"],"index":43370,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981371164,"difficulty":0.0018628836}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether Tommy is thirsty. It is publicly announced that Raymond 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Shirley can now know that Connie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Raymond","Tommy","Connie"],"index":17833,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984342456,"difficulty":0.0015657544}
+{"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 Robert. Joseph's card is shown to Joseph. George's card is shown to Joseph. George's card is shown to George. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Joseph can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Joseph","George"],"index":58412,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973579049,"difficulty":0.0026420951}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sonia can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sonia","Jean","Douglas","Cynthia"],"index":42588,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7933714986,"difficulty":0.2066285014}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"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":"Juan can now know that Cody can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cody","Phyllis","Juan"],"index":65892,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982789755,"difficulty":0.0017210245}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Jack. Gilbert's card is shown to Jack. Jack's card is shown to Karen. Jack's card is shown to Gilbert. It is publicly announced that someone picked a red card. It is publicly announced that Jack picked a red card. It is publicly announced that Karen knows whether or not nobody picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jack knows whether Gilbert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jack can now know whether Karen can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Karen","Gilbert"],"index":18450,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995774627,"difficulty":0.0004225373}
+{"premise":"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 Deanne knows whether or not nobody's forehead is muddy. It is publicly announced that Deanne knows whether Deanne's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agenta knows 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) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Nicholas can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Nicholas","Deanne"],"index":29651,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998664856,"difficulty":0.001335144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phillip knows whether or not everyone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Joshua can now know whether Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joshua","Phillip","Jeff","Kenneth"],"index":49915,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8590909243,"difficulty":0.1409090757}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sue's card is shown to Sue. Peter's card is shown to Sue. Joseph's card is shown to Mark. Mark's card is shown to Joseph. Peter's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Sue 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:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mark can now know whether Peter can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sue","Mark","Joseph","Peter"],"index":24505,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9966337085,"difficulty":0.0033662915}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Clair's card is shown to Clair. Richard's card is shown to Clair. Randy's card is shown to Clair. Randy's card is shown to Richard. Randy's card is shown to Randy. 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)","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":"Richard can now know that Clair can know whether Clair picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clair","Richard","Randy"],"index":26192,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8824831843,"difficulty":1.8824831843}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie's forehead 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 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) ] [ ! 1 ] 0","hypothesis":"Olive can now know that Eileen can know that Olive's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marjorie","Eileen","Olive"],"index":7581,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9470750093,"difficulty":0.0529249907}
+{"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 that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["James","Robert"],"index":60210,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.566863358,"difficulty":0.433136642}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Donna does not know whether Oma 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 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) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Donna","Oma"],"index":3513,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999783814,"difficulty":0.000216186}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Katharine knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Katharine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katharine","David","Louann"],"index":40674,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986611605,"difficulty":0.0013388395}
+{"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 Joseph. Paul's card is shown to Joseph. Joseph's card is shown to Paul. Paul's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 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 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether Tammy can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Tammy","Paul"],"index":54280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9621459246,"difficulty":0.0378540754}
+{"premise":"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.","smcdel_problem":"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 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":"David can now know that Danny can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Danny","James"],"index":1412,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997609258,"difficulty":0.0002390742}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna knows whether or not everyone's forehead is muddy. It is publicly announced that Edna knows whether Brian's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] Agentc knows that (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) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Joy can now know that Brian can know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brian","Edna","Joy"],"index":33344,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.6072207093,"difficulty":0.3927792907}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Corey is thirsty. It is publicly announced that Heidi does not know whether John is thirsty. It is publicly announced that Corey knows whether Corey is thirsty. It is publicly announced that Heidi 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)) ] (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) ] [ ! 3 ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Corey can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Heidi","John","Corey"],"index":33707,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joesph does not know whether Joesph's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gretchen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Gretchen can now know that Gretchen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joesph","Gretchen"],"index":58451,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9865352511,"difficulty":1.9865352511}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda is not thirsty. It is publicly announced that Lucy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Willie can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lucy","Linda","Autumn","Willie"],"index":51496,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997363687,"difficulty":0.0002636313}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Callie does not know whether Callie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that 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":"Callie can now know whether Jamie can know that Callie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Callie","Paul","Jamie"],"index":26321,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8529649377,"difficulty":0.1470350623}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (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":"Benjamin can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Elizabeth","Benjamin","Alexandria"],"index":17323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983854294,"difficulty":0.0016145706}
+{"premise":"There are three persons. Everyone is visible 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 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Judith can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Norma","Judith","John"],"index":11311,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982094765,"difficulty":0.0017905235}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel knows whether someone's forehead is muddy. It is publicly announced that Laura 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)) ] Agentb knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Laura can now know that Chad can know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Laura","Chad","Kathy"],"index":35298,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990953207,"difficulty":0.0009046793}
+{"premise":"There are two persons. Everyone is visible 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.","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)","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":"Elsie can now know that Frances can know that Elsie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elsie","Frances"],"index":64998,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981866479,"difficulty":0.0018133521}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Doris knows whether Doris is thirsty. It is publicly announced that Doris is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Doris can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lisa","Tina","Doris"],"index":61504,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997879863,"difficulty":0.0002120137}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue knows whether Sue's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Kimberly can now know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vanessa","Ronald","Sue","Kimberly"],"index":56568,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982333183,"difficulty":0.0017666817}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy's forehead is not muddy. It is publicly announced that Jeremy 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 whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jeremy can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Jeremy","Sondra"],"index":44498,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997361302,"difficulty":0.0002638698}
+{"premise":"There are four persons. Everyone is visible 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 Michell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Vernon can now know whether Dana can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michell","Dana","Virginia","Vernon"],"index":6196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996250868,"difficulty":0.0003749132}
+{"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 Ryan. Portia's card is shown to Ryan. Jennifer's card is shown to Portia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows whether (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":"Ryan can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ryan","Jennifer","Portia"],"index":67424,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shakira's card is shown to Anna. Anna's card is shown to Dave. Dave's card is shown to Dave. Anna's card is shown to Shakira. Dave's card is shown to Rebecca. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca does not know whether Shakira picked a red card. It is publicly announced that Anna knows whether Shakira picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agentc knows that 1)","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":"Rebecca can now know that Shakira can know that Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Dave","Shakira","Rebecca"],"index":36664,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9885317087,"difficulty":0.0114682913}
+{"premise":"There are two persons. Everyone is visible 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 (~(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":"Dwayne can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Edna","Dwayne"],"index":64718,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997600913,"difficulty":0.0002399087}
+{"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 Sheila is thirsty. It is publicly announced that Sheila 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 that (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Jazmin can now know that Sheila can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Jazmin","Sheila","William"],"index":52487,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9881935716,"difficulty":0.0118064284}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lester knows whether Roger's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentd knows that (Agentc knows 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":"Lester can now know that Roger can know that Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Crystal","Latricia","Roger","Lester"],"index":13013,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974038005,"difficulty":0.0025961995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Casey knows whether Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Virginia can now know that Robert can know that Virginia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Casey","Virginia","Adrian"],"index":64344,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980924726,"difficulty":0.0019075274}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether or not everyone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy. It is publicly announced that Joan's forehead is muddy. It is publicly announced that Joan knows whether Carlos's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Joan can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Carlos","Joan"],"index":8429,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.905769825,"difficulty":0.094230175}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Whitney 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) ] [ ! (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":"Jo can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Jo","Arthur","Whitney"],"index":42714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983003736,"difficulty":0.0016996264}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone 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 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":"Penny can now know whether Harriet is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Harriet","Penny","Frank"],"index":53715,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976722598,"difficulty":0.0023277402}
+{"premise":"There are two persons. Everyone is visible 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 Kathryn knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether 1)","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":"Elsie can now know whether Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kathryn","Elsie"],"index":4349,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997139573,"difficulty":0.0002860427}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows 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) ] [ ! ~(2) ] 0","hypothesis":"Jennifer can now know that Cindy can know that Jennifer's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cindy","Jennifer"],"index":30305,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9572074413,"difficulty":0.0427925587}
+{"premise":"There are four persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Landon can now know that Rachael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rachael","Flor","Landon","Raymond"],"index":59372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982574582,"difficulty":0.0017425418}
+{"premise":"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":"Gerry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Harold","Gerry"],"index":14058,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981903434,"difficulty":0.0018096566}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Benjamin's card is shown to Robert. Robert's card is shown to Benjamin. Paul's card is shown to Benjamin. Benjamin's card is shown to Paul. Robert's card is shown to Devon. It is publicly announced that someone picked a red card. It is publicly announced that Benjamin knows whether someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Benjamin picked a black card. It is publicly announced that Robert does not know whether Devon 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) ] Agentd knows whether (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Devon can now know whether Robert can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Benjamin","Paul","Devon"],"index":24397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9709387422,"difficulty":0.0290612578}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). June's card is shown to June. June's card is shown to Sonia. Sonia's card is shown to Sonia. Randolph's card is shown to Randolph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Randolph can now know that June picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["June","Sonia","Randolph"],"index":14880,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997964263,"difficulty":0.002035737}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows that (Agentb knows 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":"Claire can now know that Daniel can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Claire","Daniel","Linda","Janice"],"index":6933,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Charles's forehead is muddy. It is publicly announced that Darius's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (Agenta knows that (~(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":"Shirley can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","Regina","Darius","Charles"],"index":64388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99850595,"difficulty":0.00149405}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Addie's card is shown to Addie. John's card is shown to Addie. Patricia's card is shown to John. John's card is shown to Roy. Roy'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 John does not know whether Roy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Patricia can now know whether John can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Addie","John","Roy","Patricia"],"index":687,"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 Andre knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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:1,2,3,4 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":"Margaret can now know that Christine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Olive","Andre","Margaret","Christine"],"index":1099,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997418523,"difficulty":0.0002581477}
+{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows whether 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":"Robert can now know that Joe can know whether Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Myriam","Anthony","Robert"],"index":12392,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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":"Kathleen can now know that Eric can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kathleen","Eric","Lorretta"],"index":33943,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984213114,"difficulty":0.0015786886}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Oswaldo's card is shown to Oswaldo. Oswaldo's card is shown to Meghan. Meghan's card is shown to Meghan. Tosha's card is shown to Meghan. Oswaldo's card is shown to Tosha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Oswaldo can now know that Meghan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Oswaldo","Meghan","Tosha"],"index":44241,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980429411,"difficulty":0.0019570589}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mae does not know whether Christopher is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (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":"Lorraine can now know whether Mae can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorraine","Mae","Christopher"],"index":48789,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997164607,"difficulty":0.0002835393}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alissa 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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Alissa can now know that Frances can know whether Sol's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sol","Frances","Alissa"],"index":45323,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernie knows whether Bernie's forehead is muddy. It is publicly announced that Ellen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Jeanne can now know that George can know that Bernie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bernie","George","Ellen","Jeanne"],"index":2279,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9756733179,"difficulty":0.0243266821}
+{"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 Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen does not know whether Karen picked a red card. It is publicly announced that Karen 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)","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":"Karen can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Margaret","Karen"],"index":57057,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9882819057,"difficulty":1.9882819057}
+{"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 Roberto. Paul's card is shown to Paul. Maurice's card is shown to Paul. Dorothy's card is shown to Maurice. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Roberto does not know whether Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Paul can now know whether Roberto can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roberto","Paul","Maurice","Dorothy"],"index":58544,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979631901,"difficulty":0.0020368099}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhoda's card is shown to Mary. Mary's card is shown to Rhoda. Rhoda's card is shown to Rhoda. Jerold's card is shown to Rhoda. Mary's card is shown to Jerold. Jerold's card is shown to Jerold. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rhoda can now know that Jerold can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Rhoda","Jerold"],"index":46451,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984215498,"difficulty":0.0015784502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows 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":"John can now know whether Michael can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Dorothea","Judith","Michael"],"index":42546,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9981276393,"difficulty":0.0018723607}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charlotte's card is shown to Charlotte. Harry's card is shown to Susan. Bernard's card is shown to Susan. Bernard's card is shown to Bernard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Harry can now know whether Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Susan","Harry","Bernard"],"index":42739,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6836573482,"difficulty":0.3163426518}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherri's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Sherri can now know that Stewart can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dawn","Patricia","Stewart","Sherri"],"index":8527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984018207,"difficulty":0.0015981793}
+{"premise":"There are two persons. Everyone is visible 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":"Timothy can now know that James can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Timothy"],"index":50749,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997497201,"difficulty":0.0002502799}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Arthur. Eva's card is shown to Arthur. Robert's card is shown to Robert. Eva's card is shown to Eva. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eva can now know that Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Arthur","Robert","Eva"],"index":64663,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone 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 whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Margarete can now know that Rick can know whether Rick is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margarete","Ronald","Rick"],"index":63193,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984351993,"difficulty":0.0015648007}
+{"premise":"There are 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 (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":"Bertha can now know that Aaron can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandon","Aaron","Bertha"],"index":34084,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984629154,"difficulty":0.0015370846}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Walter 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 (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Walter can now know that Jane can know that Jane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Walter","Michael","Jane"],"index":43426,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9881792068,"difficulty":0.0118207932}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Merle does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edward can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Merle","Leslie","Edward"],"index":13265,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966515899,"difficulty":0.0033484101}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Rayna can now know whether Robert can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Paul","Rayna"],"index":32052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Reina is thirsty. It is publicly announced that Reina does not know whether James is thirsty. It is publicly announced that Shawn does not know whether or not everyone is thirsty. It is publicly announced that Reina does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (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":"Shawn can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Reina","James","Shawn"],"index":58063,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6768699884,"difficulty":1.6768699884}
+{"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 Cecilia is thirsty. It is publicly announced that Cecilia does not know whether Michael is thirsty. It is publicly announced that Michael does not know whether Cecilia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether Joseph can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cecilia","Michael","John","Joseph"],"index":18100,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997836947,"difficulty":0.0002163053}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick does not know whether William is thirsty. It is publicly announced that 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 ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! 2 ] 0","hypothesis":"William can now know that Patrick can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","David","Patrick"],"index":24493,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997867942,"difficulty":0.0002132058}
+{"premise":"There are three persons. Everyone is visible 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 Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (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":"Wanda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Wanda","Shawn"],"index":752,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983018637,"difficulty":0.0016981363}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Martha can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Martha","Diane"],"index":35378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947021604,"difficulty":0.0052978396}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tanya does not know whether Oliver is thirsty. It is publicly announced that Ann is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! 2 ] 0","hypothesis":"Janice can now know that Tanya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oliver","Ann","Janice","Tanya"],"index":9675,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.95895648,"difficulty":0.04104352}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Lauren. Kerry's card is shown to Kerry. Sandy's card is shown to Kerry. Lauren's card is shown to Sandy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows 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":"Sandy can now know that Kerry can know that Lauren picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lauren","Kerry","Sandy"],"index":20689,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978245497,"difficulty":0.0021754503}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Graciela's forehead is not muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Eula can now know whether Mark can know that Graciela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Graciela","Eula"],"index":40794,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972564578,"difficulty":0.0027435422}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not nobody's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (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":"George can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Forrest","John","Thomas","George"],"index":6246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972135425,"difficulty":0.0027864575}
+{"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 Joseph. Julie's card is shown to Julie. Jerry's card is shown to Julie. Joseph's card is shown to Jerry. Julie's card is shown to Jerry. Jerry's card is shown to Jerry. Julie's card is shown to Ashley. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ashley can now know that Joseph can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Julie","Jerry","Ashley"],"index":1657,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peter knows whether Peter is thirsty. It is publicly announced that Randi does not know whether or not everyone is thirsty. It is publicly announced that Edward does not know whether or not everyone is thirsty. It is publicly announced that Vicki does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Randi can now know that Peter can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicki","Randi","Edward","Peter"],"index":21004,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Noel's card is shown to Bettye. Ursula's card is shown to Noel. Ursula's card is shown to Ursula. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ursula can now know that Noel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bettye","Noel","Ursula"],"index":46556,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982680082,"difficulty":0.0017319918}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tamara's card is shown to Tamara. Drew's card is shown to Tamara. Tamara's card is shown to Melinda. 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 (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tamara can now know whether Melinda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tamara","Melinda","Drew"],"index":9490,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997708201,"difficulty":0.0002291799}
+{"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 Paul. Paul's card is shown to Dennis. Paul's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dennis can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Zelma","Dennis","William"],"index":29264,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997687936,"difficulty":0.0002312064}
+{"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 Patricia. Roberta's card is shown to Dan. Patricia's card is shown to Dan. Judy's card is shown to Judy. It is publicly announced that someone picked a red card. It is publicly announced that Roberta does not know whether Roberta picked a red card. It is publicly announced that Patricia knows whether or not everyone picked a red card. It is publicly announced that Patricia does not know whether Dan picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb: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 ] (Agenta 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":"Roberta can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Roberta","Patricia","Dan","Judy"],"index":18289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8109244704,"difficulty":0.1890755296}
+{"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. Steven's card is shown to Lorraine. Lorraine's card is shown to Lorraine. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether Lorraine picked a red card. It is publicly announced that Lorraine knows whether Lorraine picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows 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 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Steven can now know that Lorraine can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Lorraine"],"index":45521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997112155,"difficulty":0.0002887845}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty. It is publicly announced that Regina does not know whether David is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Melissa can know that Regina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Melissa","David","Regina"],"index":24754,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7544508576,"difficulty":0.2455491424}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Sheri can now know that David can know that Stacy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sheri","Stacy","David"],"index":12374,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983351827,"difficulty":0.0016648173}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth is thirsty. It is publicly announced that John does not know whether Devin is 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) ] 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) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Elizabeth can now know that William can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","William","Devin","Elizabeth"],"index":39345,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983379841,"difficulty":0.0016620159}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily's forehead is muddy. It is publicly announced that Emily's forehead is muddy. It is publicly announced that Emily's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Diane can now know that Kenneth can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emily","Kenneth","Vera","Diane"],"index":50167,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892885685,"difficulty":0.0107114315}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hubert'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 3)","n_announcements":1,"pbcheck":"VARS 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":"Hubert can now know whether Phillip's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hubert","Emil","Phillip"],"index":27234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997393489,"difficulty":0.0002606511}
+{"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. Karen's card is shown to Michael. Karen's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen 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 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Karen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Karen"],"index":42601,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997721314,"difficulty":0.0002278686}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret knows whether Michelle's forehead is muddy. It is publicly announced that Timothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether 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":"Bret can now know whether Timothy can know whether Bret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Timothy","Michelle","Bret"],"index":39281,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997039437,"difficulty":0.0002960563}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sue's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"David can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Sue","Connie","Crystal"],"index":2944,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998354733,"difficulty":0.001645267}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Alysia can now know that Phyllis can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Phyllis","John","Alysia"],"index":64904,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985232949,"difficulty":0.0014767051}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Jennifer can now know that Leland can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Harry","Shane","Leland","Jennifer"],"index":46289,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984825253,"difficulty":0.0015174747}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether 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) ] [ ! (Agentc knows whether 4) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Daniel can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Daniel","Danielle","Harold"],"index":62231,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997511506,"difficulty":0.0002488494}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows 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":"Clara can now know that Vernie can know whether Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Vernie","Clara","Tyler"],"index":28653,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997453094,"difficulty":0.0002546906}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosa is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that 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 Rosa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Stephen","Rosa"],"index":20402,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9838946462,"difficulty":0.0161053538}
+{"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 Roger 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 whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Diane can now know that Roger can know whether Oralia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roger","Diane","Oralia"],"index":51388,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7973666191,"difficulty":0.2026333809}
+{"premise":"There are four persons. Everyone is visible 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 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 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":"Melissa can now know that Jamie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melissa","Jamie","Mark","Katie"],"index":22583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9266421795,"difficulty":0.0733578205}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether or not everyone's forehead is muddy. It is publicly announced that Nathan'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 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Nathan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carol","Nathan"],"index":3004,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981706142,"difficulty":0.0018293858}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Megan does not know whether Lucille is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Lucille can now know that Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lucille","Tyler","Susan","Megan"],"index":18944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982659221,"difficulty":0.0017340779}
+{"premise":"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 Marvin's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy. It is publicly announced that Steven knows whether Marvin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (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":"Steven can now know that Marvin can know whether Marvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Steven","Mark","George"],"index":18932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.933380425,"difficulty":0.066619575}
+{"premise":"There are three 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 Janie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charles can now know that Janie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janie","Charles","John"],"index":18988,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949506521,"difficulty":0.0050493479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leonora does not know whether Leonora'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) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Sarah can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Sarah","Leonora"],"index":11820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarissa 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":"Johnny can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Clarissa","Johnny"],"index":1749,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981592298,"difficulty":0.0018407702}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Chae 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 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":"Chae can now know that Diane can know that Chae's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Chae","Diane"],"index":24723,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975507855,"difficulty":0.0024492145}
+{"premise":"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's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Charles can now know whether Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Stephen","Charles","Ronald"],"index":18403,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9301029444,"difficulty":0.0698970556}
+{"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 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) ] [ ! ~(Agenta knows whether 3) ] Agentb 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 3) ] 0","hypothesis":"Mimi can now know that Amber can know that Mimi is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Mimi","Amber","Nikita"],"index":54460,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99801898,"difficulty":0.00198102}
+{"premise":"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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mary can now know that Angela can know whether Jill's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Angela","Jill","Mary"],"index":38772,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996197224,"difficulty":0.0003802776}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether 1)","n_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":"Natasha can now know whether James can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","James","Natasha"],"index":43763,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994937181,"difficulty":0.0005062819}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene does not know whether or not everyone is thirsty. It is publicly announced that William does not know whether Vicky is thirsty. It is publicly announced that William does not know whether Vicky is thirsty. It is publicly announced that Vicky 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)) ] (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"William can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Irene","Vicky"],"index":42399,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975230098,"difficulty":0.0024769902}
+{"premise":"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 knows whether Roy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Roy can now know whether Wanda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carmen","Wanda","Roy","Mabel"],"index":8489,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997546077,"difficulty":0.0002453923}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephane 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 (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":"Anthony can now know that Bill can know whether Anthony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Stephane","Loretta","Bill"],"index":28347,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963245988,"difficulty":0.0036754012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Giselle does not know whether Myles is thirsty. It is publicly announced that Myles does not know whether or not everyone is thirsty. It is publicly announced that Myles does not know whether Erica is thirsty. It is publicly announced that Myles does not know whether Erica is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Erica can now know whether Myles can know whether Myles is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Giselle","Myles","Erica"],"index":45527,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983905554,"difficulty":0.0016094446}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 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":"Claude can now know that Therese can know that Claude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bridget","Claude","Daryl","Therese"],"index":66810,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957838058,"difficulty":0.0042161942}
+{"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. Gary's card is shown to Gary. Mabel's card is shown to Gary. Barbara's card is shown to Mabel. Barbara's card is shown to Clara. It is publicly announced that someone picked a red card. It is publicly announced that Gary does not know whether Clara picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Clara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Gary","Mabel","Clara"],"index":7596,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998452425,"difficulty":0.001547575}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christena does not know whether Leonard is thirsty. It is publicly announced that Christena does not know whether Elizabeth is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Christena can now know that Christena is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Christena","James","Elizabeth"],"index":24974,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9422617555,"difficulty":0.0577382445}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Celia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Joe","Celia","Beatrice"],"index":14964,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982111454,"difficulty":0.0017888546}
+{"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 Aida. Aida's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Aida can now know that Aida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aida","Kathleen","James","Steven"],"index":34679,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99766469,"difficulty":0.00233531}
+{"premise":"There are two persons. Everyone is visible 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 Christopher knows whether Donald's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Donald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agentb knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Christopher can now know that Donald can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Christopher"],"index":54272,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983156919,"difficulty":0.0016843081}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(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) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Matthew can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hulda","Matthew","Richard"],"index":12932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984970093,"difficulty":0.0015029907}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Garland does not know whether Garland's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Reuben can now know that Donna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Priscilla","Reuben","Donna","Garland"],"index":61658,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9749309421,"difficulty":0.0250690579}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that Barbara 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 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Barbara can now know whether Donna can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Donna"],"index":65444,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8764425516,"difficulty":1.8764425516}
+{"premise":"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 Clara'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":"Clara can now know that Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Clara"],"index":48177,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.923597753,"difficulty":1.923597753}
+{"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. Charles's card is shown to Bobby. Angie's card is shown to Angie. Angie's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Angie 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) ] Agentb knows that (Agentc knows whether 1)","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":"Angie can now know that Charles can know whether Bobby picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Angie","Charles","Frank"],"index":66167,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.557787478,"difficulty":0.442212522}
+{"premise":"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 Willie does not know whether Willie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Victoria can now know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Willie","Gregory","Victoria"],"index":44282,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995214939,"difficulty":0.0004785061}
+{"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 James. Sandra's card is shown to Sandra. James's card is shown to Jewel. Sandra's card is shown to Jewel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Lisa can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Sandra","Lisa","Jewel"],"index":29446,"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). Cathryn's card is shown to Anne. Walter's card is shown to Walter. Cathryn's card is shown to Walter. Walter's card is shown to Tommy. Anne's card is shown to Cathryn. It is publicly announced that someone picked a red card. It is publicly announced that Walter picked a black card. It is publicly announced that Walter does not know whether Anne picked a red card. It is publicly announced that Walter knows whether someone picked a red card. It is publicly announced that Walter does not know whether Anne 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 that (Agenta knows that (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Walter can now know that Anne can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anne","Walter","Tommy","Cathryn"],"index":64140,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Connie is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] (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)) ] [ ! ~(2) ] 0","hypothesis":"Grace can now know whether Grace is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Connie","Grace"],"index":20149,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987139702,"difficulty":0.0012860298}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether Logan's forehead is muddy. It is publicly announced that Julie knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 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: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":"Danny can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Danny","Karen","Julie","Logan"],"index":16146,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985052347,"difficulty":0.0014947653}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel 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 (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Paula can now know that Manuel can know that Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Manuel","Doris","Paula"],"index":44572,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981671572,"difficulty":0.0018328428}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Windy's card is shown to Windy. Aleida's card is shown to Windy. Aleida's card is shown to Aleida. Windy's card is shown to Calvin. It is publicly announced that someone picked a red card. It is publicly announced that Aleida 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)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Calvin can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Windy","Aleida","Calvin"],"index":20774,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983997941,"difficulty":0.0016002059}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead 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)","n_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":"Linda can now know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Stephanie","Linda"],"index":65083,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765768051,"difficulty":0.0234231949}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilyn's card is shown to Marilyn. Marilyn's card is shown to Michael. Michael's card is shown to Michael. Michael's card is shown to Katherine. 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Katherine can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marilyn","Michael","Katherine"],"index":22317,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983178377,"difficulty":0.0016821623}
+{"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 David is thirsty. It is publicly announced that Donald does not know whether David 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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","David","Ashley","Donald"],"index":57006,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997767806,"difficulty":0.0002232194}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Terry's card is shown to Matthew. Matthew's card is shown to Jason. Terry's card is shown to Jason. Jason's card is shown to Terry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 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:1,3 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jason can now know that Matthew can know that Jason picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Jason","Terry"],"index":66014,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964197874,"difficulty":0.0035802126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Sabrina knows whether Mary's forehead is muddy. It is publicly announced that Sabrina knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Renee can now know that Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sabrina","Renee","Mary","Linda"],"index":27461,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9485470653,"difficulty":1.9485470653}
+{"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. Jesse's card is shown to Robert. Robert's card is shown to Jesse. Robert's card is shown to Hector. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jesse can now know that Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Jesse","Hector"],"index":44173,"s-l":"explicit-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). Liza's card is shown to Robert. Gabriel's card is shown to James. Liza'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:4 Agentb: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:4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gabriel","Robert","James","Liza"],"index":13747,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984894991,"difficulty":0.0015105009}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica is thirsty. It is publicly announced that Eric knows whether Eric is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Eric can now know whether Jessica can know whether Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Jessica"],"index":55363,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9980373979,"difficulty":0.0019626021}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlos does not know whether Carlos's forehead is muddy. It is publicly announced that Carlos's forehead is muddy. It is publicly announced that Lorene's forehead is muddy. It is publicly announced that Annett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Carlos can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carlos","Annett","Lorene","Randolph"],"index":63925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5842683911,"difficulty":0.4157316089}
+{"premise":"There are four persons. Everyone is visible 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know that Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sandra","David","Latasha","Karen"],"index":20642,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984135628,"difficulty":0.0015864372}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Lenny can now know that Kenneth can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lenny","Douglas","Edward","Kenneth"],"index":58700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985154271,"difficulty":0.0014845729}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Ingrid can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Mary","Billy","Ingrid"],"index":10899,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983534813,"difficulty":0.0016465187}
+{"premise":"There are two persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":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":"Virginia can now know whether Carl can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Virginia","Carl"],"index":49921,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996585846,"difficulty":0.0003414154}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy. It is publicly announced that Ernesto's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"Ernesto can now know whether Susan can know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susan","Ernesto"],"index":64243,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5701498389,"difficulty":1.5701498389}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joshua can now know that Jean can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","Joshua","Jessica"],"index":14270,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984026551,"difficulty":0.0015973449}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julian knows whether or not everyone's forehead is muddy. It is publicly announced that Reynaldo does not know whether Reynaldo's forehead is muddy. It is publicly announced that George knows whether Shirley's forehead is muddy. It is publicly announced that Reynaldo does not know whether Reynaldo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Julian can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shirley","George","Julian","Reynaldo"],"index":58477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8103806376,"difficulty":0.1896193624}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Dawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Dawn can now know that Cheryl can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Galen","Dawn","Robert","Cheryl"],"index":34965,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977167845,"difficulty":0.0022832155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelita does not know whether Angelita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Angelita can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karla","Steven","Angelita","Jason"],"index":11840,"s-l":"forehead-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). Emma's card is shown to Emma. Chandra's card is shown to Chandra. Emma's card is shown to Zachary. Kevin's card is shown to Zachary. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Chandra picked a red card. It is publicly announced that Emma 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:2 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! 1 ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! 1 ] [ ! (1|2|3|4) ] 0","hypothesis":"Emma can now know whether Chandra can know that Kevin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emma","Chandra","Zachary","Kevin"],"index":67323,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9310873151,"difficulty":0.0689126849}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anthony's card is shown to Amanda. William's card is shown to William. Amanda's card is shown to Zachary. Zachary's card is shown to Zachary. Amanda's card is shown to Anthony. William's card is shown to Anthony. 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 Zachary does not know whether Anthony picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] Agenta knows whether (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Amanda can now know whether Zachary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","William","Zachary","Anthony"],"index":23514,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9965967536,"difficulty":0.0034032464}
+{"premise":"There are four persons. Everyone is visible 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) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Harold can now know that Edna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheila","Edna","Kathy","Harold"],"index":55551,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969839454,"difficulty":0.0030160546}
+{"premise":"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)) ] 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":"Beverly can now know that James can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","James","Beverly"],"index":21147,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997189641,"difficulty":0.0002810359}
+{"premise":"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) ] [ ! ~(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":"Dustin can now know that Dustin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kim","Dustin","Guadalupe","Mary"],"index":32463,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6206573844,"difficulty":0.3793426156}
+{"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 Jorge is thirsty.","smcdel_problem":"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 (1|2|3|4))","n_announcements":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":"Marvin can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Marvin","Jorge","Debra"],"index":18284,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997662902,"difficulty":0.0002337098}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myra does not know whether Myra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agenta knows 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":"Mary can now know that Jacqueline can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Mary","Christopher","Myra"],"index":27385,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983261228,"difficulty":0.0016738772}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to Amanda. Dolores's card is shown to Amanda. Dolores's card is shown to Dolores. Mary's card is shown to Dolores. Amanda's card is shown to Mary. Dolores's card is shown to Mary. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Amanda can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Dolores","Mary"],"index":13621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997755885,"difficulty":0.0002244115}
+{"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 Timothy. Joy's card is shown to Timothy. Dennis's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Dennis does not know whether Timothy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dennis can now know that Dennis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dennis","Timothy","Joy"],"index":17665,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9221695065,"difficulty":0.0778304935}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Brittany can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Christopher","Brittany"],"index":12774,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997608066,"difficulty":0.0002391934}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felicia 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 (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":"Felicia can now know whether Bonnie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Benita","Felicia","Bonnie","Johanna"],"index":52087,"s-l":"forehead_mirror-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). David's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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:3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mary can now know whether Betty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Betty","David"],"index":39265,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8503884673,"difficulty":0.1496115327}
+{"premise":"There are three persons. Everyone is visible 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 Guadalupe's forehead is muddy.","smcdel_problem":"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 whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Frank can now know that Preston can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Preston","Guadalupe"],"index":2313,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Yvonne knows whether or not nobody is thirsty. It is publicly announced that Yvonne does not know whether Julie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Anna can now know that Julie can know that Julie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anna","Lilia","Julie","Yvonne"],"index":20328,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9870251417,"difficulty":0.0129748583}
+{"premise":"There are four persons. Everyone is visible 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 Jesse's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agentc knows that (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 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"Amy can now know that Macy can know that Macy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Macy","Amy","Mary"],"index":3751,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9932724237,"difficulty":0.0067275763}
+{"premise":"There are four persons. Everyone is visible 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 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 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Ursula can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Melinda","Ursula","William","Robert"],"index":3229,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983007312,"difficulty":0.0016992688}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Duane does not know whether Erika is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that 4)","n_announcements":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":"Erika can now know that Timothy can know that David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Duane","Erika","Timothy","David"],"index":38759,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982773066,"difficulty":0.0017226934}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George does not know whether John is thirsty. It is publicly announced that Gloria does not know whether or not everyone is thirsty. It is publicly announced that Gloria does not know whether John 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows 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":"Matthew can now know whether George can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Matthew","John","George","Gloria"],"index":19598,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993879795,"difficulty":0.0006120205}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronnie's forehead is muddy. It is publicly announced that Ronald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ronnie can now know that Ronald can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Ronnie"],"index":4575,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9792891145,"difficulty":0.0207108855}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brittney's card is shown to Marion. Barbara's card is shown to Marion. Shawna's card is shown to Marion. Marion's card is shown to Barbara. Shawna's card is shown to Barbara. Marion's card is shown to Shawna. 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:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Marion picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Brittney","Barbara","Shawna"],"index":25087,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979500175,"difficulty":0.0020499825}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Velma's card is shown to Norma. Rita's card is shown to Norma. Rita's card is shown to Rita. Norma's card is shown to Bruce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rita can now know whether Velma can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Norma","Velma","Rita","Bruce"],"index":12133,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9191429019,"difficulty":0.0808570981}
+{"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 Dion 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 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":"Dion can now know that Charles can know that Dion is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Charles","Dion"],"index":30072,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969636798,"difficulty":0.0030363202}
+{"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 Martha. Doug's card is shown to Martha. Jennifer's card is shown to Jennifer. Martha's card is shown to Doug. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Doug can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Martha","Jennifer","Doug"],"index":28479,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997072816,"difficulty":0.0002927184}
+{"premise":"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 Walter's forehead is muddy. It is publicly announced that Ursula does not know whether Ursula's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that 3)","n_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":"Walter can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ursula","Walter","Robert"],"index":58682,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960674047,"difficulty":0.0039325953}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Peggy can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kyle","Joshua","Peggy","Chad"],"index":11422,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983129501,"difficulty":0.0016870499}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sheila is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 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":"James can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sheila","James","Rosita"],"index":19907,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9781070352,"difficulty":0.0218929648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amos does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1&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":"Amos can now know whether Barbara can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amos","Barbara","Kevin"],"index":49860,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976557493,"difficulty":0.0023442507}
+{"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 Sheila. Christa's card is shown to Christa. Clifford's card is shown to Christa. Mary's card is shown to Christa. Christa's card is shown to Clifford. Clifford's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3,4 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 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":"Clifford can now know that Sheila picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheila","Christa","Clifford","Mary"],"index":40457,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8188533187,"difficulty":0.1811466813}
+{"premise":"There are three persons. Everyone is visible 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 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":"Nina can now know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nina","Debra","Victor"],"index":55710,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9982606769,"difficulty":0.0017393231}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanya's card is shown to Floyd. Tanya's card is shown to Rebecca. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 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":"Floyd can now know that Sandra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tanya","Floyd","Rebecca","Sandra"],"index":18068,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984220266,"difficulty":0.0015779734}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether Larry's forehead is muddy. It is publicly announced that Rachel's forehead is not muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] Agentc knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Rachel can now know whether Larry can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Patricia","Rachel"],"index":65180,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9926813245,"difficulty":0.0073186755}
+{"premise":"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 (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) ] [ ! (1|2|3|4) ] 0","hypothesis":"Bernice can now know whether Crystal can know whether Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Crystal","Mary","Bernice","Kelly"],"index":66990,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995275736,"difficulty":0.0004724264}
+{"premise":"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 Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Christopher can now know whether Patricia can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Alice","Corey","Patricia"],"index":65332,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7686004639,"difficulty":0.2313995361}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","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":"Marion can now know that Marion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Betty","Molly","Hong"],"index":45869,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984922409,"difficulty":0.0015077591}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corrin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 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":"Rosa can now know whether Elmer can know that Corrin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corrin","Rosa","Elmer"],"index":63063,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996984005,"difficulty":0.0003015995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlotte does not know whether Charlotte's forehead is muddy. It is publicly announced that Riley does not know whether Riley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Trey can now know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlotte","Helen","Riley","Trey"],"index":35195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928463101,"difficulty":0.0071536899}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Jean does not know whether Jean'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 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) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alvin can now know whether Jean can know that Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alvin","Jean"],"index":26279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9818912148,"difficulty":0.0181087852}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon knows whether Marlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Pearline can now know that Brandon can know that Marlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pearline","Brandon","Marlene","Jimmie"],"index":11426,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981820583,"difficulty":0.0018179417}
+{"premise":"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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Richard can now know that Cheryl can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cheryl","Richard","Thomas","Patricia"],"index":47468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995802045,"difficulty":0.0004197955}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 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":"Annette can now know whether Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","Annette","Bryan"],"index":12883,"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. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Sara's card is shown to Robert. Sara's card is shown to Harold. Howard's card is shown to Harold. Harold's card is shown to Sara. Sara's card is shown to Sara. Sara's card is shown to Howard. 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:1,3 Agentb:3,4 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:3,4 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Robert can now know whether Harold can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Harold","Sara","Howard"],"index":65109,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Walter does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Clifton can now know whether Walter can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Clifton","David","Scott"],"index":10160,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997773767,"difficulty":0.0002226233}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bill does not know whether Travis is thirsty. It is publicly announced that Penny does not know whether Travis 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 that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Bill can now know that Penny can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Bill","Penny"],"index":5398,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9545812607,"difficulty":0.0454187393}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 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":"Christopher can now know whether Carol can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Christopher","Carol"],"index":67647,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.565244019,"difficulty":0.434755981}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gilbert's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gilbert knows whether Ray's forehead 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) ] 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) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nancy can now know that Ray can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gilbert","Ray","Nancy"],"index":30291,"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 Jason does not know whether Ronald is thirsty. It is publicly announced that Ronald 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) ] Agentc knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jason can now know that Johnnie can know that Shara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronald","Shara","Jason","Johnnie"],"index":47093,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9947842956,"difficulty":0.0052157044}
+{"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 Ralph. Ralph's card is shown to Catharine. Catharine's card is shown to Catharine. John's card is shown to Catharine. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ralph can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Catharine","John"],"index":11788,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984904528,"difficulty":0.0015095472}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lydia knows whether 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 (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&2&3&4)) ] 0","hypothesis":"Lydia can now know that Samantha can know that Alice's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samantha","Alice","Lydia","Grace"],"index":61040,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9506228566,"difficulty":0.0493771434}
+{"premise":"There are four persons. Everyone is visible 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 Wanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Brian can now know that Nancy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Timothy","Nancy","Wanda"],"index":63583,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983003736,"difficulty":0.0016996264}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laverne's card is shown to Penny. Laverne's card is shown to Laverne. Laverne's card is shown to Jose. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows that 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":"Penny can now know whether Jose can know that Laverne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Penny","Laverne","Jose"],"index":18323,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9870364666,"difficulty":0.0129635334}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Minnie does not know whether Minnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Warren can now know that Warren's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Minnie","John","Dennis","Warren"],"index":60878,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976613522,"difficulty":0.0023386478}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marva knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Marva can now know that Stephanie can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephanie","Marva"],"index":9085,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978233576,"difficulty":0.0021766424}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dianna knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Victoria knows whether Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jess can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Victoria","Theresa","Dianna","Jess"],"index":14286,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9957184196,"difficulty":0.0042815804}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. John's card is shown to Scott. Scott's card is shown to Mark. Scott's card is shown to John. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mark can now know that Scott can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Scott","Mark","John"],"index":13429,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984669089,"difficulty":0.0015330911}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that June does not know whether June's forehead is muddy. It is publicly announced that June's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Laurence can now know that Larry can know that Laurence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Larry","Laurence","June"],"index":21646,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7721371055,"difficulty":0.2278628945}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas 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 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":"Nicholas can now know that Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Nicholas","Angela"],"index":62544,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6798789501,"difficulty":1.6798789501}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sean knows whether or not everyone is thirsty. It is publicly announced that Harry knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Harry can now know that Sean is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cathy","Christopher","Harry","Sean"],"index":33919,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9660829902,"difficulty":0.0339170098}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmie knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (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":"Carol can now know that Jimmie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Carol","Jimmie"],"index":2023,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997550845,"difficulty":0.0002449155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janelle does not know whether Mack is thirsty. It is publicly announced that Mack 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 that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Eugenie can now know that Mack can know that Brandon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brandon","Eugenie","Mack","Janelle"],"index":63300,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.988139987,"difficulty":0.011860013}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leroy does not know whether Leroy's forehead is muddy. It is publicly announced that Leroy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Leroy can now know that Rikki can know whether Rikki's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leroy","Rikki","James","Anna"],"index":18993,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9102736712,"difficulty":0.0897263288}
+{"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 Julia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 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) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Mildred can now know whether Julia can know whether Julia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julia","Mildred","Christopher"],"index":14490,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984921217,"difficulty":0.0015078783}
+{"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 Jorge is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty. It is publicly announced that Toby is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether (~(1|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":"Mary can now know whether Jorge can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jorge","Mary","Toby"],"index":57312,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9996949434,"difficulty":0.0003050566}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Jose. Gregory's card is shown to Eugene. Eugene's card is shown to Gregory. Gregory's card is shown to Edwin. It is publicly announced that someone picked a red card. It is publicly announced that Edwin does not know whether Jose picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Gregory can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Eugene","Gregory","Edwin"],"index":25647,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997221828,"difficulty":0.0002778172}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether someone is thirsty. It is publicly announced that Jennifer does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Christopher can now know that Susanna can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","James","Jennifer","Susanna"],"index":62162,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998442471,"difficulty":0.001557529}
+{"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)","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":"Steven can now know that Mary can know that Gary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Heidi","Mary","Steven"],"index":34769,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986182451,"difficulty":0.0013817549}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alice knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 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)","n_announcements":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 that Alice is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alice","Thomas","Nathan","George"],"index":33654,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984203577,"difficulty":0.0015796423}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 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":"Karen can now know that Sarah can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Heather","Karen","Sarah"],"index":59170,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997157454,"difficulty":0.0002842546}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"David can now know whether Gretchen can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gretchen","Nancy","David","Jean"],"index":37191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8500530124,"difficulty":0.1499469876}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joan knows whether or not nobody is thirsty. It is publicly announced that Jonathan knows whether Joan 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 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))) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Jonathan can now know that Joan can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jonathan","Joan"],"index":56143,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997825027,"difficulty":0.0002174973}
+{"premise":"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 Peter's forehead is muddy. It is publicly announced that Peter knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Peter can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Peter"],"index":44899,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5929234028,"difficulty":1.5929234028}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kecia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether 1)","n_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":"Donald can now know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Kecia","Donald"],"index":11412,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994227886,"difficulty":0.0005772114}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to Matthew. Sylvia's card is shown to Kim. Kim's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia knows whether someone picked a red card. It is publicly announced that Sylvia 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 Sylvia 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 ] (Agenta knows that (~(1|2|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":"Matthew can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Sylvia","Kim"],"index":31875,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985249639,"difficulty":0.0014750361}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carl does not know whether or not everyone is thirsty.","smcdel_problem":"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 (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Carl 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","Michael","Carl","Kathleen"],"index":9319,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6882010102,"difficulty":1.6882010102}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irma's forehead is 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 (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":"Ronald can now know whether Joseph can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Ronald","Irma","Joseph"],"index":39703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996730089,"difficulty":0.0003269911}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Wilma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentb knows whether (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) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Linda can now know whether Wayne can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lesley","Linda","Wayne","Wilma"],"index":17032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995222092,"difficulty":0.0004777908}
+{"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. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Tracy can now know whether Jennifer can know that Tracy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Tracy"],"index":55834,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9024986029,"difficulty":0.0975013971}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Christopher can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Rose","Timothy"],"index":26325,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997380376,"difficulty":0.0002619624}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Tara can now know whether Charles can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Tara","Kathy","Ronald"],"index":38196,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.838868022,"difficulty":0.161131978}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice knows whether or not everyone's forehead is muddy. It is publicly announced that Dave's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Dave can now know whether Alice can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alice","Dave"],"index":35680,"s-l":"forehead_mirror-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 Ellen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Nancy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Ellen","Terry"],"index":26427,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985111356,"difficulty":0.0014888644}
+{"premise":"There are four persons. Everyone is visible 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 knows whether Sylvia's forehead is muddy. It is publicly announced that Ruth 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) ] [ ! (Agentd 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) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Ruth can now know whether Shawn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Sylvia","Shawn","Ruth"],"index":34132,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997385144,"difficulty":0.0002614856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Wilma can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Edna","Wilma","Rosemary"],"index":56738,"s-l":"internal-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 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) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Brian can now know whether Dave can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Lakisha","Brian","Dave"],"index":34834,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997845292,"difficulty":0.0002154708}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Katherine. Howard's card is shown to Howard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Howard can now know that Katherine can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Katherine","Howard"],"index":54362,"s-l":"explicit-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). Scott's card is shown to Ingrid. Ingrid's card is shown to Donald. Donald's card is shown to Donald. Scott's card is shown to Donald. Ingrid's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Scott does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know that Ingrid can know whether Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ingrid","Donald","Scott"],"index":42862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7956443429,"difficulty":0.2043556571}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody'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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Germaine can now know whether Karl can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Germaine","Joseph","Diane","Karl"],"index":39782,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996184111,"difficulty":0.0003815889}
+{"premise":"There are four persons. Everyone is visible 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 Wendy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 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:1,2,3,4 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":"Juanita can now know that Wendy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Barbara","Juanita","Tom"],"index":63292,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984158278,"difficulty":0.0015841722}
+{"premise":"There are four persons. Everyone is visible 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 Pearl knows whether Lupita's forehead is muddy. It is publicly announced that Ivey knows whether Pearl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lupita can now know whether David can know that Lupita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ivey","Pearl","Lupita"],"index":13044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995740056,"difficulty":0.0004259944}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether Norma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows whether (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 4) ] 0","hypothesis":"Norma can now know whether Jose can know that Charlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charlene","Gladys","Jose","Norma"],"index":43545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996622801,"difficulty":0.0003377199}
+{"premise":"There are 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 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":"Alexis can now know that Brian can know that Brian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cindy","Alexis","Shane","Brian"],"index":24887,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985411167,"difficulty":0.0014588833}
+{"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 Salina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Betty can now know that Salvador can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Salina","Salvador","Betty","Ronald"],"index":38082,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997135997,"difficulty":0.0002864003}
+{"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 Isabel. Isabel's card is shown to Alex. Alex's card is shown to Alex. James's card is shown to Alex. Alex's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 2)","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":"Isabel can now know that Alex picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Isabel","Alex","James"],"index":37937,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9916483164,"difficulty":0.0083516836}
+{"premise":"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 that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"William can now know that Diana can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Diana","William"],"index":59267,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977948666,"difficulty":0.0022051334}
+{"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 or not everyone is thirsty. It is publicly announced that Maxine does not know whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Willie can now know that Maxine can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maxine","Alice","Willie"],"index":33088,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979271889,"difficulty":0.0020728111}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (1|2|3|4) ] Agentd knows that (Agentb knows 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":"John can now know that Dwayne can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Dwayne","Armando","John"],"index":38059,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999717176,"difficulty":0.000282824}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mallory is not thirsty. It is publicly announced that 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) ] [ ! ~(4) ] [ ! 1 ] Agenta 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) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Randy can now know whether Mallory can know that Randy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Gayle","Quinton","Mallory"],"index":32028,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9859830737,"difficulty":0.0140169263}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcia's card is shown to Dorothy. Marcia's card is shown to Kenneth. Brenda's card is shown to Marcia. Dorothy's card is shown to Brenda. Marcia's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 1)","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":"Marcia can now know whether Brenda can know whether Dorothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorothy","Kenneth","Marcia","Brenda"],"index":64087,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979111552,"difficulty":0.0020888448}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol does not know whether or not everyone's forehead is muddy. It is publicly announced that Carol does not know 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 (1&2&3)) ] [ ! ~(Agentc knows whether 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 (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Elvia can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elvia","John","Carol"],"index":35508,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"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. Kristen's card is shown to Kristen. 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 Linda picked a red card. It is publicly announced that Kristen 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) ] Agentb 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 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Kristen can now know that Christopher can know that Christopher picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Kristen","Christopher","Roosevelt"],"index":55378,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9561077952,"difficulty":0.0438922048}
+{"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 David is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"David can now know that Thomas can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","David","Terry"],"index":9782,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985100627,"difficulty":0.0014899373}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Shelby's forehead is muddy. It is publicly announced that Joseph knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Shelby can now know whether Joseph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelby","Joseph","Brandon"],"index":65936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965835214,"difficulty":0.0034164786}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether 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 3) ] [ ! (~(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) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Candace can now know whether James can know whether Candace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffery","Candace","James"],"index":28382,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997974813,"difficulty":0.002025187}
+{"premise":"There are three persons. Everyone is visible 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 3)","n_announcements":1,"pbcheck":"VARS 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":"Leona can now know that Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leona","Lawrence","Annette"],"index":18168,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967167974,"difficulty":0.0032832026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carolyn does not know whether Cortney is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Noreen does not know whether Cortney is thirsty.","smcdel_problem":"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) ] (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) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Carolyn can now know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cortney","Carolyn","Elizabeth","Noreen"],"index":25751,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7446254492,"difficulty":0.2553745508}
+{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joshua can now know whether Sean can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bradley","Sean","Joshua","Rita"],"index":23171,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996811152,"difficulty":0.0003188848}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Faye knows whether or not nobody is thirsty. It is publicly announced that Faye 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 that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Faye can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Faye"],"index":17720,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997158647,"difficulty":0.0002841353}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether Gail is thirsty. It is publicly announced that Kenneth does not know whether Connie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Kenneth can now know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kenneth","Gail","Connie"],"index":38921,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989798665,"difficulty":0.0010201335}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esperanza knows whether Nicholas'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":"Nicholas can now know that Esperanza can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nicholas","Esperanza"],"index":16119,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984266758,"difficulty":0.0015733242}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffery does not know whether or not everyone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Jeffery does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows 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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know that Charles can know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Jeffery","James","Charles"],"index":1486,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5183298588,"difficulty":0.4816701412}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows 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":"Christina can now know whether Edward can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Christina","Edward"],"index":49284,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9924875498,"difficulty":0.0075124502}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica's forehead is muddy. It is publicly announced that Jason does not know whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jessica can now know that Delores can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Delores","Jason","Doris"],"index":31764,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
+{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that Rebecca's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Rebecca can now know that Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rebecca","Louise"],"index":43115,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9430866838,"difficulty":0.0569133162}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that Edmund knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Lila can now know that Edmund's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lila","Richard","Edmund","Eleanor"],"index":10450,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944201112,"difficulty":0.0055798888}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether Jeri's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jeffery can now know whether Patricia can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeri","Jeffery","Patricia"],"index":24775,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9409270883,"difficulty":0.0590729117}
+{"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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Lou","John"],"index":16127,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995996356,"difficulty":0.004003644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda is thirsty. It is publicly announced that Joann does not know whether or not everyone is thirsty. It is publicly announced that Linda does not know whether Renee is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] (Agentb knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Linda can now know that Renee is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joann","Linda","Renee"],"index":18074,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7643427253,"difficulty":0.2356572747}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isaac knows whether Isaac is thirsty. It is publicly announced that Isaac 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) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"George can now know whether Salvatore can know that George is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Sarah","Isaac","Salvatore"],"index":28639,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9695059061,"difficulty":0.0304940939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Barbara knows whether Barbara is thirsty. It is publicly announced that Monica does not know whether Barbara is thirsty. It is publicly announced that Margaret does not know whether Jason is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jason can now know that Margaret can know whether Monica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Jason","Monica","Margaret"],"index":38382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9918882251,"difficulty":0.0081117749}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kyle's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Danielle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danielle","Kyle","John"],"index":1971,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986515641,"difficulty":0.0013484359}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW 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 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"Roy can now know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roy","Patrick","Charles"],"index":31748,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999745667,"difficulty":0.000254333}
+{"premise":"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 Jean's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] 0","hypothesis":"Allen can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Allen","Jean","Victor"],"index":3610,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Erin knows whether Erin is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Erin can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erin","Elizabeth"],"index":60180,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984273911,"difficulty":0.0015726089}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diane's card is shown to Diane. Britta's card is shown to Frank. Diane's card is shown to Britta. Britta's card is shown to Britta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Frank can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diane","Frank","Britta"],"index":63484,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997683167,"difficulty":0.0002316833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sherry knows whether someone's forehead is muddy. It is publicly announced that Brigette does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Sherry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sherry","April","Diane","Brigette"],"index":49943,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937490225,"difficulty":0.0062509775}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Shirley knows whether Shirley's forehead is muddy. It is publicly announced that Lottie knows whether Lottie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Herman can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shirley","Lottie","Herman","Veronica"],"index":44807,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996765852,"difficulty":0.0003234148}
+{"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 Christina is thirsty. It is publicly announced that Christina does not know whether Susan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Kanesha can now know whether Susan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Christina","Susan","Kanesha"],"index":27184,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.990106523,"difficulty":0.009893477}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Joseph can now know whether Raymond can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Joseph"],"index":36139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995877147,"difficulty":0.0004122853}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is thirsty. It is publicly announced that Fred does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows 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 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Lucille can now know that Scott is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Scott","Fred","Kathryn","Lucille"],"index":45220,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9280733466,"difficulty":0.0719266534}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Noel knows whether Sook's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Donna can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sook","Sammie","Donna","Noel"],"index":46957,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997591376,"difficulty":0.0002408624}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shaun is thirsty. It is publicly announced that Shaun knows whether Shaun is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dale can now know whether Shaun can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Richard","Shaun"],"index":66844,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999370873,"difficulty":0.000629127}
+{"premise":"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 knows whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentb knows whether (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 3) ] 0","hypothesis":"Ramiro can now know whether Philip can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Ramiro","Marie","Philip"],"index":47936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995933175,"difficulty":0.0004066825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua knows whether or not nobody is thirsty. It is publicly announced that Joshua does not know whether Cindy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd 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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Joshua can now know whether James can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","James","Cindy","Joshua"],"index":38834,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995185137,"difficulty":0.0004814863}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether Cheryl's forehead is muddy. It is publicly announced that Cheryl 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 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 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Mark can now know that Everett can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Robert","Mark","Everett"],"index":11532,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984897375,"difficulty":0.0015102625}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aimee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aimee","Joseph","James","Mary"],"index":66130,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983641505,"difficulty":0.0016358495}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Maxwell. Maxwell's card is shown to Maxwell. Sean's card is shown to Sean. John's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donna can now know that Donna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Maxwell","Sean","John"],"index":21258,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978639483,"difficulty":0.0021360517}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows 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":"Carolyn can now know whether Douglas can know whether Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicky","Jesus","Douglas","Carolyn"],"index":56424,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996007085,"difficulty":0.0003992915}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"William can now know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rosa","William","Antoine","Sabrina"],"index":1326,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998311758,"difficulty":0.001688242}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harvey's card is shown to Linda. Linda's card is shown to Harvey. Linda's card is shown to Nancy. It is publicly announced that someone picked a red card. It is publicly announced that Harvey knows whether someone picked a red card. It is publicly announced that Linda does not know whether James picked a red card. It is publicly announced that Linda does not know whether James picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Nancy can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Harvey","Nancy","James"],"index":52974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985688925,"difficulty":0.0014311075}
+{"premise":"There are two persons. Everyone is visible 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 Myra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Myra can now know whether Amy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Myra","Amy"],"index":415,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997327924,"difficulty":0.0002672076}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Deborah's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd 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) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Elizabeth can now know that Melissa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Kathy","Melissa","Elizabeth"],"index":25238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983618855,"difficulty":0.0016381145}
+{"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 Joyce. Joyce's card is shown to Kathryn. Mike's card is shown to Kathryn. Joyce's card is shown to Mike. It is publicly announced that someone picked a red card. It is publicly announced that Joyce does not know whether Joyce picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 1)","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":"Kathryn can now know whether Joyce picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joyce","Kathryn","Mike"],"index":44949,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6471660733,"difficulty":0.3528339267}
+{"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 Larry. Bonnie's card is shown to Larry. Larry's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"David can now know that Larry can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Larry","Bonnie"],"index":55009,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarice knows whether Lester's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows 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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Ricardo can now know whether Clarice can know that Lester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Lester","Clarice","Ricardo"],"index":10181,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980683923,"difficulty":0.0019316077}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Heather 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 (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"John can now know that Heather can know whether Heather picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Heather"],"index":24706,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7513971329,"difficulty":0.2486028671}
+{"premise":"There are 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)","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":"Arthur can now know that Sharon can know that Sharon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Arthur","Christina"],"index":10492,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984976053,"difficulty":0.0015023947}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Earl is not thirsty. It is publicly announced that Melody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] (Agentc knows whether 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":"Earl can now know whether Douglas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Douglas","Earl","Melody"],"index":54516,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9769087434,"difficulty":0.0230912566}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adrienne is thirsty. It is publicly announced that Kyle is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] 0","hypothesis":"Callie can now know whether Callie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kyle","Callie","John","Adrienne"],"index":58122,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99894768,"difficulty":0.00105232}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Malcolm. Karen's card is shown to Karen. It is publicly announced that someone picked a red card. It is publicly announced that Karen picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Malcolm can now know that Karen can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Malcolm","Karen"],"index":50938,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7658615112,"difficulty":1.7658615112}
+{"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 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":"Mark can now know that Patricia can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Melinda","Mark","Patricia"],"index":52176,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997577071,"difficulty":0.0002422929}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James does not know whether Vicky is thirsty.","smcdel_problem":"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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Vicky can now know that Vicky is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vicky","Donna","James","Natalie"],"index":61607,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9931324124,"difficulty":0.0068675876}
+{"premise":"There are two 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. It is publicly announced that Sadie does not know whether Sadie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows 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":"Sadie can now know whether Lon can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sadie","Lon"],"index":35707,"s-l":"forehead-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 someone is 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)","n_announcements":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":"Katherine can now know whether Kimberly is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robbie","Katherine","Kimberly","Greg"],"index":20695,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963256717,"difficulty":0.0036743283}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vanessa's card is shown to John. Carlton's card is shown to John. Carlton's card is shown to Brian. Brian's card is shown to Carlton. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Brian","Vanessa","Carlton"],"index":66980,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980260134,"difficulty":0.0019739866}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Mark can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Alma","David","Mark"],"index":42501,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997383952,"difficulty":0.0002616048}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Jenny. Jenny's card is shown to Theodore. It is publicly announced that someone picked a red card. It is publicly announced that Jenny 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) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Jenny can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jenny","Theodore"],"index":17916,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981568456,"difficulty":0.0018431544}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Todd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (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":"David can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Todd","David","Sandra"],"index":53538,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996691942,"difficulty":0.0003308058}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susana does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Allen can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Susana","Allen","Lisa","Carol"],"index":51363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Pat. Ronald's card is shown to Ronald. Ronald'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:2 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:2 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pat can now know that Sarah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pat","Ronald","Sarah"],"index":1299,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983129501,"difficulty":0.0016870499}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melba's card is shown to Melba. Melba's card is shown to Douglas. It is publicly announced that someone picked a red card. It is publicly announced that Melba does not know whether Douglas picked a red card. It is publicly announced that Melba knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Douglas can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Melba","Douglas"],"index":48056,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997856021,"difficulty":0.0002143979}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ginger knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows whether (Agentc knows 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":"Ginger can now know whether Michelle can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Ginger","Michelle"],"index":33358,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997596145,"difficulty":0.0002403855}
+{"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 (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":"Gabrielle can now know that Dorothy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mario","Gabrielle","Rosaura","Dorothy"],"index":20054,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9942933321,"difficulty":0.0057066679}
+{"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 Randy. Sandra's card is shown to Thomas. Billy's card is shown to Billy. Randy's card is shown to Sandra. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Randy can now know whether Billy can know that Thomas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Thomas","Billy","Sandra"],"index":28772,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9921370149,"difficulty":0.0078629851}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether or not nobody's forehead is muddy. It is publicly announced that Linda knows whether Stevie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether 3) ] Agenta knows whether (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":"Lucille can now know whether Stevie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucille","Jennifer","Stevie","Linda"],"index":49422,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997760653,"difficulty":0.0002239347}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tom's card is shown to Tom. Tom's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 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:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Lisa can now know whether Tom can know whether Marie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Tom","Marie"],"index":24108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982607961,"difficulty":0.0017392039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bennie does not know whether Clifford is thirsty. It is publicly announced that Bennie does not know whether or not everyone is thirsty. It is publicly announced that Bennie does not know whether Clifford is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Clifford can now know that Bennie can know that Bennie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Clifford","Gertrude","Bennie"],"index":61869,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9897108674,"difficulty":0.0102891326}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that 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)","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":"Lindsay can now know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","Lindsay"],"index":50962,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.8982061744,"difficulty":0.1017938256}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee knows whether Wallace's forehead is muddy. It is publicly announced that Lee 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 (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Daniel can now know whether Wallace can know that Lee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wallace","Lee","Daniel"],"index":29351,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996774197,"difficulty":0.0003225803}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy. 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 3)","n_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":"Kimberly can now know that Mark can know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Kimberly","Marie"],"index":52453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936430454,"difficulty":0.0063569546}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Suzanne's card is shown to Suzanne. It is publicly announced that someone picked a red card. It is publicly announced that Suzanne picked a red card. It is publicly announced that Sheree knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Sheree can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sheree","Suzanne"],"index":55712,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997865558,"difficulty":0.0002134442}
+{"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 Rhonda. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Rhonda does not know whether Rhonda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Rhonda can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rhonda","Mary"],"index":58235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows 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":"Shawn can now know that Gary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shawn","Gary"],"index":1957,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9776208997,"difficulty":1.9776208997}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelley's card is shown to Kelley. Bonnie's card is shown to Kelley. Kelley's card is shown to Christine. Kelley's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kelley can now know that Bonnie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kelley","Christine","Bonnie"],"index":35197,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980849028,"difficulty":0.0019150972}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Laura 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 (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":"Jean can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Junior","Jean","Laura"],"index":34066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9075042605,"difficulty":0.0924957395}
+{"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":"Douglas can now know that Glenda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Glenda","Carrie","Douglas"],"index":51003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997603297,"difficulty":0.0002396703}
+{"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 Alan. Edward's card is shown to Alan. Alan's card is shown to Stacey. Edward's card is shown to Stacey. It is publicly announced that someone picked a red card. It is publicly announced that Alan does not know whether Alan picked a red card. It is publicly announced that Alan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Alan can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alan","John","Edward","Stacey"],"index":31961,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977534413,"difficulty":0.0022465587}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy. It is publicly announced that Shawn does not know whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_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":"Shawn can now know that Melissa can know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shawn","Terrance","Melissa"],"index":29439,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9164907932,"difficulty":0.0835092068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarvis does not know whether Jarvis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Jarvis can now know whether Diane can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jarvis","Pedro","Diane","Melvin"],"index":50050,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997623563,"difficulty":0.0002376437}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lori does not know whether Joanna is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Irina does not know whether Joanna 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 (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Irina can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Irina","Lori","Joanna"],"index":50113,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997271895,"difficulty":0.0002728105}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel'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 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":"Vickie can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Vickie","Michael","Daniel"],"index":45610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963546991,"difficulty":0.0036453009}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lynn does not know whether Michelle is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lynn can now know that Michelle can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lynn","Michelle"],"index":57791,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984382987,"difficulty":0.0015617013}
+{"premise":"There are four persons. Everyone is visible 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 George's forehead is muddy. It is publicly announced that Rachel'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 whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Robert can now know that Rachel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rachel","Robert","George","James"],"index":34304,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lamar's card is shown to Lamar. Kayla's card is shown to Kayla. Lamar's card is shown to Miriam. It is publicly announced that someone picked a red card. It is publicly announced that Miriam picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 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 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Lamar can now know whether Miriam can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lamar","Kayla","Miriam"],"index":19172,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7424197197,"difficulty":0.2575802803}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether George's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Ralph can now know that Linnie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Edward","Ralph","Linnie"],"index":49565,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999756515,"difficulty":0.000243485}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentd knows whether 1) ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Toni can now know that John can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yvonne","Lynda","Toni","John"],"index":39868,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997641444,"difficulty":0.0002358556}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Sandra's forehead is muddy. It is publicly announced that Todd knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows 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 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Todd can now know that Sandra can know whether Sandra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Todd","Sandra"],"index":25836,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995498061,"difficulty":0.0004501939}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that (~(1|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":"Jared can now know that Ruby can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Pearl","Jared","Ruby"],"index":44238,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985263348,"difficulty":0.0014736652}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne knows whether or not everyone's forehead is muddy. It is publicly announced that Marissa'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) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Marissa can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marissa","Anne","Emily"],"index":25062,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997830987,"difficulty":0.0002169013}
+{"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 Edward. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mary can now know whether Edward can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Edward"],"index":12478,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea does not know whether David is thirsty. It is publicly announced that Charles does not know whether David is thirsty. It is publicly announced that Robert does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether David is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Robert","David","Andrea"],"index":53727,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7238894701,"difficulty":0.2761105299}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether or not everyone's forehead is muddy. It is publicly announced that Dennis does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Thelma can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thelma","Dennis"],"index":1088,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9797036648,"difficulty":0.0202963352}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorenzo does not know whether 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) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Lorenzo can now know that Jose can know that Lorenzo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jose","Lorenzo","George","Patrick"],"index":49280,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9885085225,"difficulty":0.0114914775}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows 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":"Genaro can now know whether Andre can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andre","Genaro","Janet"],"index":40036,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996726513,"difficulty":0.0003273487}
+{"premise":"There are four persons. Everyone is visible 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 (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Amy can now know that Jorge can know that Jorge's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jorge","Amy","Louis","Janice"],"index":45225,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969879985,"difficulty":0.0030120015}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Catherine","Darren"],"index":18260,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973347783,"difficulty":0.0026652217}
+{"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 Daniel knows whether Rose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know whether Joseph can know that Daniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Rose","Daryl","Joseph"],"index":35574,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9961560369,"difficulty":0.0038439631}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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":"Carla can now know that Kathleen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Yasmin","Kathleen","Carla","Anthony"],"index":35069,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957940578,"difficulty":0.0042059422}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arthur's card is shown to Pedro. Shirley's card is shown to Danielle. Shirley's card is shown to Shirley. Pedro's card is shown to Arthur. Danielle's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Shirley does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Pedro can now know that Arthur can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pedro","Danielle","Shirley","Arthur"],"index":9023,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9934264421,"difficulty":0.0065735579}
+{"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 or not everyone is thirsty. It is publicly announced that Walter does not know whether Angelina is thirsty. It is publicly announced that William does not know whether Angelina is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Angelina can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Walter","Angelina","Brent"],"index":2907,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7900151014,"difficulty":0.2099848986}
+{"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 Paul. Paul's card is shown to Robyn. Robyn's card is shown to Robyn. Paul's card is shown to John. Robyn's card is shown to John. Paul'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 Robyn picked a black card. It is publicly announced that Robyn does not know whether Robert picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Paul can now know whether John can know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Robyn","John","Robert"],"index":38474,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979731441,"difficulty":0.0020268559}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Norma knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Perry can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Perry","Raymond","Norma"],"index":53798,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997205138,"difficulty":0.0002794862}
+{"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 Rachel. Rachel's card is shown to William. Jeffrey's card is shown to William. William's card is shown to Jeffrey. Jeffrey's card is shown to Jeffrey. It is publicly announced that someone picked a red card. It is publicly announced that Rachel does not know whether or not everyone picked a red card. It is publicly announced that Jeffrey 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 ] Agenta knows that (Agentb knows that 1)","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":"Rachel can now know that Ralph can know that Rachel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Ralph","William","Jeffrey"],"index":47771,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6029481888,"difficulty":1.6029481888}
+{"premise":"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 Joseph'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) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] Agentc knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Gertrude can now know that Joseph can know whether Sandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandy","Benjamin","Gertrude","Joseph"],"index":4668,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994630218,"difficulty":0.0005369782}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa does not know whether or not everyone is thirsty. It is publicly announced that Geneva does not know 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agenta knows whether 2) ] (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)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Stella can now know that Geneva is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Geneva","Stella","Theresa","Cicely"],"index":59205,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9616638422,"difficulty":0.0383361578}
+{"premise":"There are four persons. Everyone is visible 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 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":"Michael can now know whether Bryan can know whether Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Mary","Marlene","Bryan"],"index":2599,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997083545,"difficulty":0.0002916455}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether or not everyone is thirsty. It is publicly announced that Daniel does not know whether Miriam is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Daniel can now know whether Miriam can know that Ruben is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Miriam","Ruben"],"index":4925,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.991581738,"difficulty":0.008418262}
+{"premise":"There are four persons. Everyone is visible 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 Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Jerry can now know that Frances can know whether Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Stephanie","Frances","Donna"],"index":38545,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997305274,"difficulty":0.0002694726}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Timothy's card is shown to Ollie. Timothy's card is shown to Dennis. Ollie'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:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Leslie can now know whether Dennis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ollie","Dennis","Leslie","Timothy"],"index":55792,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.927393496,"difficulty":0.072606504}
+{"premise":"There are two persons. Everyone is visible 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 (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":"Louie can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anna","Louie"],"index":26703,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997423291,"difficulty":0.0002576709}
+{"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 Kimberly 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 (~(1|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":"Kimberly can now know that Nicholas can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Kimberly","Nicholas"],"index":18784,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998314023,"difficulty":0.001685977}
+{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Evelyn can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marcell","Jeremy","Evelyn","Carrol"],"index":2884,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981770515,"difficulty":0.0018229485}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Edward can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alvin","Edward"],"index":2836,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997494817,"difficulty":0.0002505183}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary knows whether someone is thirsty. It is publicly announced that Lisa does not know whether Gary is thirsty.","smcdel_problem":"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 whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lisa can now know whether Gary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Brandon","Gary","Sharon"],"index":39267,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9836502671,"difficulty":0.0163497329}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lakisha's card is shown to Kevin. Lakisha's card is shown to Jacob. Lakisha's card is shown to Hubert. Jacob's card is shown to Hubert. It is publicly announced that someone picked a red card. It is publicly announced that Jacob picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Lakisha can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lakisha","Kevin","Jacob","Hubert"],"index":45287,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997839332,"difficulty":0.0002160668}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Nicole. Richard's card is shown to Nicole. Nicole's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Richard can now know whether Nicole can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicole","Richard"],"index":60440,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9936801195,"difficulty":0.0063198805}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Veronica knows whether someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not nobody's forehead is muddy. It is publicly announced that Cynthia knows whether Veronica's forehead is muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 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":"Helen can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Veronica","Helen","Cynthia"],"index":9756,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983779192,"difficulty":0.0016220808}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trenton does not know whether Trenton's forehead is muddy. It is publicly announced that Gina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Melody can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Selina","Trenton","Melody","Gina"],"index":58062,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986712933,"difficulty":0.0013287067}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Paul can now know that Larry can know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandra","John","Larry","Paul"],"index":46965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997474551,"difficulty":0.0002525449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Julie. Lisa's card is shown to Julie. Ashley's card is shown to Julie. Brian's card is shown to Ashley. Ashley's card is shown to Brian. Brian's card is shown to Brian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Julie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Julie","Lisa","Ashley","Brian"],"index":10435,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
+{"premise":"There are three persons. Everyone is visible 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 Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Charles","Wayne"],"index":57383,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984894991,"difficulty":0.0015105009}
+{"premise":"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's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (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) ] [ ! ~(2) ] 0","hypothesis":"Hilda can now know that Lisa can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","Lisa","Hilda"],"index":43835,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999782145,"difficulty":0.000217855}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy. It is publicly announced that Jennifer knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Billy can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Catherine","Billy","Pamela","Jennifer"],"index":58743,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983273149,"difficulty":0.0016726851}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 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":"Betty can now know whether Marion can know whether Marion's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Leslie","Marion","Betty"],"index":35408,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995802045,"difficulty":0.0004197955}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether someone is thirsty. It is publicly announced that Richard 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)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"John can now know whether Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Pablo","John","James"],"index":47382,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9929814339,"difficulty":0.0070185661}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tamara knows whether Tamara's forehead is muddy. It is publicly announced that Jimmie 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Eric can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Tamara","Jimmie","Setsuko"],"index":33570,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982722998,"difficulty":0.0017277002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marion does not know whether Susan is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Paul does not know whether Marion is thirsty. It is publicly announced that Marion does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Susan can now know that Elna can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elna","Susan","Marion","Paul"],"index":45613,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6358519793,"difficulty":1.6358519793}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mohammad's card is shown to Mohammad. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Mohammad does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Mohammad can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mohammad","Michael"],"index":32031,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999769032,"difficulty":0.000230968}
+{"premise":"There are two persons. Everyone is visible 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 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":"Justin can now know whether Stephanie can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Justin","Stephanie"],"index":66603,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996744394,"difficulty":0.0003255606}
+{"premise":"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.","smcdel_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":"Melanie can now know whether Melanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerry","Scott","Melanie"],"index":20760,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.596051991,"difficulty":0.403948009}
+{"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 Andrea knows whether Darrell is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Andrea can now know whether Darrell can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrea","Darrell"],"index":64575,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Brenda","Kevin","Sara"],"index":4322,"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 is thirsty. It is publicly announced that Elton does not know whether or not everyone is thirsty. It is publicly announced that Christian is thirsty. It is publicly announced that Elton does not know whether Johnny is thirsty. It is publicly announced that Elton 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb 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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Johnny can now know that Christian can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christian","Elton","Johnny"],"index":42576,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983178377,"difficulty":0.0016821623}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy does not know whether Jimmy's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kimberly can now know that Pamela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jimmy","Pamela","Kimberly"],"index":32167,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984253645,"difficulty":0.0015746355}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|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":"Carlos can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carlos","Andrew","Earl"],"index":8518,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983009696,"difficulty":0.0016990304}
+{"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 Therese is thirsty. It is publicly announced that Andres does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] Agenta knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"James can now know that Andres can know whether Andres is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Margaret","Therese","Andres"],"index":27614,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972981811,"difficulty":0.0027018189}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Floyd's card is shown to Floyd. Herbert's card is shown to Herbert. Floyd's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Floyd can now know that Herbert can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Floyd","Herbert","Edward"],"index":10981,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph's forehead is muddy. It is publicly announced that Joshua knows whether Ralph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows whether (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) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Sharon can now know whether Amanda can know whether Joshua's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Ralph","Sharon","Amanda"],"index":49358,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999417305,"difficulty":0.000582695}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore knows whether Delores's forehead is muddy. It is publicly announced that Jesse knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows 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":"Jesse can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesse","Russel","Theodore","Delores"],"index":59196,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982871413,"difficulty":0.0017128587}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"David can now know that Kevin can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kevin","Geraldine","Mary","David"],"index":49908,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9819277525,"difficulty":1.9819277525}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dan's card is shown to Dan. Denise's card is shown to Denise. Carolyn's card is shown to Denise. Denise's card is shown to Carolyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc: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:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Denise can now know that Carolyn can know that Dan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dan","Denise","Carolyn"],"index":58056,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980934262,"difficulty":0.0019065738}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Fred does not know whether Fred's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paul","Joseph","Fred"],"index":48618,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9498595595,"difficulty":1.9498595595}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa does not know whether Sophie is thirsty. It is publicly announced that Cristina does not know whether Sophie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Brandon can now know that Lisa can know that Brandon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Brandon","Cristina","Sophie"],"index":21275,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957101345,"difficulty":0.0042898655}
+{"premise":"There are three persons. Everyone is visible 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) ] [ ! 3 ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Manuel can now know that David can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Manuel","David"],"index":60048,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984556437,"difficulty":0.0015443563}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tamara's card is shown to Myrtle. Tamara's card is shown to Mary. Maria's card is shown to Tamara. Mary's card is shown to Maria. Maria's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Maria picked a red card. It is publicly announced that Myrtle 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:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta 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:3 Agentb:3 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Myrtle can now know that Mary can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Myrtle","Mary","Tamara","Maria"],"index":67458,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8445049524,"difficulty":1.8445049524}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie knows whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (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 2) ] 0","hypothesis":"Richard can now know whether Katie can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eddie","Katie","Richard"],"index":6689,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9914331436,"difficulty":0.0085668564}
+{"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 Alison does not know whether Margret is 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 (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) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Alison can now know that Margret can know whether Hubert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mildred","Alison","Margret","Hubert"],"index":67296,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976085424,"difficulty":0.0023914576}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Melvin can now know that Annette can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melvin","Annette","David","Sarah"],"index":28011,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julie's card is shown to Tracy. Kevin's card is shown to Kurtis. Kevin's card is shown to Kevin. Kurtis's card is shown to Julie. Kevin's card is shown to Julie. It is publicly announced that someone picked a red card. It is publicly announced that Tracy does not know whether Tracy picked a red card. It is publicly announced that Julie does not know whether Julie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether 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:4 Agentb:3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Kevin can now know that Julie can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","Kurtis","Kevin","Julie"],"index":37206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999783814,"difficulty":0.000216186}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know that Delaine can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pearl","Delaine","Joshua","Justin"],"index":702,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982863069,"difficulty":0.0017136931}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Mario. Martin's card is shown to Piedad. Mario's card is shown to Martin. Piedad's card is shown to Martin. Martin's card is shown to Martin. Crystal'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:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mario can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mario","Piedad","Martin","Crystal"],"index":43013,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985311031,"difficulty":0.0014688969}
+{"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 not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Kathy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anita","Mark","Kathy"],"index":25003,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997845292,"difficulty":0.0002154708}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Christopher's card is shown to Christopher. David's card is shown to Christopher. Christopher's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc: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:1 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"David can now know that Edwin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","Christopher","David"],"index":54207,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993053019,"difficulty":0.006946981}
+{"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 Jessica does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] Agentc knows that (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Greg can now know that Jessica can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Rodger","Greg","Jessica"],"index":23244,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9866036177,"difficulty":0.0133963823}
+{"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 Katherine. Crystal's card is shown to Crystal. Jose's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jose can now know that Katherine can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Crystal","Jose","Anna"],"index":26149,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984145164,"difficulty":0.0015854836}
+{"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 Jacob. Johnathan's card is shown to William. William's card is shown to Martin. It is publicly announced that someone picked a red card. It is publicly announced that Jacob does not know whether Jacob picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jacob can now know whether Johnathan can know that Johnathan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacob","Johnathan","William","Martin"],"index":32135,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7647013068,"difficulty":1.7647013068}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentd knows 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":"Edith can now know whether Ronda can know that Edith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Edith","Frances","Ronda"],"index":52971,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992927313,"difficulty":0.0007072687}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ines does not know whether Amy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Eric can now know whether Eric is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amy","Ines","Charles","Eric"],"index":64444,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9945137501,"difficulty":0.0054862499}
+{"premise":"There are four persons. Everyone is visible 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 Emile's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Carl can now know whether Lois can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carl","Richard","Lois","Emile"],"index":7882,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996017814,"difficulty":0.0003982186}
+{"premise":"There are 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":"Blanca can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Blanca","Robert","Amy"],"index":22792,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983689189,"difficulty":0.0016310811}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agenta knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Darryl can now know whether Joseph can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darryl","Joseph","Jose"],"index":1158,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996864796,"difficulty":0.0003135204}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johanna's card is shown to Kenneth. Albert's card is shown to Johanna. Albert's card is shown to Albert. Kevin's card is shown to Albert. Albert'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:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3,4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kenneth can now know that Kevin can know that Johanna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Johanna","Albert","Kevin"],"index":44800,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9973989725,"difficulty":0.0026010275}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether Shane's forehead is muddy. It is publicly announced that Bryan 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 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":"Shane can now know whether Bryan can know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shane","Bryan"],"index":17326,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8313772678,"difficulty":0.1686227322}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hilary does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Kali can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Kali","Janene","Hilary"],"index":60363,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958135486,"difficulty":0.0041864514}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Andrea's card is shown to Arlene. It is publicly announced that someone picked a red card. It is publicly announced that Arlene knows whether Arlene picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Andrea can now know whether Arlene can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrea","Arlene"],"index":8004,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.995916903,"difficulty":0.004083097}
+{"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. Holly's card is shown to William. Brenda's card is shown to William. Holly's card is shown to Michael. Holly's card is shown to Holly. Holly's card is shown to Brenda. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agentd knows whether 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":"Michael can now know whether Brenda can know whether Brenda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Michael","Holly","Brenda"],"index":28802,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.991863966,"difficulty":0.008136034}
+{"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. Paul's card is shown to Anthony. Anthony's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Anthony does not know whether or not everyone picked a red card.","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":"Anthony can now know whether Dale can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Anthony","Paul"],"index":5219,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996931553,"difficulty":0.0003068447}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Patricia is thirsty.","smcdel_problem":"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 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":"Patricia can now know that Kevin can know that Lillian is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Kevin","Lillian","Dennis"],"index":41979,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980998635,"difficulty":0.0019001365}
+{"premise":"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 Tina's forehead is muddy. It is publicly announced that Loretta does not know whether Loretta's forehead is muddy.","smcdel_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) ] Agentc knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Elizabeth can now know that Loretta can know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loretta","Tina","Elizabeth"],"index":32670,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991061091,"difficulty":0.0008938909}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gay's card is shown to Helen. Theodore's card is shown to Theodore. Gay's card is shown to Theodore. Helen's card is shown to Gay. Theodore's card is shown to Gay. Gay's card is shown to Gay. It is publicly announced that someone picked a red card. It is publicly announced that Theodore does not know whether or not everyone picked a red card. It is publicly announced that Gay knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Helen can now know that Theodore can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Helen","Theodore","Gay"],"index":29137,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8566382527,"difficulty":1.8566382527}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 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":"Michael can now know whether Robert can know whether Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Amado","Michael","Frances"],"index":63196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997243285,"difficulty":0.0002756715}
+{"premise":"There are three persons. Everyone is visible to others. 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 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Beverley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Beverley","Noelle","Maria"],"index":31355,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980990291,"difficulty":0.0019009709}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gracie's card is shown to Alicia. Alicia's card is shown to Patricia. Gracie's card is shown to Gracie. It is publicly announced that someone picked a red card. It is publicly announced that Alicia picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Alicia can now know whether Gracie can know that Gracie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alicia","Patricia","Gracie"],"index":15711,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9154069424,"difficulty":0.0845930576}
+{"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 Deetta. Vera's card is shown to Deetta. Marie's card is shown to Marie. Vera's card is shown to Vera. It is publicly announced that someone picked a red card. It is publicly announced that Vera does not know whether Deetta picked a red card. It is publicly announced that Marie knows whether Marie picked a red card. It is publicly announced that Marie does not know whether or not everyone picked a red card. It is publicly announced that Vera knows whether Marie picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentc knows whether 2) ] (Agentb knows that 1)","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":"Marie can now know that Deetta picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Deetta","Marie","Vera"],"index":28974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6960812807,"difficulty":0.3039187193}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Patricia can now know that Stanley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Lucille","Stanley","Henry"],"index":57558,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997590184,"difficulty":0.0002409816}
+{"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. Cynthia's card is shown to Kenneth. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Cynthia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Kenneth can now know that Cynthia can know whether Cynthia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kenneth","Cynthia"],"index":39108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9881899357,"difficulty":0.0118100643}
+{"premise":"There are three 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 Aaron does not know whether Dana 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 (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Hazel can now know that Aaron can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aaron","Dana","Hazel"],"index":49812,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose is thirsty. It is publicly announced that Jose does not know whether James is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agenta knows whether 2) ] 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 ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Jose can know that Jose is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jose","James"],"index":47852,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9888329506,"difficulty":0.0111670494}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Loretta's card is shown to Keith. Keith's card is shown to Whitney. Keith's card is shown to Loretta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Whitney can now know whether Naomi picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Keith","Whitney","Loretta","Naomi"],"index":12824,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8851640821,"difficulty":0.1148359179}
+{"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 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 (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":"Craig can now know that Kenneth can know that Philip is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Craig","Kenneth","Philip"],"index":66045,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9641059637,"difficulty":0.0358940363}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tabatha knows whether someone is thirsty. It is publicly announced that Corazon knows whether or not nobody is thirsty. It is publicly announced that Ruth knows whether Ruth is thirsty. It is publicly announced that Corazon does not know whether Tabatha is thirsty.","smcdel_problem":"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 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":"Tabatha can now know that Tabatha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tabatha","Ruth","Corazon","Susan"],"index":54297,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9877200723,"difficulty":0.0122799277}
+{"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 Randy is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Randy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jack","Randy"],"index":4827,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985061288,"difficulty":0.0014938712}
+{"premise":"There are three persons. Everyone is visible 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 Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know whether Theresa can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Theresa","Chad","William"],"index":50196,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995725751,"difficulty":0.0004274249}
+{"premise":"There are four persons. Everyone is visible 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 everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] Agenta knows whether (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (1&2&3&4) ] 0","hypothesis":"James can now know whether Sheila can know that Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Pierre","Sheila","Betty"],"index":33534,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996253252,"difficulty":0.0003746748}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Domingo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Domingo can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Arthur","Simon","Allison","Domingo"],"index":10609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997282624,"difficulty":0.0002717376}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Daniel can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Daniel","Jeffrey"],"index":46905,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997784495,"difficulty":0.0002215505}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Milda can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Georgeann","Milda","Robert","Angel"],"index":41843,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Evelyn's forehead is muddy. It is publicly announced that Teresa knows whether Evelyn's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know that Teresa can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Teresa","Evelyn"],"index":62188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983075857,"difficulty":0.0016924143}
+{"premise":"There are four persons. Everyone is visible 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 (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lula can now know that Kimberly can know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mohammad","Kimberly","Lula","Ruby"],"index":43527,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961154461,"difficulty":0.0038845539}
+{"premise":"There are two persons. Everyone is visible 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 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) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Sean can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Bryan","Sean"],"index":51885,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9938812256,"difficulty":0.0061187744}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Linda can now know whether Beverly can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alex","Natasha","Beverly","Linda"],"index":18561,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997193217,"difficulty":0.0002806783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Enid's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Enid 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) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Enid can now know that Lucille can know whether Enid's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Enid","Scott","Lucille"],"index":16378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995342493,"difficulty":0.0004657507}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Thomas can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dora","Thomas","Robert"],"index":35575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996920824,"difficulty":0.0003079176}
+{"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 Margaret is thirsty. It is publicly announced that Christin 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd 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:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Margaret can now know that James can know that Roman is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roman","James","Margaret","Christin"],"index":24948,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971297383,"difficulty":0.0028702617}
+{"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 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":"Vincent can now know that Florence can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Vito","Florence","Vincent"],"index":57532,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997188449,"difficulty":0.0002811551}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brent's card is shown to Joel. Caridad's card is shown to Caridad. Caridad's card is shown to Gary. Gary's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Joel can now know that Joel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joel","Caridad","Brent","Gary"],"index":36465,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9921616912,"difficulty":0.0078383088}
+{"premise":"There are two persons. Everyone is visible 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 Joe knows whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (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":"Joe can now know that Misty can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joe","Misty"],"index":26456,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marquis's card is shown to Marquis. Marquis's card is shown to Jorge. 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 whether (Agentb 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":"Julie can now know whether Marquis can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Julie","Marquis","Jorge"],"index":8488,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995020628,"difficulty":0.0004979372}
+{"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. Janice's card is shown to Virginia. Jay's card is shown to Virginia. Janice's card is shown to Jay. 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. It is publicly announced that Virginia knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jay can now know whether Jay picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janice","Virginia","Jay"],"index":62613,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9883734584,"difficulty":1.9883734584}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores knows whether Robert's forehead is muddy. It is publicly announced that Robert knows whether Dolores'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":"Dolores can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Dolores"],"index":37315,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998352766,"difficulty":0.001647234}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica 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)) ] (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":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","John","Jessica","Melisa"],"index":12152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997437596,"difficulty":0.0002562404}
+{"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 George. Susan's card is shown to Robert. Susan's card is shown to Susan. 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 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kenneth can now know whether Robert can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Kenneth","Robert","Susan"],"index":37836,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997752309,"difficulty":0.0002247691}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Thomas can now know whether Jesse can know that Naomi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stefania","Naomi","Jesse","Thomas"],"index":42121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996722937,"difficulty":0.0003277063}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether Crystal's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether Calandra's forehead is muddy. It is publicly announced that Crystal knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jack can now know that Calandra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Jack","Calandra"],"index":55106,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9659466147,"difficulty":0.0340533853}
+{"premise":"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.","smcdel_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 that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Thelma can now know that William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thelma","William","Michelle"],"index":29606,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980164766,"difficulty":0.0019835234}
+{"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 Ella is thirsty. It is publicly announced that Ella is not thirsty. It is publicly announced that Ella is not thirsty. It is publicly announced that Margaret knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kerry can now know that Margaret can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ella","Margaret","Kerry"],"index":29307,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990510345,"difficulty":0.0009489655}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Minerva does not know whether or not everyone is thirsty. It is publicly announced that Patricia knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Patricia can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Minerva","Lennie"],"index":41888,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997246861,"difficulty":0.0002753139}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy. It is publicly announced that Kenneth knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Kenneth can now know that Mary can know whether Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Agnes","George","Mary","Kenneth"],"index":58454,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997161031,"difficulty":0.0002838969}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie does not know whether Helen is thirsty. It is publicly announced that Julie does not know whether Helen is thirsty. It is publicly announced that Julie 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)) ] (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) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Charles can now know whether Carrie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Helen","Charles","Julie"],"index":10845,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6942619085,"difficulty":0.3057380915}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Margaret's card is shown to Margaret. Margaret's card is shown to Kendra. William's card is shown to Kendra. Kendra's card is shown to Kendra. Margaret'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 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Margaret can now know whether Kendra can know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","William","Kendra","Jennifer"],"index":15042,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986812472,"difficulty":0.0013187528}
+{"premise":"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. It is publicly announced that William's forehead is not muddy. It is publicly announced that Sarah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"William can now know whether Robert can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Robert","Brooke","Sarah"],"index":30483,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990593791,"difficulty":0.0009406209}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jay is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Scott can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rita","Scott","Jay"],"index":49791,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998311162,"difficulty":0.001688838}
+{"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 Larry. Herbert's card is shown to Larry. Herbert's card is shown to Herbert. It is publicly announced that someone picked a red card. It is publicly announced that Nancy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Larry","Herbert"],"index":43863,"s-l":"explicit-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 Larry knows whether Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Larry can now know whether Leroy can know that Melva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leroy","Lori","Melva","Larry"],"index":66153,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996688366,"difficulty":0.0003311634}
+{"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 Kathleen is thirsty. It is publicly announced that Patricia 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) ] (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 2) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Kathleen can now know that Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Kathleen","Patricia","Anthony"],"index":29539,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973767996,"difficulty":0.0026232004}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Bryant's card is shown to Richard. Richard's card is shown to Bryant. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Richard can now know that Bryant can know that Bryant picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Bryant"],"index":66949,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9876438975,"difficulty":0.0123561025}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Madelene does not know whether Kathleen is thirsty. It is publicly announced that Madelene is not thirsty. It is publicly announced that Howard knows whether Madelene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Madelene can now know whether Kathleen can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Madelene","Stephen","Howard","Kathleen"],"index":27019,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5807533264,"difficulty":0.4192466736}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not everyone's forehead is muddy. It is publicly announced that Ruth knows whether or not nobody's forehead is muddy. It is publicly announced that Grace knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Ruth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ruth","Grace"],"index":59297,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998390913,"difficulty":0.001609087}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne does not know whether Anne's forehead is muddy. It is publicly announced that Anne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 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) ] [ ! ~(Agentd knows whether 4) ] [ ! 4 ] 0","hypothesis":"Orlando can now know that Roland can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Orlando","Sonia","Roland","Anne"],"index":9505,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963756204,"difficulty":0.0036243796}
+{"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 Debbie. Donald's card is shown to Debbie. Donald's card is shown to Cynthia. Debbie'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:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Donald can now know that Debbie can know whether Debbie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debbie","Cynthia","Donald"],"index":41596,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8921531439,"difficulty":1.8921531439}
+{"premise":"There are two persons. Everyone is visible 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 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":"Jessica can now know that Ashley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ashley","Jessica"],"index":50884,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997426867,"difficulty":0.0002573133}
+{"premise":"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 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) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Kenneth can now know that Pamela can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Kenneth","Pamela"],"index":31248,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994199276,"difficulty":0.0005800724}
+{"premise":"There are four persons. Everyone is visible 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 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 Elva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kathleen","Elva","Jeffery","Peter"],"index":62676,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996733427,"difficulty":0.003266573}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly is 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 (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":"Kimberly can now know whether Michele can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Ronald","Michele","Kimberly"],"index":30337,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997150302,"difficulty":0.0002849698}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Twila knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"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":"Crystal can now know that Twila can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Twila","Jennie"],"index":60623,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996478558,"difficulty":0.0003521442}
+{"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 Wilfred. Wilfred's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether John picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Wilfred","John"],"index":29286,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997183681,"difficulty":0.0002816319}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosa does not know whether Jennifer is thirsty. It is publicly announced that Rosa does not know whether or not everyone is thirsty. It is publicly announced that Sharon is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Rosa can now know that Sharon can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Rosa","Sharon"],"index":54821,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983445406,"difficulty":0.0016554594}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether Raymond's forehead is muddy. It is publicly announced that Raymond knows whether someone's forehead is muddy. It is publicly announced that Raymond's forehead is muddy. It is publicly announced that Nancy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&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) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Nancy can now know that Raymond can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Garrett","Nancy"],"index":35844,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976250529,"difficulty":0.0023749471}
+{"premise":"There are four persons. Everyone is visible 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 Bryant's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentd knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Billy can now know that Lula can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lula","Bryant","Charles","Billy"],"index":29569,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997201562,"difficulty":0.0002798438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that 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":"Daphne can now know that Karen can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Randall","Maria","Daphne"],"index":54724,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9306603074,"difficulty":0.0693396926}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carlos does not know whether Linda is thirsty. It is publicly announced that Carlos does not know whether Reginald is thirsty. It is publicly announced that Linda does not know whether Meagan is thirsty. It is publicly announced that Meagan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] (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 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] 0","hypothesis":"Linda can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","Linda","Reginald","Meagan"],"index":51154,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982429743,"difficulty":0.0017570257}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Jay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Jay can now know that Jay's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jay","Robert","Edgardo","Paul"],"index":24803,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972449541,"difficulty":0.0027550459}
+{"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 Larry. Henry's card is shown to Larry. Robert's card is shown to Robert. Henry's card is shown to Henry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ralph can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ralph","Larry","Robert","Henry"],"index":37159,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938533306,"difficulty":0.0061466694}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Arlene. Lyndon's card is shown to Lyndon. Martin's card is shown to Lyndon. It is publicly announced that someone picked a red card. It is publicly announced that Arlene does not know whether Lyndon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Arlene can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arlene","Lyndon","Martin"],"index":39387,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984593391,"difficulty":0.0015406609}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy. It is publicly announced that Cynthia knows whether someone's forehead is muddy. It is publicly announced that Joyce knows whether Marie's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Cynthia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Joyce","Robert","Cynthia"],"index":12648,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8655749559,"difficulty":1.8655749559}
+{"premise":"There are two persons. Everyone is visible 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 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":"Florence can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lon","Florence"],"index":6369,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983590245,"difficulty":0.0016409755}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernestine knows whether someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Ernestine can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maurice","Ernestine"],"index":56969,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963505268,"difficulty":0.0036494732}
+{"premise":"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 Michael 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 whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Terry","Michael","Eddy"],"index":28672,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9871776104,"difficulty":0.0128223896}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karla does not know whether or not everyone is thirsty. It is publicly announced that Tracey knows whether Karla is thirsty. It is publicly announced that Linda does not know whether Tracey is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows 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) ] 0","hypothesis":"Tracey can now know that Karla can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tracey","Karla","Linda"],"index":48047,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hugo does not know whether Heather is thirsty. It is publicly announced that Heather does not know whether Clemencia is thirsty.","smcdel_problem":"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 that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Clemencia can now know that Heather can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Desiree","Hugo","Clemencia","Heather"],"index":28592,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997064471,"difficulty":0.0002935529}
+{"premise":"There are 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 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":"Jacob can now know that Cheryl can know that Casey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cheryl","Lourdes","Casey","Jacob"],"index":37348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986458421,"difficulty":0.0013541579}
+{"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 Denise. Denise's card is shown to Flora. Flora's card is shown to Flora. It is publicly announced that someone picked a red card. It is publicly announced that Flora knows whether Flora picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Denise can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Denise","Flora","Robert"],"index":20980,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997702241,"difficulty":0.0002297759}
+{"premise":"There are two persons. Everyone is visible 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.","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)))","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":"Lisa can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mabel","Lisa"],"index":63081,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997556806,"difficulty":0.0002443194}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Evon's card is shown to Helen. Sondra's card is shown to Helen. Evon's card is shown to Evon. Helen's card is shown to Sondra. It is publicly announced that someone picked a red card. It is publicly announced that Helen knows whether Evon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 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":"Helen can now know whether Evon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Evon","Sondra"],"index":15281,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7189073563,"difficulty":1.7189073563}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Patricia can now know that Ernest's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Patricia","Ernest","Anna"],"index":32070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7756222486,"difficulty":0.2243777514}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Russell is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Alexander can now know whether Russell can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Russell","Jimmy","Alexander","Andrew"],"index":60554,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997851253,"difficulty":0.0002148747}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal's forehead is not muddy. It is publicly announced that Donald knows whether Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Crystal can now know that Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Crystal","Donald","Monica"],"index":48479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997799993,"difficulty":0.0002200007}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen does not know whether Carmen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Stefanie can now know that Carmen can know whether Carmen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stefanie","Carmen"],"index":5396,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9940028787,"difficulty":0.0059971213}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie does not know whether Eddie's forehead is muddy. It is publicly announced that Eddie does not know whether Eddie's forehead is muddy. It is publicly announced that Morgan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (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) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Eddie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eddie","Morgan"],"index":13507,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986537695,"difficulty":0.0013462305}
+{"premise":"There are four persons. Everyone is visible 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 Evan's forehead is muddy. It is publicly announced that Pamela's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Viola can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Viola","Pamela","John","Evan"],"index":23098,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997689128,"difficulty":0.0002310872}
+{"premise":"There are two persons. Everyone is visible 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 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":"Carol can now know that Monique can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Monique","Carol"],"index":26878,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997782111,"difficulty":0.0002217889}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary'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":"Susan can now know whether Mary can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Susan"],"index":14690,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997805953,"difficulty":0.0002194047}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monica's card is shown to Rudolph. Monica's card is shown to Heather. Monica's card is shown to Monica. It is publicly announced that someone picked a red card. It is publicly announced that Rudolph does not know whether Rudolph picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Heather can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rudolph","Heather","Monica"],"index":36365,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986555576,"difficulty":0.0013444424}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether 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 (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Diane can now know whether Jennifer can know whether Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Stacy","Jennifer"],"index":6378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968823195,"difficulty":0.0031176805}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Ferne. Ronnie's card is shown to Melvin. Ferne's card is shown to Melvin. It is publicly announced that someone picked a red card. It is publicly announced that Ferne does not know whether Melvin picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Ronnie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronnie","Ferne","Melvin"],"index":21496,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984881878,"difficulty":0.0015118122}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gail does not know whether Victor is thirsty. It is publicly announced that Gail does not know whether or not everyone is thirsty. It is publicly announced that Charles knows whether Gail is thirsty. It is publicly announced that Victor does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gail can now know that Victor can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Gail","Victor"],"index":15037,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebekah's card is shown to Joyce. Mary's card is shown to Tommy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joyce can now know that Rebekah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joyce","Rebekah","Tommy","Mary"],"index":41536,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984595776,"difficulty":0.0015404224}
+{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_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":"Karen can now know whether Eva can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Karen","Debra"],"index":20906,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"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 Julia. Julia's card is shown to Julia. It is publicly announced that someone picked a red card. It is publicly announced that David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"David can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Julia"],"index":62027,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976547956,"difficulty":0.0023452044}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roy does not know whether Dennis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 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) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Dennis can now know whether Elizabeth can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Roy","Willard","Dennis"],"index":25271,"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 is thirsty. It is publicly announced that Patrick does not know whether Johnny is thirsty. It is publicly announced that Johnny does not know whether Sarah is thirsty. It is publicly announced that Edith knows whether Edith is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] (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) ] [ ! ~(Agenta knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Sarah can now know that Edith is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Patrick","Edith","Sarah"],"index":42429,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9956674576,"difficulty":0.0043325424}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyrone knows whether or not nobody is thirsty. It is publicly announced that Tyrone does not know whether or not everyone is thirsty. It is publicly announced that Tyrone does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (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))) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Martha can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tyrone","Martha"],"index":43267,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997225404,"difficulty":0.0002774596}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryce can now know whether Carol can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Carol","Chelsea","Bryce"],"index":6558,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997510314,"difficulty":0.0002489686}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Herbert's card is shown to Stephanie. John's card is shown to John. John's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Herbert can now know that John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Herbert","John","David"],"index":19791,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7280882001,"difficulty":0.2719117999}
+{"premise":"There are three persons. Everyone is visible 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 Ruth'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)","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":"Kenneth can now know that Ruth can know that Kenneth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Ruth","Robert"],"index":1674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9902982116,"difficulty":0.0097017884}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy does not know whether 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 3)","n_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":"Judy can now know whether Jennifer can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stella","Judy","Jennifer"],"index":16968,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7881138325,"difficulty":0.2118861675}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jordan does not know whether Sam is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Sam can now know that James can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jordan","Sam","James"],"index":42564,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984764457,"difficulty":0.0015235543}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Donald can now know that Ann can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Donald","Ann"],"index":42188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983782768,"difficulty":0.0016217232}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentd knows that 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":"James can now know whether John can know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Timothy","Barbara","John"],"index":32114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996831417,"difficulty":0.0003168583}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Lance. Patrick's card is shown to Lance. 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 that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Cheryl can now know that Patrick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Lance","Patrick"],"index":28794,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984440207,"difficulty":0.0015559793}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley's forehead is not muddy. It is publicly announced that Stanley's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Stanley can now know that Stanley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Stanley"],"index":42225,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8239046931,"difficulty":1.8239046931}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Osvaldo 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 Jeffrey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Jeffrey can now know whether Osvaldo can know whether Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Jeffrey","Osvaldo"],"index":55504,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997283816,"difficulty":0.0002716184}
+{"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. Marguerite's card is shown to Beth. Marguerite's card is shown to Marguerite. Beth's card is shown to Donna. Donna's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Marguerite does not know whether Beth picked a red card. It is publicly announced that Marguerite knows whether Marguerite picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Donna can now know that Marguerite can know whether Beth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Beth","Marguerite","Donna"],"index":59025,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9354383349,"difficulty":0.0645616651}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Loretta can now know that Rose can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Loretta","Carmen","Rose","Burt"],"index":9513,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Larry can now know that Lucretia can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucretia","Larry","Kristin"],"index":49069,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997809529,"difficulty":0.0002190471}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentc knows 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":"Vernon can now know that Mary can know whether Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vernon","Denise","Mary"],"index":36590,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997172952,"difficulty":0.0002827048}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether or not nobody's forehead is muddy. It is publicly announced that Martin's forehead is not muddy. It is publicly announced that Phillip does not know whether Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Martin can now know whether Phillip can know that Phillip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phillip","Martin","Francis"],"index":20871,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6545600295,"difficulty":0.3454399705}
+{"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 Jennifer. Jennifer's card is shown to Charles. Colleen'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 Colleen knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 1)","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":"Jennifer can now know that Colleen can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Colleen","Charles"],"index":27948,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.994764924,"difficulty":0.005235076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Nicholas can now know that Robert can know whether Claude is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Nicholas","Alonzo","Claude"],"index":34089,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980666041,"difficulty":0.0019333959}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ferdinand does not know whether or not everyone is thirsty. It is publicly announced that Ferdinand is thirsty. It is publicly announced that Carrie 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 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 (1&2&3&4)) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Bettye can now know that Bettye is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bettye","Carrie","Ferdinand","Pearl"],"index":28658,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5909129381,"difficulty":1.5909129381}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","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 Gail's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gail","Betty","Shirley","Renee"],"index":27767,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998664856,"difficulty":0.001335144}
+{"premise":"There are four persons. Everyone is visible 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&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":"Shawn can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shawn","Brittany","Rosalind","Dennis"],"index":33423,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997084737,"difficulty":0.0002915263}
+{"premise":"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 not muddy. It is publicly announced that Florence knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Scott can now know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michelle","Scott","Florence","Barbara"],"index":33773,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929212928,"difficulty":0.0070787072}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jon does not know whether Peter is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentb knows that 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":"Jon can now know whether Don can know that Peter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jon","Don","Peter"],"index":22902,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9848393798,"difficulty":0.0151606202}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Deborah does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Mary can now know that Deborah can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Deborah","Mary"],"index":3972,"s-l":"internal-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). Ardella's card is shown to Kevin. Ardella's card is shown to Ardella. It is publicly announced that someone picked a red card. It is publicly announced that Kevin knows whether or not nobody picked a red card. It is publicly announced that Ardella knows whether Kevin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ardella can now know that Kevin can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kevin","Ardella"],"index":49578,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986339211,"difficulty":0.0013660789}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Perry's forehead is not muddy. It is publicly announced that Jo knows whether Perry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Perry can now know that Alfred can know whether Perry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Perry","Jo","Alfred"],"index":2400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999597609,"difficulty":0.000402391}
+{"premise":"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 Lillian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Joyce can now know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","Robert","Lillian","John"],"index":30122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999484539,"difficulty":0.000515461}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether or not nobody's forehead is muddy. 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 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":"Bryan can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Bryan","Gerald"],"index":59112,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.998206377,"difficulty":0.001793623}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcella's card is shown to Marcella. David's card is shown to Marcella. Marcella's card is shown to Numbers. Numbers's card is shown to Numbers. David's card is shown to David. Marcella's card is shown to Mona. Numbers's card is shown to Mona. It is publicly announced that someone picked a red card. It is publicly announced that Marcella does not know whether Mona 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) ] Agentd knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Mona can now know that Marcella can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marcella","Numbers","David","Mona"],"index":58102,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997058511,"difficulty":0.0002941489}
+{"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 Betty does not know whether Jennifer is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"David can now know whether Betty can know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Betty","Jennifer","David"],"index":31590,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988337159,"difficulty":0.0011662841}
+{"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 or not everyone is thirsty. It is publicly announced that Gwen does not know whether Ronnie is thirsty. It is publicly announced that Ronnie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ronnie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shirley","Ronnie","Gwen"],"index":39434,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983401299,"difficulty":0.0016598701}
+{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Evelyn can now know that Helen can know whether Kathleen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Helen","Evelyn","Nicholas"],"index":24451,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996102452,"difficulty":0.0003897548}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Eric can now know that Bradley can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bradley","Robert","Eric","Betty"],"index":53514,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962922931,"difficulty":0.0037077069}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Wade can now know whether Ellis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wade","Clark","Christopher","Ellis"],"index":6706,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997290969,"difficulty":0.0002709031}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sharon's card is shown to Sharon. Sharon's card is shown to Kenneth. Kenneth's card is shown to Lynwood. Lynwood's card is shown to Lynwood. Sharon's card is shown to Anthony. Anthony's card is shown to Anthony. It is publicly announced that someone picked a red card. It is publicly announced that Sharon does not know whether or not everyone picked a red card. It is publicly announced that Sharon picked a red card. It is publicly announced that Sharon does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (Agentc 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:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! 1 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Anthony can now know that Lynwood can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Kenneth","Lynwood","Anthony"],"index":16732,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997040629,"difficulty":0.0002959371}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aubrey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Aubrey can now know whether Sonia can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Aubrey","Sonia","Laura"],"index":37944,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997522235,"difficulty":0.0002477765}
+{"premise":"There are two persons. Everyone is visible 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 Lois'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)","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":"Devin can now know that Devin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Devin","Lois"],"index":40995,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982889295,"difficulty":0.0017110705}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enoch's card is shown to Enoch. Marshall's card is shown to Enoch. Enoch's card is shown to Marshall. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Enoch can now know that Charles can know that Marshall picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Enoch","Marshall"],"index":54997,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978985786,"difficulty":0.0021014214}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to John. Carlos's card is shown to John. Roy's card is shown to Judy. Carlos's card is shown to Judy. John's card is shown to Roy. Judy'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:3,4 Agentb:3,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Judy can now know whether John can know whether Carlos picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Judy","Roy","Carlos"],"index":10947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985290766,"difficulty":0.0014709234}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jason does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kevin can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Susan","Kevin"],"index":33877,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982770681,"difficulty":0.0017229319}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether or not everyone is thirsty. It is publicly announced that Saul does not know whether Dan is thirsty. It is publicly announced that Dan does not know whether or not everyone is thirsty. It is publicly announced that Dan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Saul can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Saul","Dan","Richard"],"index":66778,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8504353762,"difficulty":0.1495646238}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Muriel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Kathleen","David","Todd"],"index":32265,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9973288774,"difficulty":0.0026711226}
+{"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 Eric. Alexis's card is shown to Alexis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Kelly","Eric","Alexis"],"index":30366,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956979752,"difficulty":0.0043020248}
+{"premise":"There are three persons. Everyone is visible 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 Martha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 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 3) ] 0","hypothesis":"Martha can now know that Christopher's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Christopher","Martha"],"index":42338,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Marguerite can know that Rene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irving","Marguerite","Robert","Rene"],"index":45205,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996671677,"difficulty":0.0003328323}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marianne knows whether or not nobody's forehead is muddy. It is publicly announced that Kelly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Marianne can now know whether Kelly can know that Kelly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Kelly","Marianne","Albert"],"index":36570,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997089505,"difficulty":0.0002910495}
+{"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 Debra. Randee's card is shown to Randee. Betty's card is shown to Randee. Randee's card is shown to Ester. Debra's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Randee picked a black card. It is publicly announced that Randee does not know whether Debra picked a red card. It is publicly announced that Randee knows whether someone picked a red card. It is publicly announced that Randee does not know whether Debra 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 (Agentc knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Randee can now know whether Ester can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","Randee","Ester","Betty"],"index":51172,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8459839225,"difficulty":0.1540160775}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Floyd's card is shown to Robert. Robert's card is shown to Floyd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 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:3 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Toni can now know whether Robert can know whether Toni picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Toni","Robert","Floyd","Karen"],"index":45380,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9979121089,"difficulty":0.0020878911}
+{"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 Gladys is thirsty. It is publicly announced that Shirley does not know whether Robert is thirsty. It is publicly announced that Shirley knows whether or not nobody is thirsty. It is publicly announced that Gladys does not know whether Wanda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that Gladys is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gladys","Shirley","Wanda","Robert"],"index":11635,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9939134717,"difficulty":0.0060865283}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvette's forehead is muddy. It is publicly announced that Janet knows whether Yvette's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Janet can now know whether Micah can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Micah","Jack","Yvette","Janet"],"index":64550,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997858405,"difficulty":0.0002141595}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nigel does not know whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Nigel can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Willie","Nigel","Emily"],"index":9174,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997161031,"difficulty":0.0002838969}
+{"premise":"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 Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Carl can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carl","Adam","Frank","Gale"],"index":29077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985696077,"difficulty":0.0014303923}
+{"premise":"There are four persons. Everyone is visible 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's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (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":"Jerome can now know that Jamie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jerome","Jamie","Ellen","James"],"index":55008,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983792305,"difficulty":0.0016207695}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa does not know whether Vanessa's forehead is muddy. It is publicly announced that Vanessa 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 that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ralph can now know that Vanessa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vanessa","Douglas","Ralph","Dave"],"index":13394,"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 Donald does not know whether or not everyone is thirsty. It is publicly announced that Donald does not know whether Lloyd 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)","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":"Donald can now know that Lloyd is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lloyd","Donald"],"index":28943,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9548709393,"difficulty":0.0451290607}
+{"premise":"There are two 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 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Amy can now know that Raymond can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Amy","Raymond"],"index":62798,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983376265,"difficulty":0.0016623735}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernice's card is shown to Bernice. Jennifer's card is shown to Bernice. Luella's card is shown to Bernice. Luella's card is shown to Jennifer. Bernice's card is shown to Luella. Luella's card is shown to Luella. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 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:3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jennifer can now know whether Luella can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernice","Jennifer","Luella"],"index":35110,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997122884,"difficulty":0.0002877116}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stella does not know whether Carrie 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 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":"Carrie can now know that Carrie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Stella","Maudie","Carrie"],"index":33618,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9935144186,"difficulty":0.0064855814}
+{"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 James is not thirsty. It is publicly announced that James is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(4) ] [ ! ~(4) ] 0","hypothesis":"James can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Terry","William","James"],"index":59594,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998474896,"difficulty":0.001525104}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosann does not know whether Ruby is thirsty. It is publicly announced that Rosann does not know whether Ruby 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 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Ruby can now know that Rosann is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ruby","Rosann"],"index":1184,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9836130142,"difficulty":1.9836130142}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gustavo 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 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":"Thomas can now know whether John can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Gustavo","John"],"index":43398,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996091723,"difficulty":0.0003908277}
+{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Terry's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Terry"],"index":14533,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9937784076,"difficulty":0.0062215924}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Daniel can now know whether Cecilia can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joyce","Daniel","Cecilia"],"index":7918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997780919,"difficulty":0.0002219081}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry knows whether Barry's forehead is muddy. It is publicly announced that Barry'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 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":"Roger can now know whether Barry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Barry","Roger"],"index":14327,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are four persons. Everyone is visible to others. 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 John's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy 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 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 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) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"William can now know whether John can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Brian","Amy","William"],"index":2256,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995394945,"difficulty":0.0004605055}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Samantha does not know whether Brian 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 1) ] [ ! ~(Agentd knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Samantha can now know whether Steven is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Steven","Samantha","Paul"],"index":8592,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9941816926,"difficulty":0.0058183074}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 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":"Veronica can now know that Veronica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Kennith","Veronica"],"index":15156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980571866,"difficulty":0.0019428134}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether Craig's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Angela can now know whether Craig can know whether Craig's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Craig","Kelsey"],"index":1699,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996002316,"difficulty":0.0003997684}
+{"premise":"There are three persons. Everyone is visible 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's forehead is muddy. It is publicly announced that Stephanie knows whether Brooke's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agentc knows 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) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Stephanie can now know whether Brooke can know whether Brooke's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brooke","Pamela","Stephanie"],"index":20280,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996581078,"difficulty":0.0003418922}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rhonda is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Angie can now know that Vincent can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vincent","Rhonda","Joseph","Angie"],"index":67100,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997851253,"difficulty":0.0002148747}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Chester does not know whether Cheryl is thirsty. It is publicly announced that Cheryl does not know whether Chester is thirsty. It is publicly announced that Victor does not know whether or not everyone is thirsty. It is publicly announced that Cheryl 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 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Chester can now know that Chester is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cheryl","Chester","Victor"],"index":36708,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9008740783,"difficulty":1.9008740783}
+{"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. Mary'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 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Walter picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","David","Walter","Naomi"],"index":8041,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9688171744,"difficulty":0.0311828256}
+{"premise":"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 Joseph 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)) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Christopher can now know that Derek can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Derek","Steven","Joseph"],"index":13712,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9899629951,"difficulty":0.0100370049}
+{"premise":"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.","smcdel_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 whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Thomas can now know that David can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","David","Kathy"],"index":54067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993102551,"difficulty":0.0006897449}
+{"premise":"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 (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":"Cherie can now know that Vicki can know whether Vicki's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Michele","Vicki","Cherie"],"index":1111,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958111048,"difficulty":0.0041888952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randall does not know whether Tracy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michelle can now know whether Michelle is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michelle","Tracy","Randall","John"],"index":64642,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9953120947,"difficulty":0.0046879053}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva does not know whether or not everyone's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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)) ] (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&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Eva","James","Jermaine"],"index":33737,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979048967,"difficulty":0.0020951033}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows 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":"Virginia can now know that Phillip can know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Phillip","Leslie","Virginia"],"index":56399,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970356226,"difficulty":0.0029643774}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Beatrice 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 (~(1|2|3|4)))","n_announcements":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":"Theodore can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hector","Beatrice","Theodore","Yolanda"],"index":451,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981572032,"difficulty":0.0018427968}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Ruth'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 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Harold can now know whether Ruth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Robert","Ruth"],"index":56537,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7792820334,"difficulty":0.2207179666}
+{"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 Mary. Willard's card is shown to Willard. Charlie's card is shown to Charlie. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether William picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Mary","Willard","Charlie"],"index":56386,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984591007,"difficulty":0.0015408993}
+{"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 or not everyone is thirsty. It is publicly announced that Douglas does not know whether Irene is thirsty. It is publicly announced that Irene 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)) ] (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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Gary can now know that Douglas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gary","Irene","Douglas"],"index":60538,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9363878369,"difficulty":0.0636121631}
+{"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 Monica. Neal's card is shown to Neal. Monica's card is shown to Duane. Duane's card is shown to Duane. It is publicly announced that someone picked a red card. It is publicly announced that Neal picked a red card. It is publicly announced that Duane knows whether Duane picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Duane can now know that Monica can know whether Neal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Monica","Neal","Duane"],"index":57014,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5989060998,"difficulty":1.5989060998}
+{"premise":"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 Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Gregory can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Debra","Richard","Gregory","Curt"],"index":46335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984954596,"difficulty":0.0015045404}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agenta 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":"Janet can now know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janet","Danielle","Cynthia","Addie"],"index":5276,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.772090435,"difficulty":1.772090435}
+{"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 William. Wanda's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether William 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 that (~(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":"Charlotte can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlotte","Wanda","William"],"index":31647,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998478353,"difficulty":0.001521647}
+{"premise":"There are four persons. Everyone is visible 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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Marcus can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Marcus","Margaret","Brian"],"index":13965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997847676,"difficulty":0.0002152324}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jami does not know whether Thomas is thirsty. It is publicly announced that Cameron 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 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":"Thomas can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jami","Thomas","Cameron"],"index":52757,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. 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. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Veronica can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Veronica","Tonya","Jimmy"],"index":18230,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996987581,"difficulty":0.0003012419}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Ralph can now know that Verena is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ralph","Andrew","Verena","Stacy"],"index":15222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984866381,"difficulty":0.0015133619}
+{"premise":"There are three persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ralph can now know whether Joshua can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ralph","Joshua","Michelle"],"index":18904,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999597609,"difficulty":0.000402391}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows 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":"Ashley can now know whether Marc can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carrie","Marc","Christopher","Ashley"],"index":38639,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997846484,"difficulty":0.0002153516}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rickey knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 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":"Rickey can now know that Dennis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rickey","Dennis","Robert"],"index":49249,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979166389,"difficulty":0.0020833611}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula 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 that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Paula can now know that Frances can know that Frances is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frances","Paula"],"index":29542,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8875736594,"difficulty":1.8875736594}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanne does not know whether Michael is thirsty. It is publicly announced that Peter does not know whether Jeanne is thirsty. It is publicly announced that Jeanne 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)) ] Agenta knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jeanne can now know whether Tomas can know that Peter is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeanne","Tomas","Michael","Peter"],"index":58409,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.980066061,"difficulty":0.019933939}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is not 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 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roxie","William","Stephanie"],"index":13606,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.785662353,"difficulty":0.214337647}
+{"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. Martha's card is shown to Mary. John's card is shown to Mary. Mary's card is shown to Martha. Brittany's card is shown to Brittany. Mary's card is shown to John. Brittany's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Martha","Brittany","John"],"index":43796,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8628816009,"difficulty":1.8628816009}
+{"premise":"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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Robert can now know whether Cathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janet","Cathy","Mary","Robert"],"index":57884,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994373918,"difficulty":0.0005626082}
+{"premise":"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 does not know whether Denise's forehead is muddy.","smcdel_problem":"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":"Denise can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denise","Jeffery","Shirley"],"index":6632,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985647798,"difficulty":0.0014352202}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Rita's forehead is muddy. It is publicly announced that Connie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Connie","Arthur","Kenneth","Rita"],"index":36093,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997766614,"difficulty":0.0002233386}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fernando's card is shown to Lorraine. Lorraine's card is shown to Rebecca. Rebecca's card is shown to Rebecca. Rebecca's card is shown to Fernando. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (1|2|3|4) ] 0","hypothesis":"Ernest can now know that Fernando picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lorraine","Ernest","Rebecca","Fernando"],"index":13513,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8625956178,"difficulty":0.1374043822}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Jose. Betty's card is shown to Betty. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Jose picked a red card. It is publicly announced that Betty does not know whether Jose picked a red card. It is publicly announced that Jose does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Jose can now know that Betty can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jose","Betty"],"index":32042,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9857546091,"difficulty":0.0142453909}
+{"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 does not know whether Salvador is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","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":"David can now know whether Salvador can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Salvador"],"index":23804,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9983471632,"difficulty":0.0016528368}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 4 ] Agentd knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jenifer can now know whether John can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Joseph","Walter","Jenifer"],"index":31465,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999717176,"difficulty":0.000282824}
+{"premise":"There are two persons. Everyone is visible 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 Maureen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Maureen can now know whether Maureen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Steven","Maureen"],"index":37547,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993498921,"difficulty":0.0006501079}
+{"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 Samuel. Fred's card is shown to James. James's card is shown to Ervin. Fred's card is shown to Ervin. Samuel's card is shown to Fred. Ervin'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:2 Agentb:4 Agentc:2,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:2,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ervin can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Samuel","James","Ervin","Fred"],"index":31573,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979779124,"difficulty":0.0020220876}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thelma's card is shown to Sergio. Marian's card is shown to Sergio. Thelma's card is shown to Thelma. Marian's card is shown to Thelma. Sergio's card is shown to Randy. Randy's card is shown to Marian. Marian's card is shown to Marian. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Randy can now know whether Marian can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sergio","Thelma","Randy","Marian"],"index":5228,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9916389585,"difficulty":0.0083610415}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Jennifer can now know that Albert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Albert","Ma","Derek","Jennifer"],"index":243,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9434598088,"difficulty":0.0565401912}
+{"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 Kimberly. Kimberly's card is shown to Nicole. Nicole's card is shown to Nicole. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kimberly can now know that Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kimberly","Nicole","Edward"],"index":38169,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8363990188,"difficulty":0.1636009812}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesus does not know whether Tiffany is thirsty. It is publicly announced that Jesus does not know whether Al is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Al can now know that Tiffany is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesus","Al","Tiffany"],"index":18821,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.995116353,"difficulty":0.004883647}
+{"premise":"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) ] [ ! 2 ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Cynthia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Robert","Mary","Antonina"],"index":10831,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980159998,"difficulty":0.0019840002}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Edmund. Pauline's card is shown to Joella. Shane's card is shown to Joella. Edmund's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Edmund does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 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:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joella can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edmund","Joella","Pauline","Shane"],"index":31024,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7401973009,"difficulty":1.7401973009}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether Kathrine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 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":"Crystal can now know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathrine","Christopher","Crystal"],"index":15472,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981634021,"difficulty":0.0018365979}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fabiola's card is shown to Tony. Fabiola's card is shown to Melissa. Tony's card is shown to Fabiola. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 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":"Tony can now know whether Melissa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tony","Garrett","Melissa","Fabiola"],"index":18939,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9457307458,"difficulty":0.0542692542}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Colette does not know whether or not everyone is thirsty. It is publicly announced that Colette does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows 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 (1&2)) ] 0","hypothesis":"Colette can now know that Carlos is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Colette","Carlos"],"index":11513,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6541668773,"difficulty":0.3458331227}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morris knows whether someone's forehead is muddy. It is publicly announced that Misty does not know whether Misty's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Morris knows whether Morris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Misty can now know whether Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Misty","Morris","Amanda","Mary"],"index":26632,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991858602,"difficulty":0.0008141398}
+{"premise":"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 knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Diana can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Jorge","Robert","Diana"],"index":45463,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9906045794,"difficulty":0.0093954206}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diana knows whether Diana's forehead is muddy. It is publicly announced that Eleanore knows whether Adam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Diana can now know that Adam can know that Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adam","Eleanore","Billy","Diana"],"index":6032,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981655478,"difficulty":0.0018344522}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Abigail can now know whether Douglas can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","Valerie","Abigail","Nona"],"index":11776,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999740541,"difficulty":0.000259459}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sabrina can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammy","Lewis","Sabrina","Howard"],"index":15457,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983049631,"difficulty":0.0016950369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that David is not thirsty. It is publicly announced that Candelaria is not thirsty. It is publicly announced that David does not know whether Marcos is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agentd knows that (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) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Candelaria can now know that Marcos can know whether Jack is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marcos","David","Jack","Candelaria"],"index":20222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9844561815,"difficulty":0.0155438185}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leopoldo does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marvin can now know that Marvin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marvin","James","Leopoldo"],"index":22941,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8244888186,"difficulty":0.1755111814}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanya's card is shown to Peggy. Tanya's card is shown to Daniel. Daniel's card is shown to Tanya. It is publicly announced that someone picked a red card. It is publicly announced that Tanya picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Peggy can now know whether Daniel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Daniel","Tanya"],"index":19879,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9613566995,"difficulty":1.9613566995}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Noella knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (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":"Shizue can now know that Noella can know that Laurie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laurie","Noella","Shizue"],"index":17404,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.919477582,"difficulty":0.080522418}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverly knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Jacqueline can now know that Beverly can know that Beverly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jacqueline","Beverly","Thomas","John"],"index":3281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980015159,"difficulty":0.0019984841}
+{"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 Carl. Tara's card is shown to Carl. Tara's card is shown to Tara. 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)","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":"Robin can now know whether Robin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robin","Carl","Alex","Tara"],"index":10856,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9719154239,"difficulty":0.0280845761}
+{"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. Candace's card is shown to Michael. Betty's card is shown to Candace. It is publicly announced that someone picked a red card. It is publicly announced that Candace picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Betty can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Michael","Candace"],"index":17185,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999730885,"difficulty":0.000269115}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jo's card is shown to Michelle. Lasandra's card is shown to Josiah. Michelle's card is shown to Lasandra. Lasandra's card is shown to Jo. Jo's card is shown to Jo. It is publicly announced that someone picked a red card. It is publicly announced that Lasandra does not know whether or not everyone picked a red card. It is publicly announced that Lasandra picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Lasandra can now know that Jo can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Josiah","Lasandra","Jo"],"index":27656,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9897340536,"difficulty":0.0102659464}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence knows whether someone's forehead is muddy. It is publicly announced that Clarence does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Felipe can now know that Clarence can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Clarence","Felipe"],"index":13453,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9757562876,"difficulty":0.0242437124}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! 1 ] (Agentb knows that (~(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":"Lorenzo can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Lorenzo","Teri"],"index":45646,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984477758,"difficulty":0.0015522242}
+{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that James knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 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":["Linda","Donna","Leonardo","James"],"index":48529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995849729,"difficulty":0.0004150271}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Sol. Mary's card is shown to Sol. Michael'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:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Sol can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Sol","Mary","Edward"],"index":29204,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.920658052,"difficulty":1.920658052}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glenn knows whether 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) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glenn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Frances","Glenn","Mary"],"index":11257,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984840751,"difficulty":0.0015159249}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lola does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows 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":"Lola can now know whether Diane can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Lola","William","Diane"],"index":47778,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997790456,"difficulty":0.0002209544}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle 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) ] [ ! (Agenta knows whether 3) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Barbara can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michelle","Barbara","Marc","Lee"],"index":21816,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997557998,"difficulty":0.0002442002}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joel's card is shown to Joel. Joel's card is shown to Cameron. Cameron's card is shown to Cameron. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Cameron can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joel","Cameron"],"index":12242,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985876083,"difficulty":0.0014123917}
+{"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. It is publicly announced that William does not know whether Kim is thirsty. It is publicly announced that Delphia does not know whether Kim is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 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 (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kim can now know that Kim is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jorge","Delphia","Kim","William"],"index":20193,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5808041096,"difficulty":0.4191958904}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"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":"Joseph can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Milton","Leon"],"index":28770,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9942820072,"difficulty":0.0057179928}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 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":"Dave can now know that Connie can know that Connie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dave","Connie","Dale","Carolyn"],"index":14241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984972477,"difficulty":0.0015027523}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tamika does not know whether Paul is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether someone is thirsty. It is publicly announced that Paul does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Tamika","Paul"],"index":18202,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delores knows whether Estella's forehead is muddy. It is publicly announced that Estella knows whether Estella's forehead is muddy. It is publicly announced that Delores knows whether Delores's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Estella can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Delores","Estella"],"index":23369,"s-l":"forehead_mirror-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's forehead is muddy. It is publicly announced that Donald knows whether or not everyone'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 (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Betty can now know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Corliss","Donald","Betty","Barbra"],"index":34880,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9129653573,"difficulty":0.0870346427}
+{"premise":"There are four persons. Everyone is visible 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 or not nobody'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) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Jennifer can now know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Andrew","Jennifer","Heather","Willie"],"index":46691,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9634585381,"difficulty":0.0365414619}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not everyone's forehead is muddy. It is publicly announced that Lillian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows 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)) ] [ ! ~(1) ] 0","hypothesis":"Jesse can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lillian","Rebecca","Jesse"],"index":54607,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984682202,"difficulty":0.0015317798}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Camille's card is shown to Camille. Camille's card is shown to Debbie. It is publicly announced that someone picked a red card. It is publicly announced that Camille does not know whether Debbie picked a red card. It is publicly announced that Camille 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) ] [ ! ~(Agenta knows whether 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 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Debbie can now know whether Camille can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Camille","Debbie"],"index":60522,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9838411212,"difficulty":0.0161588788}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Richard's card is shown to Richard. Richard's card is shown to Scott. Scott's card is shown to Scott. It is publicly announced that someone picked a red card. It is publicly announced that Scott knows whether Richard picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Scott can now know that Richard can know that Scott picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Scott"],"index":39508,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9919495583,"difficulty":0.0080504417}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Manuel's card is shown to Helene. Barbara's card is shown to Barbara. Helene's card is shown to Manuel. It is publicly announced that someone picked a red card. It is publicly announced that Manuel 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 whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Barbara can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helene","Barbara","Manuel"],"index":66058,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.637575984,"difficulty":0.362424016}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Emilio's card is shown to Robert. Phillip's card is shown to Emilio. Emilio's card is shown to Phillip. Phillip's card is shown to Phillip. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ryan can now know whether Robert can know whether Emilio picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ryan","Robert","Emilio","Phillip"],"index":57940,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984710813,"difficulty":0.0015289187}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amanda's card is shown to William. William's card is shown to Tammy. Tammy's card is shown to Amanda. 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 (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":"Tammy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Tammy","Amanda"],"index":27725,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985432625,"difficulty":0.0014567375}
+{"premise":"There are four persons. Everyone is visible 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 Amy knows whether Amy's forehead is muddy. It is publicly announced that Dorthy's forehead is muddy. It is publicly announced that Steven knows whether Dorthy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agenta knows whether (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":"Dorthy can now know whether Amy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dorthy","Amy","Steven","Jessica"],"index":42447,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997450709,"difficulty":0.0002549291}
+{"premise":"There are three persons. Everyone is visible 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 everyone's forehead is muddy.","smcdel_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":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ashley","Norman","Michael"],"index":8421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99976331,"difficulty":0.00023669}
+{"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 Yu is thirsty. It is publicly announced that Yu does not know whether Annie is thirsty. It is publicly announced that Annie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Yu can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mathew","Yu","Annie","Albert"],"index":38173,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978385568,"difficulty":0.0021614432}
+{"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 Marlon. James's card is shown to James. Erica's card is shown to James. Erica's card is shown to Erica. It is publicly announced that someone picked a red card. It is publicly announced that Erica does not know whether Michael picked a red card. It is publicly announced that Marlon does not know whether James picked a red card. It is publicly announced that Erica does not know whether or not everyone picked a red card. It is publicly announced that James does not know whether Michael 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) ] (Agenta knows whether 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":"Marlon can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marlon","James","Erica","Michael"],"index":49206,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5288760066,"difficulty":1.5288760066}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. Stephen's card is shown to Doug. Doug's card is shown to Doug. It is publicly announced that someone picked a red card. It is publicly announced that Stephen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Scott can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stephen","Scott","Doug"],"index":50222,"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's forehead is muddy. It is publicly announced that Irene does not know whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sandra can now know whether Dexter can know whether Irene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Irene","Eugene","Sandra","Dexter"],"index":26759,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995361567,"difficulty":0.0004638433}
+{"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 Victoria 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) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Victoria","Julie","Kevin"],"index":47324,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986181259,"difficulty":0.0013818741}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roberto does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Roberto knows whether someone is thirsty. It is publicly announced that Roberto knows whether Roberto is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Roberto can now know that Joe can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roberto","Joe"],"index":28577,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9912993312,"difficulty":0.0087006688}
+{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Marcus"],"index":62538,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985301495,"difficulty":0.0014698505}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Sean can now know that Michelle can know that Michelle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ronald","Michelle","Sean"],"index":13030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99836272,"difficulty":0.00163728}
+{"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 Lillian is thirsty. It is publicly announced that Cecil does not know whether Charles is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know whether Cecil is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cecil","Charles","Lillian","Perry"],"index":7017,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9960412979,"difficulty":1.9960412979}
+{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know whether Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","Gene","Walter","Robert"],"index":12915,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997275472,"difficulty":0.0002724528}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucinda does not know whether or not everyone is thirsty. It is publicly announced that Sheila knows whether someone is thirsty. It is publicly announced that Sheila is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! 2 ] 0","hypothesis":"Sean can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pat","Sheila","Lucinda","Sean"],"index":28032,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984030128,"difficulty":0.0015969872}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn's forehead is muddy. It is publicly announced that Shawn knows whether Joan's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 1) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Joan can now know that Shawn can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joan","Bradley","Shawn"],"index":10714,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996650219,"difficulty":0.0003349781}
+{"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 Patricia is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Russell 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 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Russell can now know that Pablo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","John","Pablo","Russell"],"index":22252,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9958771467,"difficulty":0.0041228533}
+{"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.","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 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":"Dina can now know whether Belinda can know whether Belinda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Belinda","Dina","Robert"],"index":62157,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9958708882,"difficulty":0.0041291118}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alicia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Alicia can now know that Samantha can know that Samantha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Samantha","Margaret","Michelle","Alicia"],"index":32413,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983878136,"difficulty":0.0016121864}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Paul can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Vincent","Greg","Mark"],"index":48421,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997649789,"difficulty":0.0002350211}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether 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) ] [ ! (Agentd knows whether 4) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Dennis can now know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darlene","Dennis","Heidy","Henry"],"index":673,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980928302,"difficulty":0.0019071698}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vickie does not know whether Carlos is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1&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":"Carlos can now know whether Vickie can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carlos","Vickie","Sheila"],"index":46505,"s-l":"internal-1","deberta_pred":1,"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 William knows whether or not nobody is thirsty. It is publicly announced that William does not know whether Walter is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 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":"Walter can now know whether Jeffrey can know whether Jeffrey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Walter","William","Jeffrey"],"index":46284,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9976638556,"difficulty":0.0023361444}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Warren's card is shown to Warren. Patsy's card is shown to Linda. Patsy's card is shown to Patsy. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether or not everyone picked a red card. It is publicly announced that everyone 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 (1&2&3&4)) ] [ ! (1&2&3&4) ] (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Linda can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathleen","Warren","Linda","Patsy"],"index":64143,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9907185435,"difficulty":0.0092814565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Melissa can now know that Albert can know whether Molly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Molly","Albert","Melissa"],"index":15391,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996254444,"difficulty":0.0003745556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane does not know whether Jane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(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":"Michael can now know that Eric can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","George","Michael","Jane"],"index":24530,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9718125463,"difficulty":0.0281874537}
+{"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 Nicolasa. Robert's card is shown to Anthony. Anthony's card is shown to Robert. Nicolasa's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Nicolasa picked a black card. It is publicly announced that Nicolasa does not know whether Samuel picked a red card. It is publicly announced that Nicolasa does not know whether Samuel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agenta 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:3 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Nicolasa can now know that Anthony can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicolasa","Anthony","Robert","Samuel"],"index":13873,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999777019,"difficulty":0.000222981}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bill knows whether Susie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Deborah can now know whether Susie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susie","Deborah","Bill","Craig"],"index":14368,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996820688,"difficulty":0.0003179312}
+{"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 Maria is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows whether 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":"Maria can now know that Thomas can know whether Maria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Maria","David"],"index":11582,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9947734475,"difficulty":0.0052265525}
+{"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 Claude. Emilia's card is shown to Steven. Claude's card is shown to John. Emilia's card is shown to John. Steven's card is shown to Emilia. Emilia's card is shown to Emilia. It is publicly announced that someone picked a red card. It is publicly announced that Emilia picked a red card. It is publicly announced that Claude 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 (Agentb knows that 2)","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":"Emilia can now know whether Steven can know that Steven picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Claude","Steven","John","Emilia"],"index":25787,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9200748801,"difficulty":0.0799251199}
+{"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 Brandon is thirsty. It is publicly announced that John knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"William can now know whether Brandon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Brandon","John"],"index":14611,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9923370481,"difficulty":0.0076629519}
+{"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 Danny. David's card is shown to Danny. Thomas's card is shown to Thomas. David's card is shown to Thomas. Danny's card is shown to Frances. Thomas's card is shown to David. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frances can now know whether Danny can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Thomas","Frances","David"],"index":40865,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997031093,"difficulty":0.0002968907}
+{"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. Deborah's card is shown to Sean. Deborah's card is shown to Deborah. Michael's card is shown to Deborah. Sean's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Deborah picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 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:3 Agentc:3,4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Deborah can now know that Michael can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leo","Sean","Deborah","Michael"],"index":55449,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ginny can now know that Rudolph can know whether Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Rudolph","Ginny","Doris"],"index":66197,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996203184,"difficulty":0.0003796816}
+{"premise":"There are three persons. Everyone is visible 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'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 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":"Carol can now know whether Joseph can know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","James","Carol"],"index":52079,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996520281,"difficulty":0.0003479719}
+{"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. Naomi's card is shown to William. Cynthia's card is shown to Dana. Cynthia's card is shown to Naomi. Cynthia's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Naomi does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Cynthia can now know that William can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Dana","Naomi","Cynthia"],"index":44986,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996962547,"difficulty":0.0003037453}
+{"premise":"There are two persons. Everyone is visible 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 or not nobody's forehead is muddy. It is publicly announced that Sandra knows whether Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sandra can now know whether Joyce can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandra","Joyce"],"index":30414,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995835423,"difficulty":0.0004164577}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. 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 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Becky can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Becky","Karen"],"index":31308,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983805418,"difficulty":0.0016194582}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shari knows whether someone's forehead is muddy. It is publicly announced that Steven does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shari can now know that Steven can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Steven","Shari"],"index":15380,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9498566985,"difficulty":1.9498566985}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harmony 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 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":"Carl can now know whether Harmony can know whether Harmony is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carl","Harmony","Doug"],"index":40520,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99876827,"difficulty":0.00123173}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frederick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Frederick can now know that Randy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frederick","Barbara","Randy","Linda"],"index":51162,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5939893126,"difficulty":0.4060106874}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Louis. Louis's card is shown to Kim. Mark's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Mark knows whether Mark picked a red card. It is publicly announced that Mark knows whether or not everyone picked a red card. It is publicly announced that Louis does not know whether Mark picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Louis can now know that Louis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Louis","Mark","Kim"],"index":10520,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8397103548,"difficulty":1.8397103548}
+{"premise":"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 Ashley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know whether Alexa can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ashley","Alexa"],"index":18663,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Glenn can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Glenn","Brian"],"index":26143,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983316064,"difficulty":0.0016683936}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robby's card is shown to Andrew. Ted's card is shown to Andrew. Robby's card is shown to Robby. Andrew's card is shown to Ted. Robby's card is shown to Ted. 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 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robby can now know whether Ted picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Robby","Ted"],"index":25573,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7239716053,"difficulty":0.2760283947}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (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":"Mary can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mary","David"],"index":61202,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9547320604,"difficulty":0.0452679396}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sam does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Marlene can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sam","Francis","Barry","Marlene"],"index":2674,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979096055,"difficulty":0.0020903945}
+{"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 Lynette. Lynette's card is shown to Lynette. Theron's card is shown to Lynette. John's card is shown to Theron. Lynette's card is shown to Daniel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1 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:1,2,3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Theron can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Lynette","Theron","Daniel"],"index":65067,"s-l":"explicit-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). Hazel's card is shown to Hazel. Bessie's card is shown to Clifford. 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 Clifford does not know whether Clifford picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Clifford can now know whether Hazel can know whether Hazel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hazel","Clifford","Bessie"],"index":51845,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9928869605,"difficulty":0.0071130395}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eloise's card is shown to Eloise. Michelle's card is shown to Eloise. Michelle's card is shown to Michelle. Marion's card is shown to Michelle. Bruce's card is shown to Marion. Michelle's card is shown to Bruce. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marion can now know that Michelle can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eloise","Michelle","Marion","Bruce"],"index":20441,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.964502573,"difficulty":0.035497427}
+{"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 everyone is thirsty. It is publicly announced that Diana is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Diana can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Diana","Michael"],"index":18379,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8177379966,"difficulty":0.1822620034}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis does not know whether or not everyone's forehead is muddy. It is publicly announced that Harlan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] (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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Harlan can now know whether Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nancy","Louis","Harlan","Doris"],"index":21618,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993761182,"difficulty":0.0006238818}
+{"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 Bob. Brian's card is shown to Brian. Bob's card is shown to Benjamin. Brian's card is shown to Benjamin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 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:2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Bob can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bob","Brian","Robert","Benjamin"],"index":28710,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997751117,"difficulty":0.0002248883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Ruth can now know whether Joey can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joey","Lea","Ruth","Lyn"],"index":16088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997562766,"difficulty":0.0002437234}
+{"premise":"There are two persons. Everyone is visible 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 not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ruth can now know that Ariel can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ariel","Ruth"],"index":56690,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996352196,"difficulty":0.0003647804}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bart does not know whether or not everyone is thirsty. It is publicly announced that Bart knows whether Bart is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kevin can now know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kevin","Bart"],"index":40741,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9947152734,"difficulty":0.0052847266}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jessie can now know whether Thomas can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Dale","Jessie"],"index":7052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7663590908,"difficulty":0.2336409092}
+{"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 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":"Cody can now know that Curt can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nathanial","Curt","Michael","Cody"],"index":10561,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985615611,"difficulty":0.0014384389}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernard does not know whether Bruce is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Christopher can now know whether Bruce can know whether Christopher is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bernard","Bruce","Christopher"],"index":52353,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978367686,"difficulty":0.0021632314}
+{"premise":"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's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agentb knows 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":"Raymond can now know whether Kimberly can know that Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Willie","Kimberly","Raymond"],"index":2743,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9041911364,"difficulty":0.0958088636}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy. It is publicly announced that George knows whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Mary can now know that George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Mary","Robert","George"],"index":26161,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979445338,"difficulty":0.0020554662}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy. It is publicly announced that Kenneth does not know whether Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Dorothy can now know that Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Annette","Dorothy","Carmelita"],"index":65622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9532199502,"difficulty":0.0467800498}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ana does not know whether Ana's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Humberto can now know whether Ana can know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raeann","Dorothy","Ana","Humberto"],"index":42227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991814494,"difficulty":0.0008185506}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Argelia does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Marjorie can now know that Argelia can know whether Laura is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carol","Argelia","Laura","Marjorie"],"index":2984,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5001038313,"difficulty":1.5001038313}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Luke does not know whether Leila is thirsty. It is publicly announced that Luke 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 (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":"Luke can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leila","Luke"],"index":42757,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy.","smcdel_problem":"VARS 1,2 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":"Donna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["April","Donna"],"index":27139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977825284,"difficulty":0.0022174716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ted's forehead is not muddy. It is publicly announced that Ted knows whether Ted's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Richard can now know whether George can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Richard","Ted"],"index":58640,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996265173,"difficulty":0.0003734827}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marvin's card is shown to Marvin. Aaron's card is shown to Marvin. Marvin's card is shown to Aaron. Aaron's card is shown to Aaron. Thomas's card is shown to Aaron. Aaron'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:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marvin can now know whether Thomas can know that Marvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Aaron","Thomas"],"index":30373,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8025584221,"difficulty":0.1974415779}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erma is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Georgina can now know that Georgia can know that Scott is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Georgina","Georgia","Scott","Erma"],"index":47019,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9868777394,"difficulty":0.0131222606}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows 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":"Barbara can now know that Evelyn can know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Marian","Evelyn"],"index":32175,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964680672,"difficulty":0.0035319328}
+{"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 Vincent. Regina's card is shown to Regina. Michael'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:2 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know that Regina picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vincent","Regina","Michael","Karen"],"index":62570,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983429909,"difficulty":0.0016570091}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawnta knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Shawnta can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andre","Emanuel","Shawnta"],"index":61834,"s-l":"internal-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 Allen does not know whether or not everyone is thirsty. It is publicly announced that Rose 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) ] (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 3) ] 0","hypothesis":"Rose can now know that Allen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rose","Allen","Gary"],"index":32561,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9492763281,"difficulty":1.9492763281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Allen can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dawn","Danielle","Joshua","Allen"],"index":39018,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99973768,"difficulty":0.00026232}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Gary can now know that Jane can know that Douglas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jane","Gary","Steven","Douglas"],"index":35096,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984961748,"difficulty":0.0015038252}
+{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 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":"Kerry can now know that Walter can know that Walter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephanie","Kerry","Walter"],"index":51733,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9896097183,"difficulty":0.0103902817}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maribel does not know whether Royce is thirsty. It is publicly announced that Royce does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agentb knows whether (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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Monique can now know whether Maribel can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Royce","Monique","Maribel"],"index":37253,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9930915833,"difficulty":0.0069084167}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Deborah's card is shown to Mary. Katie's card is shown to Katie. Mary's card is shown to Deborah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1 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":["Mary","Katie","Deborah"],"index":10573,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983503819,"difficulty":0.0016496181}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Paula's card is shown to Paula. David's card is shown to Marianne. Marianne's card is shown to Marianne. It is publicly announced that someone picked a red card. It is publicly announced that Paula does not know whether Marianne picked a red card. It is publicly announced that David knows whether 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) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb 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:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Paula can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Paula","David","Marianne","Catherine"],"index":49917,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9948700666,"difficulty":0.0051299334}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Pamela's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Pamela can now know that Kenneth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pamela","Kenneth"],"index":994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998329699,"difficulty":0.001670301}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Larry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Larry","Patricia"],"index":30106,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984290004,"difficulty":0.0015709996}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caitlin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that 1)","n_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":"Caitlin can now know whether Lois can know that Caitlin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Caitlin","Theodore","Lois"],"index":41893,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5979687572,"difficulty":0.4020312428}
+{"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 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":"Eva can now know that Eva is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Abigail","Jeffrey","Eva"],"index":32222,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984200001,"difficulty":0.0015799999}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Iona does not know whether or not everyone is thirsty. It is publicly announced that Iona does not know whether Johnathan 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) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Johnathan can now know that Mark can know that Johnathan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Iona","Mark","Johnathan"],"index":52258,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5471154451,"difficulty":1.5471154451}
+{"premise":"There are three persons. Everyone is visible 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 everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Zachary can now know that Emily can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randi","Zachary","Emily"],"index":53766,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996870756,"difficulty":0.0003129244}
+{"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 Beatrice is thirsty. It is publicly announced that Beatrice 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)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ronald can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Beatrice","Dorothy","Rodger"],"index":6651,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966919422,"difficulty":0.0033080578}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"Joseph can now know that Gilda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Gilda","Randal","Kelly"],"index":50168,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5825780034,"difficulty":0.4174219966}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Norma can now know that Norma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Norma","Carlos","Damaris","Ramona"],"index":34947,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980003238,"difficulty":0.0019996762}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darrell does not know whether Brittany is thirsty. It is publicly announced that Rudolph does not know whether Darrell is thirsty. It is publicly announced that Rudolph does not know whether Brittany is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] Agentb knows 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rudolph can now know that Brittany can know whether Brittany is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Darrell","Rudolph","Brittany"],"index":67159,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988594055,"difficulty":0.0011405945}
+{"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 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) ] [ ! (1&2&3&4) ] 0","hypothesis":"Irma can now know whether William can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Irma","William","Douglas"],"index":11841,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.997402966,"difficulty":0.002597034}
+{"premise":"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 someone's forehead is muddy. It is publicly announced that Ollie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Janice can now know that Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Ollie","Gerald","Mike"],"index":15279,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99189502,"difficulty":0.00810498}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows 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) ] [ ! (1&2) ] 0","hypothesis":"Catherine can now know whether Patricia can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Patricia"],"index":22385,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999612987,"difficulty":0.000387013}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joshua knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Daniel can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joshua","Ruth","Daniel","Thomas"],"index":43042,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984993935,"difficulty":0.0015006065}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Elizabeth can now know whether Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Nancy","Rosa","Sarah"],"index":18357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995949864,"difficulty":0.0004050136}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eric's card is shown to Eric. Kathleen's card is shown to Eric. Eric's card is shown to Leona. Leona's card is shown to Kathleen. Kathleen's card is shown to Kathleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Eric can now know that Eric picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Leona","Kathleen"],"index":41001,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961357713,"difficulty":0.0038642287}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether Adam is thirsty. It is publicly announced that Jason does not know whether Adam is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows whether 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":"Jason can now know whether Amanda can know whether Jason is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adam","Amanda","Jason"],"index":21934,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974932671,"difficulty":0.0025067329}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Jessica can now know whether Michelle can know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michelle","Anthony","Jessica","Alicia"],"index":30079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993261099,"difficulty":0.0006738901}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myron does not know whether or not everyone's forehead is muddy. It is publicly announced that Myron does not know whether Myron's forehead is muddy. It is publicly announced that Brad's forehead is muddy. It is publicly announced that Brad knows whether Myron's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brad can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Myron","Brad"],"index":44765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975484014,"difficulty":0.0024515986}
+{"premise":"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 knows whether Edgar's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Clifton can now know whether Joe can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Joe","Clifton","Edgar"],"index":53393,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9461075664,"difficulty":1.9461075664}
+{"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 Debra 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 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":"Dale can now know that Samuel can know that Debra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Samuel","Debra","Dale"],"index":58687,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977593422,"difficulty":0.0022406578}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario knows whether or not nobody's forehead is muddy.","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&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":"Sara can now know whether Mario can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sara","Mario"],"index":65376,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9528006911,"difficulty":0.0471993089}
+{"premise":"There are two persons. Everyone is visible 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 Hildred's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agenta knows that (~(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":"Hildred can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Hildred","Jennifer"],"index":48066,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984523058,"difficulty":0.0015476942}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tara does not know whether Frank is thirsty. It is publicly announced that Frank is thirsty. It is publicly announced that Frank knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows that 1)","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":"Tara can now know whether Brandon can know that Tara is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tara","Frank","Brandon"],"index":13794,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9867175817,"difficulty":0.0132824183}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Fred's card is shown to Mary. George's card is shown to Fred. Coleen's card is shown to Coleen. Mary'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:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Fred","Coleen","George"],"index":43960,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983778,"difficulty":0.0016222}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa does not know whether Teresa's forehead is muddy. It is publicly announced that Jonathan does not know whether Jonathan'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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb 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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"George can now know whether Jonathan can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jonathan","George","Teresa"],"index":42179,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7795401812,"difficulty":1.7795401812}
+{"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 Doris. Kathryn's card is shown to Doris. Teresa's card is shown to Teresa. Kathryn's card is shown to Teresa. Doris's card is shown to Linda. Linda's card is shown to Kathryn. Kathryn's card is shown to Kathryn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,4 Agentc:1 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Doris can now know whether Kathryn can know whether Kathryn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Doris","Teresa","Linda","Kathryn"],"index":62289,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9959988594,"difficulty":0.0040011406}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalinda does not know whether Rosalinda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Peter can now know whether Rosalinda can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Michael","Dorothy","Rosalinda"],"index":65844,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997668862,"difficulty":0.0002331138}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Rita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Gertrude can now know that Gertrude's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Rita","Matthew","Gertrude"],"index":4570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980331063,"difficulty":0.0019668937}
+{"premise":"There are four persons. Everyone is visible 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 Steven's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Mary can now know that Steven's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cesar","Claudia","Steven","Mary"],"index":54851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996958971,"difficulty":0.003041029}
+{"premise":"There are four persons. Everyone is visible 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 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":"Frances can now know whether Jack can know whether Jack's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Anita","Bradley","Jack"],"index":57322,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996836185,"difficulty":0.0003163815}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ginny's card is shown to Ginny. Willis's card is shown to Ginny. Ginny's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 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:1,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ginny can now know that Jennifer can know that Ginny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ginny","Jennifer","Willis","Lynda"],"index":30854,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962790608,"difficulty":0.0037209392}
+{"premise":"There are 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 (~(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":"Velma can now know that Kathy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Kathy","Velma"],"index":20685,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983531237,"difficulty":0.0016468763}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernest knows whether Ernest 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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Chad can now know that Chad is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Chad","Barbara","Ernest"],"index":46926,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980041385,"difficulty":0.0019958615}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether someone's forehead is muddy. It is publicly announced that Scott knows whether someone's forehead is muddy. It is publicly announced that Lawrence knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Scott can now know that Jason's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lawrence","Jason","Frank","Scott"],"index":12754,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977703094,"difficulty":0.0022296906}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy. It is publicly announced that Rhoda's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] Agenta knows whether (Agentb knows whether (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":"Rhoda can now know whether Donna can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rhoda","Donna"],"index":12866,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shawn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows 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":"Mark can now know whether Sean can know whether Sean is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tony","Mark","Shawn","Sean"],"index":46096,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973740578,"difficulty":0.0026259422}
+{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (~(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":"Donald can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donald","Isabel","Matthew"],"index":35101,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998518765,"difficulty":0.001481235}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Earl 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) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Mary","Robert","Emma"],"index":46574,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5322064161,"difficulty":0.4677935839}
+{"premise":"There are three persons. Everyone is visible 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 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 1) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Anne can now know that Mark can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Anne","Mark"],"index":66383,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982878566,"difficulty":0.0017121434}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Dorothy can now know whether Dean can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francine","Dean","Erin","Dorothy"],"index":57556,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9968597889,"difficulty":1.9968597889}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Oliver can now know whether Leona can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Leona","Lessie","Oliver"],"index":50708,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997021556,"difficulty":0.0002978444}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether or not nobody's forehead is muddy. It is publicly announced that Fred knows whether Christina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Christina can now know whether Fred can know whether Fred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Christina","Fred"],"index":52520,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5210182071,"difficulty":1.5210182071}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Salvador's card is shown to Salvador. Billy's card is shown to Paul. Levi's card is shown to Paul. Paul's card is shown to Levi. Levi's card is shown to Levi. It is publicly announced that someone picked a red card. It is publicly announced that Salvador does not know whether Levi 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:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Salvador can now know whether Billy can know whether Levi picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Salvador","Paul","Billy","Levi"],"index":15300,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997920692,"difficulty":0.002079308}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Daniel does not know whether or not everyone is thirsty. It is publicly announced that Deborah does not know whether Hilda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Deborah can now know whether Deborah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Deborah","Hilda","Daniel"],"index":62944,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988173842,"difficulty":0.0011826158}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Martha can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martha","Janet","Betty","Jennifer"],"index":36500,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9590353966,"difficulty":1.9590353966}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW 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 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Richard can now know that Joan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Johnathon","Joan"],"index":33015,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981016517,"difficulty":0.0018983483}
+{"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 George. George's card is shown to Antonia. 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 George does not know whether Antonia picked a red card. It is publicly announced that George does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Antonia can now know whether George can know that George picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["George","Antonia"],"index":45540,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848077297,"difficulty":0.0151922703}
+{"premise":"There are two persons. Everyone is visible 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 Gregory's forehead is muddy. It is publicly announced that Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows 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":"Gregory can now know that Luis can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gregory","Luis"],"index":51594,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997859597,"difficulty":0.0002140403}
+{"premise":"There are four persons. Everyone is visible 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 Charles's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Charles can now know whether Diana can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Moshe","Charles","Terry","Diana"],"index":8355,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995720983,"difficulty":0.0004279017}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Paul can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kendall","Jeffrey","Paul"],"index":39958,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984662533,"difficulty":0.0015337467}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catharine knows whether or not nobody's forehead is muddy. It is publicly announced that Pauline knows whether Catharine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Catharine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Catharine","Pauline"],"index":21739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982749224,"difficulty":0.0017250776}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rod knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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 3) ] 0","hypothesis":"Robert can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rod","Robert","Carol","Frank"],"index":5230,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9988652468,"difficulty":0.0011347532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Omar can now know that John can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Omar","John","Lee","Lana"],"index":1319,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997797608,"difficulty":0.0002202392}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 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":"Leonard can now know that Jacob can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Amy","Jacob","Leonard"],"index":35146,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948155284,"difficulty":0.0051844716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacque does not know whether or not everyone is thirsty. It is publicly announced that Jacque does not know whether Bradley is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that (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":"Jacque can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bradley","Gwendolyn","Jacque"],"index":5183,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997714162,"difficulty":0.0002285838}
+{"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 Michael. Laci's card is shown to Laci. Judy's card is shown to Laci. Mary's card is shown to Laci. Mary's card is shown to Judy. Judy's card is shown to Mary. It is publicly announced that someone 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:3 Agentb:2,3,4 Agentc:4 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentd knows that 3)","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":"Laci can now know that Mary can know that Judy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Laci","Judy","Mary"],"index":54823,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.993497014,"difficulty":0.006502986}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows 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":"Treva can now know whether Shirley can know whether Treva's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tamara","Jodi","Shirley","Treva"],"index":38736,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996938705,"difficulty":0.0003061295}
+{"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. Devon's card is shown to Devon. Sierra's card is shown to Devon. Helen's card is shown to Sierra. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Devon can now know whether Sierra can know that Sierra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Devon","Sierra"],"index":55756,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5656923056,"difficulty":0.4343076944}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows that (1&2&3&4))","n_announcements":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":"Luther can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Hoyt","Michael","Luther","Julie"],"index":35794,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985211492,"difficulty":0.0014788508}
+{"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 Lydia does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Lydia can now know that Yvette can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lydia","Yvette"],"index":35659,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8499546051,"difficulty":0.1500453949}
+{"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 Julie. Mark's card is shown to James. Dorothy's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,4 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":["Mark","Julie","James","Dorothy"],"index":48296,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944967628,"difficulty":0.0055032372}
+{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Deborah can now know whether Iris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vivian","Hubert","Deborah","Iris"],"index":54765,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999586165,"difficulty":0.000413835}
+{"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 Kim. Kim's card is shown to Kim. It is publicly announced that someone picked a red card. It is publicly announced that Kim knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kim can now know that Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Kim"],"index":51817,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982206225,"difficulty":0.0017793775}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy. It is publicly announced that Martha'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) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Bobby can now know whether Martha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bobby","Martha"],"index":41035,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997238517,"difficulty":0.0002761483}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Eleanor","Paul"],"index":64968,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928193688,"difficulty":0.0071806312}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Roy. Roy's card is shown to Curtis. Curtis's card is shown to Curtis. Curtis's card is shown to Renita. Renita's card is shown to Renita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Renita can now know whether Curtis can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roy","Curtis","Renita"],"index":40649,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Abbey knows whether Abbey's forehead is muddy. It is publicly announced that Abbey'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 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) ] [ ! 1 ] 0","hypothesis":"Abbey can now know whether Remedios can know whether Abbey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Abbey","Remedios"],"index":30058,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997224212,"difficulty":0.0002775788}
+{"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 Mary is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Mary can now know that Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Jonathan","Robert"],"index":35297,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Athena knows whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Michael can now know that Athena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Athena","Dorothy","Michael"],"index":48347,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9969661832,"difficulty":0.0030338168}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patricia is not thirsty. It is publicly announced that Richard knows whether Patricia is thirsty. It is publicly announced that Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] 0","hypothesis":"Patricia can now know whether Clinton can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Clinton","Deborah","Patricia"],"index":20560,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994130135,"difficulty":0.0005869865}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (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":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Naomi","James"],"index":38419,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997258782,"difficulty":0.0002741218}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frederick does not know whether Clark is thirsty. It is publicly announced that Frederick does not know whether Clark is thirsty. It is publicly announced that Frederick knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Ryan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ryan","Clark","Frederick"],"index":33689,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985652566,"difficulty":0.0014347434}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Esther's card is shown to Esther. Craig's card is shown to Esther. Jason's card is shown to Esther. Craig's card is shown to Guy. Craig's card is shown to Craig. Craig's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Esther does not know whether Guy 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) ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:3 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jason can now know that Craig can know whether Guy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Esther","Guy","Craig","Jason"],"index":60373,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8871403337,"difficulty":0.1128596663}
+{"premise":"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 does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joey can now know that Justin can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Justin","Joey","Elizabeth"],"index":41298,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997789264,"difficulty":0.0002210736}
+{"premise":"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. 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: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))) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Jennifer","Jason","James"],"index":19702,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986559153,"difficulty":0.0013440847}
+{"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 Lorie is thirsty. It is publicly announced that Amy does not know whether Reina is thirsty. It is publicly announced that Amy does not know whether Lorie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 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":"Jane can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amy","Lorie","Reina","Jane"],"index":22802,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
+{"premise":"There are four persons. Everyone is visible 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 Eric's forehead is muddy. It is publicly announced that John knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd 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":["Joyce","Eric","Edward","John"],"index":45193,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982640147,"difficulty":0.0017359853}
+{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"William can now know whether Morgan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Morgan","William","Jeanna","Aaron"],"index":42470,"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 Tammie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows whether 4)","n_announcements":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":"Earl can now know that Mary can know whether Earl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Guy","Tammie","Earl"],"index":60640,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7865428329,"difficulty":0.2134571671}
+{"premise":"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 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":"William can now know whether Mark can know that Tamara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tamara","Mark","William"],"index":46088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972651005,"difficulty":0.0027348995}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Edward can now know whether Hector can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Edward","Elmer","Hector"],"index":55630,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997153878,"difficulty":0.0002846122}
+{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Travis knows whether Diana's forehead is muddy.","smcdel_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 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Diana can now know that Travis can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Mark","Diana"],"index":47180,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9871610999,"difficulty":0.0128389001}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Latasha is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows whether 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":"Joseph can now know whether Latasha is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Veronica","Latasha","Keli","Joseph"],"index":55960,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7995314002,"difficulty":0.2004685998}
+{"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 (~(1|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":"Hillary can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maude","Hillary","Genevieve"],"index":31500,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997312427,"difficulty":0.0002687573}
+{"premise":"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. It is publicly announced that Ray does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"James can now know whether Ray can know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ray","James"],"index":56411,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7287795544,"difficulty":0.2712204456}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thomas's card is shown to Sarah. Sarah's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Sarah can now know whether Sarah picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sarah","Thomas"],"index":40733,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7719162107,"difficulty":1.7719162107}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amos's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Jason can now know that Amos can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clifford","Jason","Amos"],"index":44001,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997829795,"difficulty":0.0002170205}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Arcelia knows whether Arcelia 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 (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Arcelia can now know whether Billy can know whether Bonnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Billy","Bonnie","Arcelia"],"index":16764,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972463846,"difficulty":0.0027536154}
+{"premise":"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. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Sara 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 whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Sara can now know whether James can know that Shayla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","James","Sara","Shayla"],"index":24211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9800772667,"difficulty":0.0199227333}
+{"premise":"There are four persons. Everyone is visible 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 Christopher's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 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) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Justin can now know whether Christopher can know that Cynthia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Justin","Christopher","Richard","Cynthia"],"index":14478,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996688366,"difficulty":0.0003311634}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Helen can now know whether Patty can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Patty","Helen","Belinda"],"index":65450,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974527955,"difficulty":0.0025472045}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Lisa can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Lisa"],"index":29103,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984089732,"difficulty":0.0015910268}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna does not know whether Mohammad is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Mohammad can now know whether Jeannine can know that Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeannine","Donna","Mohammad","Williams"],"index":4686,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9815276265,"difficulty":0.0184723735}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shauna does not know whether Shauna's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jacob can now know that Jacob's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linda","Jacob","Shauna"],"index":18050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924227595,"difficulty":0.0075772405}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernest does not know whether Melvin is thirsty. It is publicly announced that Ernest does not know whether Stephanie is thirsty.","smcdel_problem":"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 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Melvin can now know that Ernest can know whether Bobby is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ernest","Melvin","Bobby","Stephanie"],"index":56605,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9947015047,"difficulty":0.0052984953}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carla's card is shown to Ana. Christina's card is shown to Ana. Ana's card is shown to Rachelle. Christina's card is shown to Rachelle. Rachelle's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,4 Agentc:3 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:2,4 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ana can now know whether Rachelle can know that Carla picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ana","Carla","Rachelle","Christina"],"index":49407,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9117313027,"difficulty":0.0882686973}
+{"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 Bert. Daniel's card is shown to Bert. Bert's card is shown to James. Bert'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:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Bert can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bert","James","Daniel"],"index":39604,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981303811,"difficulty":0.0018696189}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Fredrick is thirsty. It is publicly announced that Rita knows whether Fredrick 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 (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":"Rita can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rita","Connie","Fredrick"],"index":34041,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997810721,"difficulty":0.0002189279}
+{"premise":"There are four persons. Everyone is visible 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 Terry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Myrtle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Peter","Linda","Myrtle"],"index":43926,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982734919,"difficulty":0.0017265081}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Jeanne. Jeanne's card is shown to Donnell. 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 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":"Susan can now know whether Jeanne can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeanne","Susan","Donnell"],"index":3213,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997034669,"difficulty":0.0002965331}
+{"premise":"There are three persons. Everyone is visible 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.","smcdel_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":"William can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","William","Martha"],"index":60435,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996298552,"difficulty":0.0003701448}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monique knows whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Monique can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Monique","Misti","Dale"],"index":48278,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983281493,"difficulty":0.0016718507}
+{"premise":"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 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 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Calvin can now know whether James can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Stella","Calvin"],"index":46779,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9766814113,"difficulty":0.0233185887}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Cheryl. Stacy's card is shown to Cheryl. Andrew's card is shown to Stacy. Cheryl's card is shown to Andrew. Cheryl's card is shown to Elouise. Stacy's card is shown to Elouise. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stacy can now know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cheryl","Stacy","Andrew","Elouise"],"index":49182,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977737069,"difficulty":0.0022262931}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward does not know whether Mark is thirsty. It is publicly announced that Edward does not know whether Delores 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) ] (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 3) ] 0","hypothesis":"Mark can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Mark","Delores"],"index":34239,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999717176,"difficulty":0.000282824}
+{"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 Stephanie. Justin's card is shown to Justin. Otis's card is shown to Justin. Donald's card is shown to Justin. Justin'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 Stephanie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Justin can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Justin","Otis","Donald"],"index":23962,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6738021374,"difficulty":0.3261978626}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Eugene can now know that Shawn can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Eugene","Shawn","Charlene"],"index":63307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996109605,"difficulty":0.0003890395}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gloria","Terry","Thomas","Fredrick"],"index":51653,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998329103,"difficulty":0.001670897}
+{"premise":"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 Mindi's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mindi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Dolly can now know that Mindi's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Terrance","Dolly","Mindi"],"index":45520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9325314164,"difficulty":0.0674685836}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Teddy's card is shown to Emily. Emily's card is shown to Teddy. Jennifer's card is shown to Teddy. Teddy's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teddy can now know whether Jennifer picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Emily","Teddy","Jennifer"],"index":63467,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7084209323,"difficulty":1.7084209323}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Connie can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Connie","Frances"],"index":419,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984099865,"difficulty":0.0015900135}
+{"premise":"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 Michael knows whether Doyle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Michael can now know whether Doyle can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Doyle","Michael"],"index":26814,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997562766,"difficulty":0.0002437234}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frank's card is shown to Mary. Mary's card is shown to Nichelle. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank does not know whether Nichelle picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mary can now know whether Nichelle can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Nichelle","Frank"],"index":48991,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997057319,"difficulty":0.0002942681}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eloy does not know whether or not everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Bart can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eloy","Bart"],"index":41508,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9960869551,"difficulty":0.0039130449}
+{"premise":"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 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Joe can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Mark","Joe","Heather"],"index":42766,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928213954,"difficulty":0.0071786046}
+{"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 Joshua is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 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 2) ] 0","hypothesis":"Joshua can now know that Brenda can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Joshua","Brenda","Julie"],"index":6800,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9981538653,"difficulty":0.0018461347}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcus is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agenta knows 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":"Donald can now know whether Charles can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Marcus","Donald","Herman"],"index":63889,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6092300415,"difficulty":0.3907699585}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy. It is publicly announced that Mike knows whether Larry's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Mike can now know whether Larry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Larry","Mike"],"index":19030,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996900558,"difficulty":0.0003099442}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Aaron knows whether or not nobody is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Danielle can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Aaron","James","Danielle"],"index":13582,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999715507,"difficulty":0.000284493}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reynaldo knows whether or not everyone's forehead is muddy. It is publicly announced that Angela'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 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Joseph can now know that Byron's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Byron","Angela","Reynaldo"],"index":1048,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.962492466,"difficulty":0.037507534}
+{"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 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 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether Marie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","David","Michael","Marie"],"index":29624,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995141029,"difficulty":0.0004858971}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina does not know whether Tina's forehead is muddy. It is publicly announced that Annette knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Tina can now know whether Annette can know whether Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annette","Tina"],"index":41465,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991426468,"difficulty":0.0008573532}
+{"premise":"There are three persons. Everyone is visible 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 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":"Joseph can now know that Allison's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Antonina","Allison","Joseph"],"index":26118,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963032007,"difficulty":0.0036967993}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joseph is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Joseph can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joseph","Maryanne"],"index":66478,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7059283853,"difficulty":0.2940716147}
+{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Ashley can now know that Cherie can know that Cherie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Shannon","Ashley","Cherie"],"index":45278,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983438253,"difficulty":0.0016561747}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (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":"Corliss can now know that Richard can know that Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Richard","Corliss"],"index":22191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963693619,"difficulty":0.0036306381}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Duane. Myrna's card is shown to Duane. Myrna's card is shown to Myrna. Terry's card is shown to Olympia. Myrna's card is shown to Terry. It is publicly announced that someone picked a red card. It is publicly announced that Myrna does not know whether Terry picked a red card. It is publicly announced that Myrna knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Olympia can now know whether Terry can know that Olympia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Duane","Myrna","Olympia","Terry"],"index":59614,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8494510651,"difficulty":0.1505489349}
+{"premise":"There are three persons. Everyone is visible 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 Francis knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Francis can now know that Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Francis","Debra"],"index":17384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959394932,"difficulty":0.0040605068}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jennie knows whether Jennie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentb knows that (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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Alfonso can now know that Kelvin can know that Mark is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennie","Alfonso","Kelvin","Mark"],"index":49450,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998225987,"difficulty":0.001774013}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether someone's forehead is muddy. It is publicly announced that Arlene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Pauline can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Travis","Christopher","Arlene","Pauline"],"index":14665,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997746348,"difficulty":0.0002253652}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 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) ] [ ! 4 ] 0","hypothesis":"Shawn can now know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josette","Vicki","Shawn","Margaret"],"index":11477,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.8203622103,"difficulty":0.1796377897}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Dean can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Dean","Marla","Maribel"],"index":35858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984428287,"difficulty":0.0015571713}
+{"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. Martha's card is shown to Helen. Maria's card is shown to Martha. 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 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":"Helen can now know whether Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","Donald","Helen","Martha"],"index":33187,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8358110785,"difficulty":0.1641889215}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecil 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 (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":"Cecil can now know that Jose can know whether Raymond's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ken","Jose","Cecil","Raymond"],"index":819,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999717772,"difficulty":0.000282228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether 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":"Vera can now know that Raymond can know whether Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vera","Raymond","Tonie","James"],"index":61764,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9935888052,"difficulty":0.0064111948}
+{"premise":"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 Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] 0","hypothesis":"Kathy can now know that Edward can know whether Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edward","Kathy"],"index":25840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995151758,"difficulty":0.0004848242}
+{"premise":"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'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) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Sylvia can now know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Sylvia","Doris","Helen"],"index":12650,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995747209,"difficulty":0.0004252791}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ada's card is shown to Ada. William's card is shown to Ada. Ada's card is shown to Harry. William's card is shown to Harry. Ada's card is shown to William. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ada can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ada","Harry","William"],"index":65218,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983385801,"difficulty":0.0016614199}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether or not everyone is thirsty. It is publicly announced that Christopher does not know whether James is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Jesus knows 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&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Christopher can now know that Jesus can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jesus","James","Christopher"],"index":54729,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6169556379,"difficulty":0.3830443621}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Marie knows whether Harry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Harry can now know that Leana can know whether Leana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marie","Harry","Leana"],"index":37368,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7550287247,"difficulty":1.7550287247}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Micheal's card is shown to Sonia. Micheal's card is shown to Micheal. It is publicly announced that someone picked a red card. It is publicly announced that Sonia knows whether Sonia picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sonia can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sonia","Micheal"],"index":10963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986200333,"difficulty":0.0013799667}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jillian knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Anthony can now know whether Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anthony","Jillian","Christopher","Stephen"],"index":26033,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9620984793,"difficulty":0.0379015207}
+{"premise":"There are three persons. Everyone is visible 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 Ronnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"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":"Thomas can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harold","Thomas","Ronnie"],"index":12513,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995111227,"difficulty":0.0004888773}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Claudia does not know whether Christopher is thirsty. It is publicly announced that Dave does not know whether Claudia is thirsty. It is publicly announced that Christopher is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Christopher can now know that Christopher is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Claudia","Christopher","Dave"],"index":31446,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.849976778,"difficulty":0.150023222}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Peggy is not thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Peggy does not know whether Jerry is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know whether Bradley is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bradley","Peggy","Jerry"],"index":31507,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9893632531,"difficulty":0.0106367469}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Marie. It is publicly announced that someone picked a red card. It is publicly announced that Marie does not know whether Marie picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Robert can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Marie"],"index":911,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985979199,"difficulty":0.0014020801}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Edith can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Sue","Edith"],"index":42969,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9847962856,"difficulty":0.0152037144}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether someone is thirsty. It is publicly announced that William knows whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"William can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kevin","Ora","William"],"index":53057,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990630746,"difficulty":0.0009369254}
+{"premise":"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 does not know whether Timothy's forehead is muddy. It is publicly announced that Dorthy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agenta knows whether (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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] 0","hypothesis":"Eddie can now know whether Dorthy can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eddie","Timothy","John","Dorthy"],"index":65962,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980042577,"difficulty":0.0019957423}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is muddy. It is publicly announced that Frank does not know whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Steven can now know whether Frank can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","Steven","Ruth"],"index":46943,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991167188,"difficulty":0.0008832812}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Peggy's card is shown to Peggy. Mary's card is shown to Peggy. Peggy's card is shown to Mayme. Mary's card is shown to Mayme. Mary's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know whether Peggy can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peggy","Mayme","Mary"],"index":18602,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981910586,"difficulty":0.0018089414}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernestine knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Andrew can now know whether Deann can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernestine","Andrew","Deann"],"index":47246,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9858658314,"difficulty":0.0141341686}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Octavia's card is shown to Billye. Lisa's card is shown to Billye. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Octavia can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Octavia","Lisa","Billye"],"index":67251,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998362124,"difficulty":0.001637876}
+{"premise":"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 John's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Constance can now know whether Grace can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","John","Constance","Grace"],"index":38096,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.984310627,"difficulty":0.015689373}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows whether 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":"Beverly can now know that Mary can know whether Beverly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Beverly"],"index":49796,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999194324,"difficulty":0.000805676}
+{"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":"Major can now know that Randy can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","John","Larry","Major"],"index":48049,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997614026,"difficulty":0.0002385974}
+{"premise":"There are three persons. Everyone is visible 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 Fletcher's forehead is muddy.","smcdel_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":"William can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katherine","William","Fletcher"],"index":52817,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984925985,"difficulty":0.0015074015}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Petronila does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Petronila","Richard","James","Melissa"],"index":5819,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Mae can now know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Jimmy","John","Mae"],"index":66557,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984498024,"difficulty":0.0015501976}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eddie does not know whether Sharon 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 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) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"John can now know whether James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sharon","Eddie","James","John"],"index":14624,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 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) ] [ ! 3 ] 0","hypothesis":"Betty can now know that Ruby can know whether Ruby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruby","Betty","Patricia"],"index":58363,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9542159438,"difficulty":0.0457840562}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Alvin can now know that Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jonathan","Paul","Shalonda","Alvin"],"index":33539,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9771853089,"difficulty":0.0228146911}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Sharon. Sherri's card is shown to Sharon. Sharon's card is shown to James. Sherri's card is shown to James. Sharon's card is shown to Sherri. Sherri's card is shown to Sherri. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sherri can now know that James can know that Sherri picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","James","Sherri"],"index":55979,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970178604,"difficulty":0.0029821396}
+{"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. Lynda's card is shown to Cecil. Robert's card is shown to Lynda. Cecil's card is shown to Lynda. It is publicly announced that someone picked a red card. It is publicly announced that Robert does not know whether Cecil 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:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2&3)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Cecil","Lynda"],"index":31027,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9943318367,"difficulty":0.0056681633}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shelley is not thirsty. It is publicly announced that Aline knows whether Shelley is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Aline can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shelley","Aline","Jeffrey"],"index":53125,"s-l":"internal-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's forehead is muddy. It is publicly announced that Xavier does not know whether Xavier's forehead is muddy. It is publicly announced that Barbera does not know whether Barbera's forehead is muddy. It is publicly announced that Xavier 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 (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Barbara can now know that James can know that Xavier's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbera","Barbara","Xavier","James"],"index":41201,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9844685197,"difficulty":0.0155314803}
+{"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 James. James's card is shown to Thomas. Thomas's card is shown to Marilyn. Luis's card is shown to Marilyn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know whether Luis can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Thomas","Luis","Marilyn"],"index":9841,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9114383459,"difficulty":0.0885616541}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Connie 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 whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (1|2) ] 0","hypothesis":"Janell can now know whether Connie can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Connie","Janell"],"index":10274,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995786548,"difficulty":0.0004213452}
+{"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. Christina's card is shown to Christina. It is publicly announced that someone picked a red card. It is publicly announced that Mark does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Christina can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Christina","Jeffrey"],"index":13814,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.892000854,"difficulty":0.107999146}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elbert does not know whether or not everyone is thirsty. It is publicly announced that Elbert knows whether Elbert is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether 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":"Karen can now know whether Elbert can know whether Elbert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Karen","Elbert"],"index":9741,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998705864,"difficulty":0.001294136}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alvin","Mary","Harley","Jennifer"],"index":47782,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982985854,"difficulty":0.0017014146}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aurelia'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 that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Lillian can now know whether Aurelia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lillian","Aurelia"],"index":66730,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995322227,"difficulty":0.0004677773}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone'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) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Kimberly can now know whether Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bruce","Kimberly","Mark","Clare"],"index":65480,"s-l":"forehead_mirror-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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(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":"Fallon can now know whether Charles can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Charles","Fallon"],"index":35183,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999712646,"difficulty":0.000287354}
+{"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":"Andrea can now know that Sophie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vivian","Andrea","Sophie","Earl"],"index":29409,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938976169,"difficulty":0.0061023831}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Lillian. Lillian's card is shown to Gregorio. Lawrence's card is shown to Gregorio. Gregorio'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 Gregorio knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Lillian can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lillian","Gregorio","Lawrence"],"index":31424,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997720122,"difficulty":0.0002279878}
+{"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 Elwood. Elwood's card is shown to Kisha. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Donald can now know that Donald picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Ashley","Elwood","Kisha"],"index":10614,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984629154,"difficulty":0.0015370846}
+{"premise":"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) ] (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":"Lisa can now know whether Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lisa","Jason","Randall","Carolyn"],"index":66,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9915906191,"difficulty":1.9915906191}
+{"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 Roland. William's card is shown to Roland. Roland's card is shown to Raymond. Raymond's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Roland does not know whether Roland 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 (Agentb 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":"Roland can now know whether Raymond can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roland","Raymond","William"],"index":5295,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996979237,"difficulty":0.0003020763}
+{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Joe can now know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marilyn","Joe"],"index":56346,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984052777,"difficulty":0.0015947223}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leandro's card is shown to Jennifer. Walter's card is shown to Walter. Leandro's card is shown to Susan. Leandro's card is shown to Leandro. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether Susan picked a red card. It is publicly announced that Walter picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 2 ] 0","hypothesis":"Walter can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennifer","Walter","Susan","Leandro"],"index":64646,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997803569,"difficulty":0.0002196431}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eddie knows whether Eddie'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 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 2) ] 0","hypothesis":"Eddie can now know whether Patricia can know that Eddie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Eddie"],"index":10417,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
+{"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 Vicki. Ian's card is shown to Vicki. Vicki's card is shown to Maurice. Maurice's card is shown to Ian. Ian's card is shown to Ian. It is publicly announced that someone picked a red card. It is publicly announced that Maurice picked a black card. It is publicly announced that Maurice picked a black card. It is publicly announced that Clarence 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 whether (1|2|3|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":"Maurice can now know whether Clarence can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vicki","Maurice","Clarence","Ian"],"index":57995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Robin. Sandra's card is shown to Robin. Sherry's card is shown to Sherry. Andrea's card is shown to Sherry. Sherry's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 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":"Sherry can now know that Robin can know that Sandra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robin","Sherry","Andrea","Sandra"],"index":20770,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976923466,"difficulty":0.0023076534}
+{"premise":"There are four persons. Everyone is visible 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 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":"Margot can now know that Elizabeth can know that Margot's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dorothy","Margot","Joel","Elizabeth"],"index":22680,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9952706695,"difficulty":0.0047293305}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marilynn's card is shown to Marilynn. Barbara's card is shown to Rosa. Rosa's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Barbara picked a red card. It is publicly announced that Marilynn does not know whether Rosa picked a red card. It is publicly announced that John picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Marilynn can now know that Rosa can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marilynn","John","Rosa","Barbara"],"index":12458,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968247414,"difficulty":0.0031752586}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Fay can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Fay","Dawn"],"index":41628,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997828603,"difficulty":0.0002171397}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Gary. Charlie's card is shown to Gary. Gary's card is shown to Charlie. 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) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Gary can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Robert","Charlie"],"index":57436,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980097413,"difficulty":0.0019902587}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela does not know whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentb knows 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":"Angela can now know whether Teodoro can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sandra","Teodoro","Angela"],"index":3782,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9182172418,"difficulty":0.0817827582}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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":"Jamie can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverly","Richard","Cleo","Jamie"],"index":63135,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996007085,"difficulty":0.0003992915}
+{"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 Peter. Herman's card is shown to Herman. Herman's card is shown to Frank. 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)) ] Agentc knows that (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":"Frank can now know that Peter can know whether Herman picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peter","Herman","Frank"],"index":13176,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9907916784,"difficulty":0.0092083216}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW 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":"Nancy can now know that Elizabeth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","James","Nancy"],"index":56660,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983237386,"difficulty":0.0016762614}
+{"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 John. Michael's card is shown to Annie. Annie's card is shown to Theresa. John's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Theresa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Annie","Theresa","Michael"],"index":31278,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997686744,"difficulty":0.0002313256}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Seymour can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","Seymour","Ruth","Sandra"],"index":40667,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roy's card is shown to Madonna. Madonna's card is shown to Roy. Andrea's card is shown to Roy. Betty's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Betty does not know whether Madonna picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Madonna can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Madonna","Roy","Betty","Andrea"],"index":8397,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999720037,"difficulty":0.000279963}
+{"premise":"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 Alejandro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether Leo can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stanley","Helen","Leo","Alejandro"],"index":42509,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.972982347,"difficulty":0.027017653}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether Christina 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 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) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Christina can now know whether Wendell is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christina","Wendell","Melissa","Phillip"],"index":29374,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9943557978,"difficulty":0.0056442022}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rita's card is shown to Alice. Alice's card is shown to Chad. Chad's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Chad knows whether someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Chad does not know whether Chad 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)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alice can now know whether Rita can know that Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alice","Chad","Rita"],"index":34021,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8533592224,"difficulty":0.1466407776}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy. It is publicly announced that Aaron does not know whether Aaron's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Aaron can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Matthew","Douglas","Aaron"],"index":11673,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9546611905,"difficulty":1.9546611905}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allison's card is shown to Allison. Maria's card is shown to Allison. Margaret's card is shown to Maria. Maria's card is shown to David. David's card is shown to Margaret. Margaret's card is shown to Margaret. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Margaret can now know that Allison can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Allison","Maria","David","Margaret"],"index":8851,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958875775,"difficulty":0.0041124225}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita does not know whether Rita's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentc knows whether 3)","n_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":"Daniel can now know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Julian","Rita","Daniel"],"index":31028,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9853459597,"difficulty":0.0146540403}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Scott can now know that Richard can know that Zachary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Zachary","Denise","Scott"],"index":543,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.967792213,"difficulty":0.032207787}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy does not know whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 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) ] 0","hypothesis":"Kenneth can now know that Randy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Randy","Steven","Kenneth"],"index":40364,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998341918,"difficulty":0.001658082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucinda does not know whether Lucinda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Michael can now know whether Gloria can know whether Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Kenneth","Lucinda","Michael"],"index":3080,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9072183371,"difficulty":0.0927816629}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Xavier does not know whether Javier is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Xavier knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Roy can now know whether Javier is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammy","Xavier","Javier","Roy"],"index":21327,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9586485624,"difficulty":0.0413514376}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deann's card is shown to Deann. Annette's card is shown to Deann. Deann's card is shown to Annette. Tamar's card is shown to Tamar. It is publicly announced that someone picked a red card. It is publicly announced that Annette picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Deann can now know that Annette can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deann","Annette","Tamar"],"index":59587,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7235605717,"difficulty":1.7235605717}
+{"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 Douglas knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Kay can now know that Latoya is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Kay","Douglas","Latoya"],"index":63183,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937667847,"difficulty":0.0062332153}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew 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) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Andrew can now know that Andrew is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Andrew","Craig","Johnny"],"index":54102,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9822683334,"difficulty":0.0177316666}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentc knows that 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":"Robert can now know that Michele can know that Marlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frank","Marlene","Michele","Robert"],"index":27370,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994771421,"difficulty":0.005228579}
+{"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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Salvatore can now know whether Clarence can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jackie","Salvatore","John","Clarence"],"index":1695,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987673759,"difficulty":0.0012326241}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eileen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Eileen can now know whether Juliet can know that Oswaldo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Eileen","Oswaldo","Juliet"],"index":5303,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996680021,"difficulty":0.0003319979}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mary can now know that James can know whether Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","James","Nina","Mary"],"index":35965,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997310042,"difficulty":0.0002689958}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Jean can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jean","James"],"index":32633,"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. Each person draws a card, face unrevealed (red or black). Christy's card is shown to Christy. Mattie's card is shown to Christy. Christy's card is shown to Stephanie. Stephanie's card is shown to Stephanie. Mattie's card is shown to Mattie. Mattie's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Janet does not know whether Christy picked a red card. It is publicly announced that Christy knows whether or not nobody picked a red card. It is publicly announced that Mattie does not know whether Janet picked a red card. It is publicly announced that Stephanie 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)) ] Agentd knows whether (Agentc knows that (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":"Janet can now know whether Mattie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christy","Stephanie","Mattie","Janet"],"index":8361,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997748733,"difficulty":0.0002251267}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John knows whether John is thirsty. It is publicly announced that John does not know whether Janet 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 whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Janet can now know whether John can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janet","John"],"index":41314,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (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) ] [ ! ~(1) ] 0","hypothesis":"Carmen can now know whether Latoya's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carmen","Lewis","Jeffery","Latoya"],"index":27500,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994018078,"difficulty":0.0005981922}
+{"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 Walter. Arthur's card is shown to Walter. William's card is shown to William. Arthur's card is shown to William. Walter'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:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Walter can know that Walter picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Walter","William","Arthur"],"index":42579,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956650138,"difficulty":0.0043349862}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not everyone'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) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Giuseppe can now know whether Sam's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Raymond","Sam","Giuseppe"],"index":53245,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994444251,"difficulty":0.0005555749}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jarrod'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 (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Christine can now know whether Jarrod can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrin","Jarrod","Christine","James"],"index":67433,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gustavo knows whether or not nobody's forehead is muddy. It is publicly announced that Judith does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (~(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":"Judith can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gustavo","Lucille","Judith"],"index":40833,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979858398,"difficulty":0.0020141602}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is muddy. It is publicly announced that Tiffany 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 (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Frances can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tiffany","Art","Frances","Nora"],"index":31787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997196794,"difficulty":0.0002803206}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emil's card is shown to Lois. Kevin's card is shown to Emil. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin knows whether or not everyone picked a red card. It is publicly announced that Emil does not know whether Lois 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 2)","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":"Emil can now know that Lois can know whether Emil picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lois","Emil","Kevin"],"index":23449,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5845060945,"difficulty":0.4154939055}
+{"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. Colleen's card is shown to Marjorie. Emily's card is shown to Marjorie. Colleen's card is shown to Colleen. Emily's card is shown to Colleen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether 2)","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":"Colleen can now know whether Marjorie can know whether Colleen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marjorie","Colleen","Emily"],"index":33390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9975334406,"difficulty":0.0024665594}
+{"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 Dan. Angela's card is shown to Dan. Dan's card is shown to Frankie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dan can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dan","Roger","Angela","Frankie"],"index":63751,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9960839748,"difficulty":0.0039160252}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Robert's card is shown to Thomas. Thomas's card is shown to Thomas. Edward's card is shown to Edward. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 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:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know that Edward can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Thomas","Edward"],"index":5206,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.528580308,"difficulty":0.471419692}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Todd's card is shown to Todd. Timothy's card is shown to Jeffery. Todd's card is shown to Timothy. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Jeffery picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Timothy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Todd","Jeffery","Timothy"],"index":19317,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7587486506,"difficulty":1.7587486506}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Aaron can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aaron","Devon","Leslie","Eva"],"index":11935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978786707,"difficulty":0.0021213293}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows 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|2|3|4))) ] 0","hypothesis":"Donna can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Donna","Amber","Tracy"],"index":43901,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997614026,"difficulty":0.0002385974}
+{"premise":"There are three persons. Everyone is visible 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 Janet's forehead is muddy. It is publicly announced that Janet knows whether Ernestine's forehead is muddy. It is publicly announced that Brian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows that (Agentb knows that (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":"Ernestine can now know that Janet can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ernestine","Janet","Brian"],"index":35932,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983731508,"difficulty":0.0016268492}
+{"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 Kenneth. Adrian's card is shown to Nicole. Kathryn's card is shown to Adrian. It is publicly announced that someone picked a red card. It is publicly announced that Nicole does not know whether Nicole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Adrian can now know that Nicole can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Nicole","Adrian","Kathryn"],"index":15965,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9996995926,"difficulty":0.0003004074}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Betty. Betty's card is shown to Pamela. Pamela's card is shown to Pamela. Jaime's card is shown to Jaime. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Pamela can now know whether Sharon can know whether Pamela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Pamela","Sharon","Jaime"],"index":868,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987624884,"difficulty":0.0012375116}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Cory. Jessica's card is shown to Kristan. Jessica's card is shown to Nancy. Kristan's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 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 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cory can now know whether Kristan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Cory","Kristan","Nancy"],"index":4783,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9875385761,"difficulty":1.9875385761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sean does not know whether Jay is thirsty.","smcdel_problem":"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 (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Karen can now know whether Dolores can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dolores","Karen","Jay","Sean"],"index":48472,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8252419829,"difficulty":0.1747580171}
+{"premise":"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) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"David can now know whether Steven can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Steven","David"],"index":10170,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6253997087,"difficulty":1.6253997087}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ross's forehead is not muddy. It is publicly announced that Bob knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Bob can now know whether Ross's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bob","Ross","Roland"],"index":29887,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995997548,"difficulty":0.0004002452}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brandy is thirsty. It is publicly announced that Jo 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 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) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jo can now know that Holly can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Holly","Brandy","Frank","Jo"],"index":52950,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9915583134,"difficulty":0.0084416866}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (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":"Livia can now know that Carl can know that Jordan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Livia","Jordan","Carl","Sabrina"],"index":7985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.996420145,"difficulty":0.003579855}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2 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":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","John"],"index":26156,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983147383,"difficulty":0.0016852617}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows whether (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":"Arthur can now know whether Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joshua","Arthur","Robert"],"index":8201,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997655749,"difficulty":0.0002344251}
+{"premise":"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 someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Bradley'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 (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Leesa can now know whether Jacqueline can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Leesa","Bradley","Jacqueline"],"index":48043,"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 is thirsty. It is publicly announced that Rosemary does not know whether Carol is thirsty. It is publicly announced that Richard does not know whether Ronnie is thirsty. It is publicly announced that Ronnie does not know whether Rosemary is thirsty. It is publicly announced that Rosemary 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 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) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Carol can now know that Carol is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Carol","Rosemary","Ronnie"],"index":54248,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9923311472,"difficulty":0.0076688528}
+{"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 Jack is thirsty. It is publicly announced that Diane does not know whether James is thirsty. It is publicly announced that Jack is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Jack can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Thomas","James","Jack","Diane"],"index":976,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997256398,"difficulty":0.0002743602}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas does not know whether Natalie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Thomas can now know whether Steven can know that Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Natalie","Steven","Thomas"],"index":65757,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.5839701295,"difficulty":0.4160298705}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana does not know whether Katrina is thirsty. It is publicly announced that Martha does not know whether Diana is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Diana can now know whether Katrina can know that Katrina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Martha","Katrina","Harry"],"index":19532,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8746024966,"difficulty":1.8746024966}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebecca's card is shown to Rebecca. Mario's card is shown to Rebecca. Rebecca's card is shown to Mario. It is publicly announced that someone picked a red card. It is publicly announced that Rebecca knows whether or not everyone picked a red card. It is publicly announced that Mario 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 whether (1&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":"Mario can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Rebecca","Mario"],"index":5697,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8737146854,"difficulty":1.8737146854}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to John. Heather's card is shown to Joe. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Joe knows whether or not everyone 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 whether (1&2&3)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether Joe can know that Joe picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Joe","Heather"],"index":16390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8960309029,"difficulty":0.1039690971}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Denise can now know that Jeffery can know whether Denise's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Jeffrey","Jeffery","Denise"],"index":42451,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997169375,"difficulty":0.0002830625}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (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: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":"Joseph can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Jennifer","Keenan","Joseph"],"index":48001,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978715181,"difficulty":0.0021284819}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kasey's card is shown to Kasey. Helen's card is shown to Kasey. Kasey's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Kasey can now know that Helen can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kasey","Helen"],"index":30808,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9926396608,"difficulty":0.0073603392}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"William can now know whether Sylvester can know that Sylvester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Jonathan","William","Sylvester"],"index":48686,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996266365,"difficulty":0.0003733635}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (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 ] 0","hypothesis":"Barbara can now know whether Karen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Barbara","Karen","Brendan"],"index":36967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997346997,"difficulty":0.0002653003}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 4 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Shawna can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shawna","Anna","Mary","Sylvia"],"index":2873,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9880644679,"difficulty":0.0119355321}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Daniel can now know that Tiffany can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","Daniel","Patrick","Tiffany"],"index":29184,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997867942,"difficulty":0.0002132058}
+{"premise":"There are three persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 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 Ignacio can know that Mary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Ignacio","Edward"],"index":23059,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996660948,"difficulty":0.0003339052}
+{"premise":"There are two persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agenta knows whether (Agentb knows 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 ] 0","hypothesis":"Robert can now know whether Rosalie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Rosalie"],"index":13967,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999787271,"difficulty":0.000212729}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felicia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 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":"Felicia can now know that James can know that Whitney's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Felicia","James","Whitney"],"index":30863,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9476923943,"difficulty":0.0523076057}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether Theresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Frank","Paul","Theresa","Sheba"],"index":33840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995660186,"difficulty":0.0004339814}
+{"premise":"There are four persons. Everyone is visible 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 Mary knows whether Beatrice's forehead is muddy. It is publicly announced that Joseph 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 that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agentc knows whether 4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Mary can now know that Richard can know whether Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Joseph","Mary","Beatrice"],"index":64962,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996985197,"difficulty":0.0003014803}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Naomi knows whether Ronnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows 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":"Ronnie can now know that Ramona can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ronnie","Dana","Naomi","Ramona"],"index":8509,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9893364906,"difficulty":0.0106635094}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 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":"Phyllis can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","Leonard","Phyllis"],"index":42604,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997606874,"difficulty":0.0002393126}
+{"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. Sarah's card is shown to Gary. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Sarah does not know whether Gary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (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":"Gary can now know whether Sarah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gary","Sarah"],"index":28758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6251158714,"difficulty":0.3748841286}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jennifer can now know that Latoya can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Shirley","Latoya","David"],"index":21006,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984117746,"difficulty":0.0015882254}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"William can now know whether Lola can know that Gerald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gerald","Lola","William"],"index":63515,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996773005,"difficulty":0.0003226995}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kent does not know whether or not everyone's forehead is muddy. It is publicly announced that Minnie 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)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Minnie can now know that Kent can know whether Kent's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Minnie","Bradley","Carla","Kent"],"index":51342,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5991976857,"difficulty":0.4008023143}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathaniel's card is shown to Ellen. Ellen's card is shown to Lisa. Lisa's card is shown to Petra. Ellen'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:4 Agentb:1 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nathaniel can now know whether Lisa can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ellen","Lisa","Petra","Nathaniel"],"index":55157,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9995802045,"difficulty":0.0004197955}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Duane's card is shown to Christopher. Christopher's card is shown to Duane. It is publicly announced that someone picked a red card. It is publicly announced that Duane picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Duane can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christopher","Duane"],"index":46213,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976818562,"difficulty":0.0023181438}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandi knows whether Iva's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Iva does not know whether Iva's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|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":"Iva can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brandi","Ethel","Iva"],"index":47181,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983462095,"difficulty":0.0016537905}
+{"premise":"There are three persons. Everyone is visible 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) ] [ ! 3 ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tyler","Terry","David"],"index":20345,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979959726,"difficulty":0.0020040274}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Thomas knows whether Rebecca's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentb knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know that Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Thomas","David","Rebecca"],"index":44779,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997788072,"difficulty":0.0002211928}
+{"premise":"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 Peter knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Joann can now know whether Peter can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Peter","Joann"],"index":776,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.985491693,"difficulty":0.014508307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlton knows whether or not nobody's forehead is muddy. It is publicly announced that Joshua's forehead is not muddy. It is publicly announced that Alisha does not know whether Alisha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (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))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Carlton can now know whether Joshua can know whether Alisha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alisha","Joshua","Carlton"],"index":15651,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998739779,"difficulty":0.001260221}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laveta knows whether Miguel's forehead is muddy. It is publicly announced that Laveta knows whether or not everyone's forehead is muddy. It is publicly announced that Miguel knows whether Laveta'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) ] 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 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Miguel can now know that Laveta can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Laveta","Miguel"],"index":2905,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981360435,"difficulty":0.0018639565}
+{"premise":"There are 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":"Marie can now know that Bonnie can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marie","Mary","Bonnie","Tamara"],"index":38626,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996180534,"difficulty":0.0003819466}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Travis can now know that Tyrone can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tyrone","Inez","Darlene","Travis"],"index":12654,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997703433,"difficulty":0.0002296567}
+{"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 Daniel. Kristen's card is shown to Elizabeth. Daniel's card is shown to Kristen. Irma's card is shown to Kristen. Daniel's card is shown to Irma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Irma can now know whether Daniel can know that Kristen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Elizabeth","Kristen","Irma"],"index":42773,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9435341358,"difficulty":0.0564658642}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicole does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Nicole can now know that Betty can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Van","Michael","Nicole","Betty"],"index":60665,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998042345,"difficulty":0.001957655}
+{"premise":"There are 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 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":"Christopher can now know whether Frank can know that Anne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Clarissa","Anne","Christopher"],"index":39666,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996724129,"difficulty":0.0003275871}
+{"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 or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether (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":"Mary can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mary","David"],"index":17023,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9700345993,"difficulty":0.0299654007}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Angela 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) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Joseph can now know that Angela can know that Angela's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Joseph","Leslie"],"index":27954,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9740415812,"difficulty":0.0259584188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Mark can now know whether Nancy can know whether Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Henry","Mark","Tina"],"index":28182,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995253086,"difficulty":0.0004746914}
+{"premise":"There are four persons. Everyone is visible 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 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":"Sherry can now know whether Angelica can know that Angelica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","Sherry","Alesia","Angelica"],"index":2739,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999671936,"difficulty":0.000328064}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Clifford can now know whether Nellie can know that Clifford's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clifford","Daniel","Rose","Nellie"],"index":60470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9353080988,"difficulty":0.0646919012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felice does not know whether Felice's forehead is muddy. It is publicly announced that Marlin knows whether Marlin's forehead is muddy. It is publicly announced that Marlin knows whether Marlin's forehead is muddy.","smcdel_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) ] 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) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Felice can now know that Mona can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mona","Felice","Marlin"],"index":28700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984069467,"difficulty":0.0015930533}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claude's card is shown to Claude. Ruth's card is shown to Ruth. Ruth's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Claude does not know whether Michael 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) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Michael can now know whether Claude can know that Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Claude","Ruth","Michael"],"index":53222,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9626227021,"difficulty":0.0373772979}
+{"premise":"There are three persons. Everyone is visible 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 Kecia's forehead is muddy.","smcdel_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 (1&2&3))","n_announcements":1,"pbcheck":"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":"Kecia can now know that Michael can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Anthony","Kecia"],"index":2057,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996054769,"difficulty":0.0003945231}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luke's card is shown to Jerome. Linda's card is shown to Michelle. Michelle's card is shown to Luke. Michelle's card is shown to Linda. Linda's card is shown to Linda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Luke can now know whether Michelle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jerome","Michelle","Luke","Linda"],"index":5367,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7211518288,"difficulty":0.2788481712}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Ethel is thirsty. It is publicly announced that Richard does not know whether Ethel is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Richard can now know that Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ethel","Richard"],"index":45957,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9415147305,"difficulty":0.0584852695}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla knows whether or not nobody's forehead is muddy. It is publicly announced that Angelo 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 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":"Angelo can now know that Karla can know that Karla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Angelo","Karla"],"index":34209,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.7923565507,"difficulty":0.2076434493}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Vivian. Kevin's card is shown to Ellan. Vivian's card is shown to Kevin. Ellan's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Vivian can now know that Ellan can know whether Vivian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Vivian","Ellan","Kevin"],"index":8814,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7436295748,"difficulty":1.7436295748}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brent's card is shown to Brent. Lloyd's card is shown to Brent. Brent's card is shown to Joseph. Robert's card is shown to Robert. Brent's card is shown to Lloyd. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:3 Agentd:1 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:1,4 Agentb:1 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brent","Joseph","Robert","Lloyd"],"index":11661,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999778688,"difficulty":0.000221312}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Terry knows whether or not everyone is thirsty. It is publicly announced that Carmen 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|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Carmen can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carmen","Terry"],"index":16597,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984161854,"difficulty":0.0015838146}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shannon's card is shown to Shannon. Elsie's card is shown to Gilbert. Jessie's card is shown to Jessie. Shannon's card is shown to Elsie. It is publicly announced that someone picked a red card. It is publicly announced that Gilbert does not know whether Shannon picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Shannon picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] Agentb knows whether (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (~(1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Gilbert can now know whether Elsie can know that Shannon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shannon","Gilbert","Jessie","Elsie"],"index":49208,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9566926956,"difficulty":0.0433073044}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmelita's card is shown to Richard. Michael's card is shown to Earl. Earl's card is shown to Carmelita. Michael's card is shown to Carmelita. Richard's card is shown to Michael. Earl'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:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2,4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carmelita can now know whether Michael can know whether Richard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Earl","Carmelita","Michael"],"index":40473,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986988306,"difficulty":0.0013011694}
+{"premise":"There are 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 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":"Barry can now know that Meredith can know that Brendon's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brendon","Meredith","Barry"],"index":4039,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986112118,"difficulty":0.0013887882}
+{"premise":"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 knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Yvonne can now know whether Tara can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Yvonne","Tara","Heather"],"index":40857,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99975878,"difficulty":0.00024122}
+{"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 Reginald. Michelle's card is shown to Galen. 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 (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Galen can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Reginald","Galen","Michelle"],"index":58155,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997239709,"difficulty":0.0002760291}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paul is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Dacia can now know whether Paul can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paul","John","Dacia"],"index":22423,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973255396,"difficulty":0.0026744604}
+{"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. Evelyn's card is shown to Gladys. Karon's card is shown to Jeffrey. Evelyn's card is shown to Evelyn. It is publicly announced that someone picked a red card. It is publicly announced that Karon does not know whether Evelyn 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 Jeffrey does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Karon can now know that Jeffrey can know whether Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gladys","Karon","Jeffrey","Evelyn"],"index":55220,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8248391151,"difficulty":1.8248391151}
+{"premise":"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) ] 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) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know whether Kim can know that Kim's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Mary","Mathew"],"index":11609,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5876282454,"difficulty":1.5876282454}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth's forehead is muddy. It is publicly announced that James knows 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) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Ruth can now know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Evelyn","Ruth","Jennifer","James"],"index":24200,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6400895715,"difficulty":0.3599104285}
+{"premise":"There are four persons. Everyone is visible 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 1,2,3,4 LAW Top OBS Agenta: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 that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Howard can now know whether Sue can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Howard","Kim","Elizabeth","Sue"],"index":26387,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996114373,"difficulty":0.0003885627}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nydia's card is shown to Lynn. Lynn's card is shown to Nydia. It is publicly announced that someone picked a red card. It is publicly announced that Sonia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sonia can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynn","Sonia","Nydia"],"index":26040,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8682888746,"difficulty":1.8682888746}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leonard knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that 1)","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":"Nancy can now know that Leslie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leslie","Nancy","Leonard"],"index":16268,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9985496402,"difficulty":0.0014503598}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"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":"Marie can now know that Frederick can know that Frederick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frederick","Dan","Marie"],"index":24047,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9592051506,"difficulty":0.0407948494}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. John's card is shown to Cynthia. It is publicly announced that someone picked a red card. It is publicly announced that Matthew does not know whether Cynthia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Matthew can now know that Cynthia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Matthew","Cynthia"],"index":24626,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9958240986,"difficulty":0.0041759014}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cory knows whether or not nobody is thirsty. It is publicly announced that Bennett does not know whether Cory is thirsty. It is publicly announced that Geraldine does not know whether Bennett is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Bennett can now know that Geraldine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bennett","Cory","Geraldine"],"index":7794,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953532219,"difficulty":0.0046467781}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Charlotte can now know whether Dana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Dana","Charlotte"],"index":13881,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9959841967,"difficulty":0.0040158033}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Randall's card is shown to Randall. James's card is shown to Randall. Randall's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"James can now know that Randall can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Randall","James"],"index":33146,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984717965,"difficulty":0.0015282035}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Brenda's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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) ] (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) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mary can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Brenda","Mary","Helen"],"index":5497,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997506738,"difficulty":0.0002493262}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentc knows 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":"Kristie can now know whether Denver can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Harold","Denver","Kristie"],"index":36311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997091889,"difficulty":0.0002908111}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eddie's card is shown to Eddie. Eric's card is shown to Eddie. Jody's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Jody picked a black card. It is publicly announced that John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 4 ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! 4 ] 0","hypothesis":"Jody can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eddie","Jody","Eric","John"],"index":21416,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5821166039,"difficulty":1.5821166039}
+{"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. Shasta's card is shown to Shasta. Cary's card is shown to Cary. It is publicly announced that someone picked a red card. It is publicly announced that Michael does not know whether Cary 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 Shasta does not know whether Cary picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Shasta can now know that Michael can know whether Shasta picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Shasta","Cary"],"index":93,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8032312989,"difficulty":0.1967687011}
+{"premise":"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 Jesse's forehead is muddy. It is publicly announced that Frances 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 (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jesse can now know that Jerry can know whether Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Jerry","Jesse","Frances"],"index":62657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991500378,"difficulty":0.0008499622}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kimberley's card is shown to Kimberley. Kimberley's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether James 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 that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"James can now know that Kimberley can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kimberley","James"],"index":10837,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.954254508,"difficulty":1.954254508}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Judy","David","Judith"],"index":51799,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980339408,"difficulty":0.0019660592}
+{"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 Linda does not know whether Victoria 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 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":"Victoria can now know whether Robert can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Victoria","Linda"],"index":654,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997695088,"difficulty":0.0002304912}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremiah knows whether or not nobody's forehead is muddy. It is publicly announced that Fred 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 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":"Fred can now know that Jeremiah can know whether Jeremiah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Fred","Jeremiah"],"index":53616,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995293617,"difficulty":0.0004706383}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pablo's forehead is not muddy. It is publicly announced that Patsy knows whether Marsha's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marsha can now know that Patsy can know that Pablo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marsha","Patsy","Pablo"],"index":7226,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9948248863,"difficulty":0.0051751137}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tommy's card is shown to Tommy. 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 whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Victoria can now know whether Sharon picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Tommy","Brian","Sharon"],"index":21331,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9550871849,"difficulty":0.0449128151}
+{"premise":"There are two persons. Everyone is visible 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 knows whether Jeanette's forehead is muddy. It is publicly announced that Jeanette'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 (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":"Jeanette can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Damon","Jeanette"],"index":42169,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974609613,"difficulty":0.0025390387}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Dennis. Dennis's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Dennis does not know whether Richard 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 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":"Richard can now know that Dennis can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Richard"],"index":46937,"s-l":"explicit-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). Nathaniel's card is shown to Dana. Dana's card is shown to Nathaniel. Richard's card is shown to Nathaniel. Dana's card is shown to Richard. Richard's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nathaniel can now know that Richard can know that Nathaniel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dana","Nathaniel","Richard"],"index":6972,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970865846,"difficulty":0.0029134154}
+{"premise":"There are two 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. It is publicly announced that Fredrick knows whether or not nobody's forehead is muddy. It is publicly announced that Fredrick knows whether Fredrick's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Fredrick can now know whether Jack's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jack","Fredrick"],"index":61127,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994928837,"difficulty":0.0005071163}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Richard can now know that Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Richard","Margaret","Willie"],"index":57069,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979249239,"difficulty":0.0020750761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Henry 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 (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Daisy can now know that Jaime can know that Henry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Jaime","Daisy","Robert"],"index":32276,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9809311032,"difficulty":0.0190688968}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valeria knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"Valeria can now know that Stephen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Valeria","Stephen","Robert"],"index":16417,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983160496,"difficulty":0.0016839504}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula knows whether someone's forehead is muddy. It is publicly announced that Lesia 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 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":"Paula can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lesia","Paula"],"index":39005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985281229,"difficulty":0.0014718771}
+{"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 Alexis is thirsty. It is publicly announced that Alexis does not know whether Louis is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Jennifer can now know that Louis can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Jennifer","Alexis","Mark"],"index":47700,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
+{"premise":"There are three 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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Claude can now know that Josie can know whether Josie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josie","Agnes","Claude"],"index":57676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9883092642,"difficulty":0.0116907358}
+{"premise":"There are four persons. Everyone is visible 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 Emil knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michel can now know whether Elizabeth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Emil","Karol","Elizabeth","Michel"],"index":49145,"s-l":"forehead_mirror-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 Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Tracy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Joseph can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Felicia","Tracy","Joseph"],"index":10263,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984169006,"difficulty":0.0015830994}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not nobody's forehead is muddy. It is publicly announced that Ryan 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 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":"Ryan can now know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ryan","Laura"],"index":14355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994526505,"difficulty":0.0005473495}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Melissa can now know that Barbara can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Melissa","Betty","Tommie"],"index":29252,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982681274,"difficulty":0.0017318726}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Hilda does not know whether Wayne is thirsty. It is publicly announced that Adell does not know whether Paula is thirsty. It is publicly announced that Paula does not know whether Hilda is thirsty. It is publicly announced that Hilda 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)) ] (Agentc knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Hilda can now know that Paula is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adell","Wayne","Hilda","Paula"],"index":63073,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953018427,"difficulty":0.0046981573}
+{"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 Sara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 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) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Jessica can now know whether Darcie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karin","Sara","Jessica","Darcie"],"index":37863,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9881487489,"difficulty":0.0118512511}
+{"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. Raven's card is shown to Andrew. Christopher's card is shown to Cynthia. Raven's card is shown to Christopher. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrew can now know that Cynthia can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Cynthia","Christopher","Raven"],"index":25945,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9845476747,"difficulty":0.0154523253}
+{"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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (1&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":"Samantha can now know that Janet can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Samantha","Janet"],"index":34177,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9895883799,"difficulty":0.0104116201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Krystle is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":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":"Misty can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Krystle","Misty","Joannie","Cynthia"],"index":30415,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997373223,"difficulty":0.0002626777}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Nicolas's card is shown to Jessica. Jessica's card is shown to Carl. Nicolas's card is shown to Nicolas. Nicolas'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:1,3 Agentb:1 Agentc:3 Agentd:3 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:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicolas can now know whether Nicolas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Carl","Nicolas","Ruth"],"index":40512,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9869725108,"difficulty":0.0130274892}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jamie knows whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth'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 (~(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":"Elizabeth can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jamie","Elizabeth"],"index":34987,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984809756,"difficulty":0.0015190244}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mildred can now know whether Chana can know whether Danny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Danny","Mildred","Chana"],"index":6313,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992384911,"difficulty":0.0007615089}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cory 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&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":"Cory can now know that Andrew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cory","Andrew"],"index":49653,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9683306813,"difficulty":0.0316693187}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bob's card is shown to Jennifer. Eddie's card is shown to Bob. It is publicly announced that someone picked a red card. It is publicly announced that Eddie does not know whether Eddie picked a red card. It is publicly announced that Eddie knows whether or not nobody 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) ] [ ! (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:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jennifer can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eddie","Jennifer","Bob"],"index":36284,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
+{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Ebony can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Ebony","Silvia"],"index":28055,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984600544,"difficulty":0.0015399456}
+{"premise":"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 Eugenia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (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) ] 0","hypothesis":"Rose can now know that Jana can know whether Jana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eugenia","Rose","Violet","Jana"],"index":35663,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.991230011,"difficulty":0.008769989}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 1)","n_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":"Chris can now know that Mildred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mildred","Dorothy","Chris"],"index":20511,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976503253,"difficulty":0.0023496747}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ron knows whether someone's forehead is muddy. It is publicly announced that Ron knows whether Janet's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Janet can now know whether Ron can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Robert","Ron"],"index":49786,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7653000355,"difficulty":0.2346999645}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Janice is thirsty. It is publicly announced that Katherine does not know whether Larry is thirsty. It is publicly announced that Joseph knows whether or not nobody is thirsty. It is publicly announced that Joseph is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentb knows whether (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) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Katherine can now know whether Janice can know whether Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Katherine","Joseph","Janice"],"index":50592,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984039664,"difficulty":0.0015960336}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oscar knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"Chauncey can now know that Oscar can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Oscar","Chauncey","Marta"],"index":21664,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997808337,"difficulty":0.0002191663}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Patricia can now know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Joseph","Eugene"],"index":47663,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9692980647,"difficulty":0.0307019353}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Gloria. Elizabeth's card is shown to Gloria. Jessica's card is shown to Dean. Jessica's card is shown to Elizabeth. Gloria's card is shown to Jessica. Dean's card is shown to Jessica. It is publicly announced that someone picked a red card. It is publicly announced that Jessica picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Dean can now know that Gloria can know that Elizabeth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gloria","Dean","Elizabeth","Jessica"],"index":58908,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9587597251,"difficulty":0.0412402749}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ignacia does not know whether Weston is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether someone is thirsty. It is publicly announced that Weston does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ignacia can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ignacia","Weston"],"index":22859,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.996350646,"difficulty":0.003649354}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christina knows whether 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) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Christina can now know that Regina can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Regina","Thomas","Christina"],"index":10555,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984971285,"difficulty":0.0015028715}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bessie knows whether someone's forehead is muddy. It is publicly announced that Bessie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 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 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":"Bessie can now know whether Melissa can know whether Melissa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bessie","Melissa"],"index":11114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996628761,"difficulty":0.0003371239}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimber does not know whether Jimmy is thirsty. It is publicly announced that Jimmy does not know whether Bridgette is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kimber can now know that Jimmy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bridgette","Alvin","Jimmy","Kimber"],"index":4373,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963978529,"difficulty":0.0036021471}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether Derek is thirsty. It is publicly announced that Anderson does not know whether Willie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Willie can now know that Willie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anderson","Derek","Willie","Frank"],"index":26097,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9847739935,"difficulty":0.0152260065}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reuben does not know whether Reuben's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Anthony knows whether or not everyone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agenta knows that (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Everett can now know that Irene can know that Reuben's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Everett","Anthony","Reuben","Irene"],"index":41312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7786930799,"difficulty":0.2213069201}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nora's card is shown to Nora. Keith's card is shown to Nora. Judith'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 Judith knows whether Nora 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) ] (Agentb knows that 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":"Judith can now know that Nora picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nora","Judith","Keith"],"index":2424,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9958431125,"difficulty":1.9958431125}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether Diane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (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":"Alexandria can now know whether Brian can know whether Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Alexandria","Brian"],"index":17541,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999545753,"difficulty":0.000454247}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether Robert's forehead is muddy. It is publicly announced that Henry does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Henry'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 whether (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Henry can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Henry","Robert"],"index":42880,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.943652451,"difficulty":1.943652451}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wade 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 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":"Guillermo can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donald","Guillermo","Wade","Polly"],"index":13090,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997261167,"difficulty":0.0002738833}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ingrid does not know whether or not everyone is thirsty. It is publicly announced that Julie knows whether Julie is thirsty. It is publicly announced that Charles is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Charles can now know that Louis is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ingrid","Charles","Julie","Louis"],"index":11553,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.983094275,"difficulty":0.016905725}
+{"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 Annie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Raymond can now know whether Daniel can know that Annie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Maria","Raymond","Daniel"],"index":13838,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9886942506,"difficulty":0.0113057494}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joyce's card is shown to Joyce. Lorena's card is shown to Lorena. 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 whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Joyce can now know whether Lorena can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Lorena"],"index":20859,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994335771,"difficulty":0.0005664229}
+{"premise":"There are four persons. Everyone is visible 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 Emmett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Donna can now know whether Emmett can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sonia","Emmett","Donna","Brian"],"index":25111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997659326,"difficulty":0.0002340674}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Franklyn does not know whether Franklyn'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) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jacob can now know that Franklyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacob","Franklyn","Maureen","Mary"],"index":28824,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978314042,"difficulty":0.0021685958}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lori's card is shown to Edward. Edward's card is shown to Lori. Lori's card is shown to Clifford. Lori's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that Clifford knows whether or not everyone picked a red card. It is publicly announced that Kathy does not know whether Clifford picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Lori can now know that Edward picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edward","Lori","Clifford","Kathy"],"index":5963,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8921657205,"difficulty":0.1078342795}
+{"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 nobody 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))) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know whether Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Robert"],"index":37122,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988904595,"difficulty":0.0011095405}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juan's card is shown to Juan. Angelique's card is shown to Juan. Angelique's card is shown to Angelique. Ignacio's card is shown to Angelique. Juan's card is shown to Ignacio. Angelique's card is shown to Ignacio. Ignacio's card is shown to Ignacio. 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) ] (Agentb knows that 2)","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":"Angelique can now know that Angelique picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Juan","Angelique","Ignacio"],"index":8535,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9963040352,"difficulty":0.0036959648}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_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":"Emma can now know that Roberta can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Roberta","Emma","Mark"],"index":16558,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984155893,"difficulty":0.0015844107}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Enrique's card is shown to Enrique. Enrique'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 Eric knows whether Eric picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Enrique can now know that Eric can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Enrique","Eric"],"index":2518,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joanne can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joanne","James","Rickey","Patrick"],"index":63319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.649230659,"difficulty":0.350769341}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Conrad 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))) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jovita can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Shawn","Jovita","Conrad"],"index":61408,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972848892,"difficulty":0.0027151108}
+{"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 Brendan. Steven's card is shown to Bobby. Brendan's card is shown to Cedric. It is publicly announced that someone picked a red card. It is publicly announced that Bobby does not know whether Bobby picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bobby can now know whether Cedric can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Brendan","Bobby","Cedric"],"index":40470,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.509706974,"difficulty":1.509706974}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josefina does not know whether or not everyone is thirsty. It is publicly announced that Trevor does not know whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 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)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Trevor can now know that Josefina can know whether Trevor is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Josefina","David","Trevor"],"index":37789,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8542023301,"difficulty":1.8542023301}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela does not know whether Pamela's forehead is muddy. It is publicly announced that Pamela does not know whether Pamela'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 (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Pamela can now know whether Kathleen can know whether Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Pamela"],"index":5252,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991668463,"difficulty":0.0008331537}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonia knows whether Neil is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Neil knows whether Neil is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (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) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Antonia can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Antonia","Neil"],"index":17546,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9197686315,"difficulty":1.9197686315}
+{"premise":"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 James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mike can now know that James can know that Mike's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mike","James"],"index":4366,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981702566,"difficulty":0.0018297434}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gail's card is shown to Susan. Bryan's card is shown to Bryan. Bryan's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Bryan does not know whether Gail picked a red card. It is publicly announced that Bryan does not know whether Gail picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Susan can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gail","Susan","Bryan","Robert"],"index":45006,"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's forehead is muddy. It is publicly announced that Patrick does not know whether or not everyone's forehead is muddy. It is publicly announced that Iris knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Iris can now know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patrick","Veronica","Iris","Tracy"],"index":25191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5688973069,"difficulty":0.4311026931}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether Linda can know whether William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Thelma","Antonio","William"],"index":19757,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996846914,"difficulty":0.0003153086}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Gerald can now know that Carmen can know whether Cortney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cortney","Carmen","Janice","Gerald"],"index":21903,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995391369,"difficulty":0.0004608631}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether someone's forehead is muddy. It is publicly announced that Patrick knows whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] (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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Charles","Katherine","Adam"],"index":15745,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9984560013,"difficulty":0.0015439987}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether someone's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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":"Alesha can now know that Alesha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Joel","Alesha"],"index":52166,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980600476,"difficulty":0.0019399524}
+{"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 Rosie 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 (~(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":"Janice can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rosie","Janice","Richard"],"index":23579,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965632558,"difficulty":0.0034367442}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dean can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Dean","Irene"],"index":4813,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997342229,"difficulty":0.0002657771}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erich's card is shown to Mary. Debra's card is shown to Gregoria. Mary's card is shown to Erich. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Debra can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Debra","Gregoria","Erich"],"index":36431,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy. It is publicly announced that Carl does not know whether Carl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lillian can now know whether Dorothy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Carl","Lillian"],"index":2115,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997736812,"difficulty":0.0002263188}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 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 1) ] 0","hypothesis":"David can now know that Robert can know that Laverna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Laverna","Robert","Wilford"],"index":7108,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985479712,"difficulty":0.0014520288}
+{"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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Steven","Robert","Dori","Sue"],"index":56600,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978030324,"difficulty":0.0021969676}
+{"premise":"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 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 3)","n_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":"Ramon can now know that Christine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aline","Ramon","Christine"],"index":23848,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982428551,"difficulty":0.0017571449}
+{"premise":"There are 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 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":"Max can now know whether Alice can know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","Peter","Velma","Max"],"index":53783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999673605,"difficulty":0.000326395}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lea does not know whether Veronica is thirsty. It is publicly announced that Veronica does not know whether Twanna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Twanna can now know whether Veronica can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Twanna","Rosalie","Veronica","Lea"],"index":50787,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9997816682,"difficulty":0.0002183318}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberta's forehead is not muddy. It is publicly announced that Alexander knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Roberta can now know that Roberta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alexander","Roberta","Robert"],"index":27319,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9750928879,"difficulty":0.0249071121}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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 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":"Justin can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Charles","Justin","Annie"],"index":42152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995948672,"difficulty":0.0004051328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (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":"Virginia can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tami","Virginia","Eunice","Mary"],"index":57974,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979069233,"difficulty":0.0020930767}
+{"premise":"There are three persons. Everyone is visible 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 Ellis's forehead is muddy.","smcdel_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 (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) ] 0","hypothesis":"Ellis can now know that Susan can know that Ellis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ellis","Clarence","Susan"],"index":63026,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99725914,"difficulty":0.00274086}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Colleen knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 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":"Colleen can now know that Colleen is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawrence","Colleen","Opal"],"index":15884,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9551880956,"difficulty":1.9551880956}
+{"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 Patricia. Joseph's card is shown to Joseph. Joan's card is shown to Joseph. Patricia'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 knows whether Patricia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Joseph can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Joseph","Joan"],"index":31624,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986103773,"difficulty":0.0013896227}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Christy's card is shown to Christy. Kristine's card is shown to Christy. Christy's card is shown to Bryan. Bryan's card is shown to Bryan. Bryan's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bryan can now know that Kristine can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christy","Kristine","Bryan","Jessica"],"index":59416,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997774959,"difficulty":0.0002225041}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julius knows whether or not nobody's forehead is muddy. It is publicly announced that Benito's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows whether (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":"Julius can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tom","Benito","Julius"],"index":21761,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9996153116,"difficulty":0.0003846884}
+{"premise":"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 Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agenta knows that (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"William can now know that Barbara can know whether Kris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Kris","Barbara"],"index":31759,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995835423,"difficulty":0.0004164577}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brian is not thirsty. It is publicly announced that Tammy does not know whether Jose is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Stephanie can now know that Stephanie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephanie","Tammy","Jose","Brian"],"index":58547,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9895641804,"difficulty":0.0104358196}
+{"premise":"There are four persons. Everyone is visible 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 Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lauran can now know that Cleo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Cleo","Frank","Lauran"],"index":43743,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984698892,"difficulty":0.0015301108}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dudley's card is shown to Dudley. Dale's card is shown to Dale. It is publicly announced that someone picked a red card. It is publicly announced that Dudley does not know whether or not everyone picked a red card. It is publicly announced that Dudley 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 (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)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Dudley can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dudley","Dale"],"index":7076,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9748672843,"difficulty":0.0251327157}
+{"premise":"There are three persons. Everyone is visible 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 or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows 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":"Jennifer can now know that Linda can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Catherine","Jennifer"],"index":58876,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9995440841,"difficulty":0.0004559159}
+{"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 Amber. Debra's card is shown to Amber. Amber's card is shown to Isaac. Isaac's card is shown to Isaac. Mike's card is shown to Isaac. Amber's card is shown to Debra. Amber's card is shown to Mike. Debra's card is shown to Mike. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2,4 Agentc:1 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mike can now know that Debra picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Amber","Isaac","Debra","Mike"],"index":41396,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978451729,"difficulty":0.0021548271}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antonio 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))","n_announcements":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":"Oscar can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Antonio","Donna","Oscar","Elizabeth"],"index":49480,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997885406,"difficulty":0.002114594}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Frances can now know that Karen can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Frances","Shawn","Chad"],"index":41712,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997711778,"difficulty":0.0002288222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose 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":"Rose can now know whether David can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rose","Chung","Lawrence","David"],"index":38737,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997761846,"difficulty":0.0002238154}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Renea can now know that Ruth can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Renea","Ruth","Thomas"],"index":41286,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985539317,"difficulty":0.0014460683}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Shirley can now know that Francis can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","Patricia","Laurie","Shirley"],"index":53966,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984667897,"difficulty":0.0015332103}
+{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows that 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":"Martha can now know whether Zachary can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barton","Martha","Aaron","Zachary"],"index":49027,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9905303121,"difficulty":0.0094696879}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not everyone's forehead is muddy. It is publicly announced that Shelia's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Joshua can now know whether Shelia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joshua","Shelia"],"index":53299,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9997834563,"difficulty":0.0002165437}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy. It is publicly announced that Ethel knows whether someone's forehead is muddy. It is publicly announced that Johnny knows whether 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentc knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Daniel can now know that Ethel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Gary","Daniel","Ethel"],"index":22384,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973444343,"difficulty":0.0026555657}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marlene knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","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":"Kimberly can now know that Marlene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marlene","Kimberly"],"index":1418,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979423881,"difficulty":0.0020576119}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diamond does not know whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows whether 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":"Robert can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diamond","Robert","Claire"],"index":9910,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988152981,"difficulty":0.0011847019}
+{"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. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Christopher can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christopher","Monica","Richard"],"index":23242,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9997552037,"difficulty":0.0002447963}
+{"premise":"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 Julia does not know whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 3)","n_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":"Helen can now know that Melanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Helen","Julia","Melanie"],"index":55047,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936019778,"difficulty":0.0063980222}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norene 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Christopher can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rosa","Norene","Alonzo","Christopher"],"index":4282,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987570047,"difficulty":0.0012429953}
+{"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. Patricia's card is shown to Patricia. Cindy's card is shown to Patricia. Cindy's card is shown to Terri. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Marissa can now know that Patricia can know that Cindy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marissa","Patricia","Cindy","Terri"],"index":2939,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980500937,"difficulty":0.0019499063}
+{"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 Marcia. Milton's card is shown to Marcia. Marcia's card is shown to Milton. Milton's card is shown to Milton. Milton's card is shown to Carmen. Carmen's card is shown to Carmen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Milton can now know whether Carmen can know that Marcia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marcia","Milton","Carmen"],"index":31895,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9228440523,"difficulty":1.9228440523}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Angla can now know that Angla's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angla","Terry","Richard","Marie"],"index":36781,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9868663549,"difficulty":0.0131336451}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy. It is publicly announced that Edward's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentb knows that (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Evelyn can now know that Amber can know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jerry","Evelyn","Edward","Amber"],"index":13869,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987498522,"difficulty":0.0012501478}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathaniel is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agenta knows whether 1)","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":"Jennifer can now know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jennifer","Nathaniel","Connie"],"index":60230,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9985054731,"difficulty":0.0014945269}
+{"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 Willie does not know whether Lynn is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Lynn does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lynn can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Lynn","Willie"],"index":45780,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975569248,"difficulty":0.0024430752}
+{"premise":"There are three persons. Everyone is visible 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 Cora's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Cora can now know that Steve can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cora","Marilyn","Steve"],"index":51850,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991802573,"difficulty":0.0008197427}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alexandra 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 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":"Alexandra can now know that Phyllis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robbie","Alexandra","Phyllis","Dan"],"index":20191,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981307387,"difficulty":0.0018692613}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charlie knows whether or not nobody'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) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Susan can now know that Floyd's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charlie","Floyd","Susan"],"index":34245,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978992939,"difficulty":0.0021007061}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb 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) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Jaquelyn can now know whether Frances can know whether Jaquelyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jaquelyn","Frances","Theodore"],"index":53238,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993940592,"difficulty":0.0006059408}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Valentin's card is shown to Betty. Betty's card is shown to Gladys. Gladys's card is shown to Valentin. 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) ] Agentc knows that (Agenta 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":"Gladys can now know that Norma can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Betty","Gladys","Valentin"],"index":41351,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993607402,"difficulty":0.0006392598}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lester is not thirsty. It is publicly announced that Herschel knows whether or not everyone is thirsty. It is publicly announced that Lester 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 that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Herschel can now know that Lester can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Herschel","Andre","Lester","Deann"],"index":21040,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989013672,"difficulty":0.0010986328}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Max does not know whether Max's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Mary can now know that Rebecca can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rebecca","Bianca","Mary","Max"],"index":58369,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985105395,"difficulty":0.0014894605}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Dedra knows whether Dedra's forehead is muddy. It is publicly announced that Fletcher knows whether Fletcher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Christopher can now know that Dedra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dedra","Fletcher","Fernando","Christopher"],"index":5343,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981237054,"difficulty":0.0018762946}
+{"premise":"There are four persons. Everyone is visible 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) ] (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) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] 0","hypothesis":"Heath can now know whether Heath's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Leonard","Troy","Ashton","Heath"],"index":62683,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993013144,"difficulty":0.0006986856}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (~(1|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":"Bernice 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":["Bernice","James"],"index":44373,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9853231907,"difficulty":0.0146768093}
+{"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 Vernon. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Vernon can now know whether Jason can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jason","Vernon"],"index":30730,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9801124334,"difficulty":0.0198875666}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tami's card is shown to Tami. Tami's card is shown to Blaine. Mae's card is shown to Blaine. Blaine's card is shown to Mae. 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) ] Agentc knows whether (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":"Mae can now know whether Tami can know that Blaine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tami","Blaine","Mae"],"index":17219,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8967155218,"difficulty":0.1032844782}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to David. Emily's card is shown to Emily. Richard's card is shown to Emily. Charles's card is shown to Emily. Charles's card is shown to Richard. Emily'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 Richard does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,3,4 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows that 2)","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":"Charles can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Emily","Richard","Charles"],"index":16606,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935218692,"difficulty":0.0064781308}
+{"premise":"There are three persons. Everyone is visible 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. 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) ] [ ! ~(1) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Gene can now know that Chad can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","John","Chad"],"index":10711,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990006089,"difficulty":0.0009993911}
+{"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 David knows whether David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (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":["David","Lisa","Jose"],"index":27172,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9362701774,"difficulty":0.0637298226}
+{"premise":"There are two persons. Everyone is visible 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 Jesse's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(1) ] 0","hypothesis":"Jesse can now know that Jesse's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jesse","Joyce"],"index":37693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9838693738,"difficulty":0.0161306262}
+{"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 Clayton. Kurt's card is shown to Kurt. Jason's card is shown to Amy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kurt can now know whether Jason picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jason","Clayton","Kurt","Amy"],"index":10570,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9612818956,"difficulty":0.0387181044}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shayla does not know whether or not everyone's forehead is muddy. It is publicly announced that Shayla knows whether Sharon's forehead is muddy. It is publicly announced that Shayla 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 whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Garry can now know whether Shayla's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sharon","Robert","Shayla","Garry"],"index":6484,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991618395,"difficulty":0.0008381605}
+{"premise":"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. It is publicly announced that Cecil knows whether Heather's forehead is muddy. It is publicly announced that Cecil does not know whether Cecil's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentc knows 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 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Heather can now know that Cecil can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Lula","Cecil","Heather"],"index":39504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960898161,"difficulty":0.0039101839}
+{"premise":"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 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 whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Stephen can now know whether Joseph can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","William","Stephen"],"index":27479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8855143189,"difficulty":0.1144856811}
+{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Marguerite can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gabriela","George","Marguerite"],"index":11121,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993599057,"difficulty":0.0006400943}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrea does not know whether Andrea's forehead is muddy. It is publicly announced that Andrea does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Carol can now know that Andrea can know that Andrea's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Andrea","Carol"],"index":27297,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7957153916,"difficulty":1.7957153916}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores knows whether Aaron's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Cristopher can now know that Aaron can know that Dolores's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cristopher","Dolores","Dana","Aaron"],"index":37484,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983193278,"difficulty":0.0016806722}
+{"premise":"There are three persons. Everyone is visible 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 Anna's forehead is muddy. It is publicly announced that Tonia's forehead is not muddy. It is publicly announced that George knows whether Tonia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Tonia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tonia","Anna","George"],"index":51629,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989939332,"difficulty":0.0010060668}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jessica's card is shown to Jessica. Jessica's card is shown to Stanley. James's card is shown to Stanley. It is publicly announced that someone picked a red card. It is publicly announced that Jessica knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Stanley can now know that Jessica can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Stanley","James"],"index":59491,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994077682,"difficulty":0.0005922318}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentc knows whether (Agentd knows 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":"Celia can now know whether Richard can know whether Kathy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eula","Kathy","Celia","Richard"],"index":63322,"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'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 3)","n_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":"Leona can now know that Johnny's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leona","Casey","Johnny"],"index":1122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9908549786,"difficulty":0.0091450214}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Liza knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Danielle can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kristie","Liza","Danielle"],"index":40781,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981284738,"difficulty":0.0018715262}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Jay's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 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":"Jay can now know that Karie can know that Karie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carlos","Karie","Jay"],"index":11281,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971477389,"difficulty":0.0028522611}
+{"premise":"There are four persons. Everyone is visible 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 Ardath's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Gregory can now know that Sylvia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Gregory","Shawn","Ardath"],"index":6208,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983108044,"difficulty":0.0016891956}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Eddie can now know whether Thomas can know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Eddie","Thomas","Mildred"],"index":49240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9978054166,"difficulty":0.0021945834}
+{"premise":"There are two persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|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":"Carrie can now know that George can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Carrie","George"],"index":20239,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990142584,"difficulty":0.0009857416}
+{"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 Diana is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] Agentd 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"John can now know that Theodore can know whether Leticia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Leticia","Diana","Theodore","John"],"index":41556,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982469082,"difficulty":0.0017530918}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Virgil can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virgil","Leonard","Mark"],"index":61966,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988723397,"difficulty":0.0011276603}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manual knows whether Manual is thirsty. It is publicly announced that Jeffrey does not know whether Manual is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentb 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) ] [ ! (Agentc knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jeffrey can now know that Margie can know whether Manual is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margie","Jeffrey","Manual"],"index":63308,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8427801728,"difficulty":0.1572198272}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria does not know whether Anthony is thirsty. It is publicly announced that Anthony does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joyce can now know that Gloria can know that Joyce is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Gloria","Joyce"],"index":47734,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9206799865,"difficulty":0.0793200135}
+{"premise":"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 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) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lisa can now know that Holly can know whether Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Katelyn","Holly","Lisa","Donald"],"index":33646,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.996437788,"difficulty":0.003562212}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathleen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Kathleen can now know that Rita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathleen","Rita"],"index":46868,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993658662,"difficulty":0.0006341338}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Theresa can now know whether Judy can know whether Judy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Raymond","Theresa","Laurence","Judy"],"index":55147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9899004102,"difficulty":0.0100995898}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Thomas can now know that Patricia can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Glen","Thomas","Patricia"],"index":45710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994543195,"difficulty":0.0005456805}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy 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 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":"Robert can now know whether Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Timothy","Bertha"],"index":56044,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994105101,"difficulty":0.0005894899}
+{"premise":"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 someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agenta knows that 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":"Andrew can now know that Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Gregory"],"index":44413,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9935798645,"difficulty":0.0064201355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ned does not know whether or not everyone's forehead is muddy. It is publicly announced that Lakesha knows whether or not everyone's forehead is muddy. It is publicly announced that Ned does not know whether Ned's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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) ] Agentc knows that (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Bonita can now know that Ned can know that Bonita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Lakesha","Bonita","Ned"],"index":21080,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.954092443,"difficulty":1.954092443}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathleen does not know whether Diane is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows that 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":"Diane can now know whether Timothy can know that Timothy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Diane","Kathleen","Timothy"],"index":8480,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9945540428,"difficulty":0.0054459572}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mona's card is shown to Richard. Richard's card is shown to Mona. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] Agenta knows that (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":"Richard can now know that Mona can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Mona"],"index":24294,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993213415,"difficulty":0.0006786585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alberto does not know whether Jeffrey is thirsty. It is publicly announced that Jeffrey does not know whether Jane is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb 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 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alberto can now know that Jane is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jane","Jeffrey","Alberto"],"index":51582,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972581863,"difficulty":0.0027418137}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andree's card is shown to Andree. Clyde's card is shown to Andree. Andree's card is shown to Fred. Clyde's card is shown to Fred. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Andree can now know whether Clyde can know that Andree picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andree","Clyde","Fred"],"index":11000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9278125167,"difficulty":0.0721874833}
+{"premise":"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 knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows whether (~(1|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":"Theresa can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Theresa","Brian"],"index":44523,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994521737,"difficulty":0.0005478263}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 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":"Paula can now know whether Michael is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paula","Michael","Deanna"],"index":35740,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972884655,"difficulty":0.0027115345}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd 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:1,2,3,4 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":"Debra can now know that Clementine can know that Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vivian","Frances","Clementine","Debra"],"index":26845,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974870682,"difficulty":0.0025129318}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis knows whether Sheila's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Travis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sheila","Annette","Travis","Robert"],"index":10915,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987334609,"difficulty":0.0012665391}
+{"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 Daniel 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|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":"Daniel can now know whether Rita can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Daniel","Rita"],"index":59927,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993118048,"difficulty":0.0006881952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Denise can now know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amanda","Nicole","Denise","Bryan"],"index":14628,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.637182653,"difficulty":0.362817347}
+{"premise":"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 Luis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 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 4) ] 0","hypothesis":"David can now know that Luis can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gregorio","Donald","David","Luis"],"index":21653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9724668264,"difficulty":0.0275331736}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jaime is thirsty. It is publicly announced that Eartha does not know whether Dexter is 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) ] Agentd knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jaime can now know whether Eartha can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eartha","John","Dexter","Jaime"],"index":36282,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.835724175,"difficulty":0.164275825}
+{"premise":"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. It is publicly announced that Amanda does not know whether Amanda's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows whether (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":"Amanda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Elizabeth","Amanda"],"index":62398,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8599433303,"difficulty":0.1400566697}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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":"Terry can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","Jay","Terry","Kimberly"],"index":61016,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999369204,"difficulty":0.000630796}
+{"premise":"There are three persons. Everyone is visible 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 Adele's forehead is muddy. It is publicly announced that Adele knows whether Amanda's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Amanda can now know whether Adele can know that Adele's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Amanda","Adele","Patricia"],"index":4115,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993206263,"difficulty":0.0006793737}
+{"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) ] [ ! ~(2) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Joe can now know whether Mary is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joe","John","Mary","Carolyn"],"index":35887,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978215694,"difficulty":0.0021784306}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy. It is publicly announced that Gregory knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Catherine can now know whether Gregory can know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Gregory"],"index":16938,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9667216539,"difficulty":0.0332783461}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows 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":"Charles can now know that Alfred can know that Alfred's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","James","Alfred","Bridgett"],"index":16136,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962182641,"difficulty":0.0037817359}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Linda's card is shown to Linda. Rhonda's card is shown to Jordan. Linda's card is shown to Rhonda. Rhonda's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Rhonda can now know that Jordan can know whether Rhonda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Jordan","Rhonda"],"index":12748,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9975138903,"difficulty":0.0024861097}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy knows whether Judy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Judy can now know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Adeline","Patricia","Thelma","Judy"],"index":27664,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993793964,"difficulty":0.0006206036}
+{"premise":"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 Gloria's forehead is muddy. It is publicly announced that Andrew's forehead is muddy. It is publicly announced that Victor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agentc knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Andrew can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gloria","Victor","Andrew","Chelsea"],"index":33483,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994686246,"difficulty":0.0005313754}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly knows whether Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kelly can now know whether Paul can know that Eugene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eugene","Paul","Kelly"],"index":7145,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994723201,"difficulty":0.0005276799}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward knows whether Edward is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1&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":"Consuelo can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessica","Consuelo","Edward"],"index":50684,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989570379,"difficulty":0.0010429621}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lloyd's card is shown to Gertrude. Gertrude's card is shown to Norma. Lloyd's card is shown to Norma. Norma's card is shown to Lloyd. Lloyd's card is shown to Lloyd. It is publicly announced that someone picked a red card. It is publicly announced that Norma knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Gertrude can now know that Lloyd picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gertrude","Norma","Lloyd"],"index":40574,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9957392216,"difficulty":0.0042607784}
+{"premise":"There are 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)","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":"Rebecca can now know that Edna can know that Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Edna","Russell"],"index":63587,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986043572,"difficulty":0.0013956428}
+{"premise":"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 Samuel's forehead is muddy. It is publicly announced that Debra does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Samuel can now know that Debra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Debra","Samuel"],"index":12172,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988902211,"difficulty":0.0011097789}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows that 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":"Lula can now know that Elizabeth can know that Donna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lula","Donna","Sharon","Elizabeth"],"index":795,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9894031286,"difficulty":0.0105968714}
+{"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) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Chad can now know that Laurie can know that Laurie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chad","Emily","Curtis","Laurie"],"index":8237,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6404073834,"difficulty":0.3595926166}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] 0","hypothesis":"Taylor can now know that Linda can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Taylor","Linda"],"index":5621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9910199046,"difficulty":0.0089800954}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Samantha can now know whether Ethel can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ethel","John","Samantha","Isaac"],"index":39494,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999248445,"difficulty":0.000751555}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tasha 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":"Lee can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tasha","Roberto","Lee","Jordan"],"index":43937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969688058,"difficulty":0.0030311942}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian does not know whether Christian's forehead is muddy. It is publicly announced that Christian's forehead is not muddy. It is publicly announced that Christian 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":"Joan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christian","Joan"],"index":41199,"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 Crystal's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Caroline can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","Summer","Crystal","Caroline"],"index":37972,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994009733,"difficulty":0.0005990267}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Shirley is thirsty. It is publicly announced that Richard knows whether or not nobody is thirsty. It is publicly announced that Shirley knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Shirley can now know that Richard can know whether Shirley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Shirley","Richard"],"index":66498,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9709944129,"difficulty":1.9709944129}
+{"premise":"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":"Lee can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lee","Russell","Marcelino","Lillie"],"index":33767,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994413257,"difficulty":0.0005586743}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mae does not know whether Diana is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Helen can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kelly","Mae","Diana","Helen"],"index":28781,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994193316,"difficulty":0.0005806684}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether or not everyone's forehead is muddy. It is publicly announced that Andre's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] [ ! (1|2) ] 0","hypothesis":"Donna can now know that Andre can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donna","Andre"],"index":66139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994118214,"difficulty":0.0005881786}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joann's card is shown to Andrew. Andrew's card is shown to Joann. Jeffrey's card is shown to Jeffrey. Jeffrey'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 Joann 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) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Andrew can now know that Joann can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Joann","Jeffrey","Doris"],"index":67224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9928988218,"difficulty":0.0071011782}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Matthew's card is shown to Matthew. Suzan's card is shown to Roger. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Matthew can now know whether Matthew picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Matthew","Roger","Jillian","Suzan"],"index":67272,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5855861902,"difficulty":0.4144138098}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver knows whether Verna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Oliver can now know that Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Verna","Oliver","Michelle","Sarah"],"index":31385,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982257485,"difficulty":0.0017742515}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea is not thirsty. It is publicly announced that Kathy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Andrea can now know that Donald can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathy","Nancy","Donald","Andrea"],"index":27364,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9405927658,"difficulty":0.0594072342}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rhonda knows whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Jose's forehead is muddy. It is publicly announced that Rhonda'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 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! ~(3) ] 0","hypothesis":"Jose can now know that Rhonda can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Michael","Rhonda"],"index":56783,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9893499017,"difficulty":0.0106500983}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Milford's card is shown to Grover. Ida's card is shown to Lisa. Milford's card is shown to Lisa. Grover's card is shown to Milford. It is publicly announced that someone picked a red card. It is publicly announced that Ida does not know whether Ida picked a red card. It is publicly announced that Grover picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 1 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! 1 ] 0","hypothesis":"Grover can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grover","Lisa","Ida","Milford"],"index":21949,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9856963158,"difficulty":0.0143036842}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marvin does not know whether Rosemary is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Marvin can now know that Rosemary can know whether Marvin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marvin","Rosemary"],"index":60047,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9872318506,"difficulty":1.9872318506}
+{"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 Rochel. Rochel's card is shown to David. Rochel's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Christopher knows whether or not everyone picked a red card. It is publicly announced that David knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rochel","David","Christopher"],"index":55172,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994196892,"difficulty":0.0005803108}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruth knows 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) ] (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":"John can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ruth","John","Joshua"],"index":56030,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994877577,"difficulty":0.0005122423}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke's forehead is muddy. It is publicly announced that Carl knows whether someone's forehead is muddy. It is publicly announced that Carl knows whether Sheila's forehead is muddy. It is publicly announced that Carl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carl can now know that Sheila can know whether Sheila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luke","Sheila","Carl"],"index":307,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994581342,"difficulty":0.0005418658}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 Henry can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Henry","Adina","Carolyn","James"],"index":32139,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988754392,"difficulty":0.0011245608}
+{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Darren can know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darren","James","Lori","Michael"],"index":2117,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994080067,"difficulty":0.0005919933}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leonard does not know whether or not everyone is thirsty. It is publicly announced that Leonard knows whether Leonard 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) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Leonard can now know whether Gale can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leonard","Gale"],"index":19076,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994881153,"difficulty":0.0005118847}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan knows whether Valentin is thirsty. It is publicly announced that Valentin knows whether Susan is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Susan can now know that Valentin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Susan","Valentin"],"index":36636,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9599264264,"difficulty":1.9599264264}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether or not nobody'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 Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Joseph can now know that Jane can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jane","Joseph"],"index":35615,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994743466,"difficulty":0.0005256534}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeffrey does not know whether or not everyone is thirsty. It is publicly announced that Norma does not know whether Blanche is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Jeffrey can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Norma","Jeffrey","Blanche"],"index":15315,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938388467,"difficulty":0.0061611533}
+{"premise":"There are four persons. Everyone is visible 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 William's forehead is not 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) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] Agentc knows whether (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(2) ] [ ! ~(2) ] 0","hypothesis":"Dee can now know whether William can know that Vivian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","William","Dee","Vivian"],"index":6176,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994499087,"difficulty":0.0005500913}
+{"premise":"There are three persons. Everyone is visible 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 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) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Irene can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Debbie","Irene","Mary"],"index":28780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999042213,"difficulty":0.000957787}
+{"premise":"There are four persons. Everyone is visible 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 Dennis's forehead is muddy. It is publicly announced that Barbara knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc 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) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Elfriede can now know that Barbara can know that Lillian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Dennis","Elfriede","Lillian"],"index":2682,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982784986,"difficulty":0.0017215014}
+{"premise":"There are 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 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":"Kelvin can now know that Kelvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","Mary","Kelvin","Charles"],"index":52647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984019399,"difficulty":0.0015980601}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Sylvia does not know whether Sylvia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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) ] 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 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jodi can now know that Sylvia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvia","Jodi","Angela","Charles"],"index":51803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999442637,"difficulty":0.000557363}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 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":"Kevin can now know that Tyler can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tyler","Kevin","Marjorie"],"index":48453,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.994568944,"difficulty":0.005431056}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marsha's card is shown to James. James's card is shown to James. William's card is shown to James. Marsha'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:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Marsha can now know whether James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marsha","James","William"],"index":61250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992341995,"difficulty":0.0007658005}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead is muddy. It is publicly announced that Donna'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) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] (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) ] [ ! 4 ] [ ! 4 ] [ ! ~(3) ] 0","hypothesis":"Annette can now know that Annette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Annette","Imogene","Frederick","Donna"],"index":57994,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967570901,"difficulty":0.0032429099}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW 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":"John can now know that Karen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Tammy","John"],"index":14423,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993262291,"difficulty":0.0006737709}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gina does not know whether or not everyone's forehead is muddy. It is publicly announced that Gina 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":"Gwendolyn can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gwendolyn","Gina"],"index":27837,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979179502,"difficulty":0.0020820498}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kenneth does not know whether or not everyone is thirsty. It is publicly announced that John does not know whether Ron is thirsty. It is publicly announced that Kenneth does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Kenneth can now know whether John can know whether Kenneth is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Ron","John"],"index":39270,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991064668,"difficulty":0.0008935332}
+{"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 Rachel. Robert's card is shown to Dora. Rachel's card is shown to Timothy. Rachel'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:4 Agentc:1 Agentd: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:3 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dora can now know that Timothy can know whether Timothy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rachel","Dora","Timothy","Robert"],"index":30075,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6478337646,"difficulty":0.3521662354}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel knows whether someone's forehead is muddy.","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":"Edward can now know that Joel can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Joel","Edward"],"index":9726,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989680052,"difficulty":0.0010319948}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"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 that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Howard can now know that Claudia can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Larry","Howard","Claudia"],"index":5079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9965342283,"difficulty":0.0034657717}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cornelius knows whether Bonnie is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Bonnie knows whether Bonnie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bonnie can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cornelius","Bonnie"],"index":10532,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994945526,"difficulty":0.0005054474}
+{"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 Katie. Michael's card is shown to Katie. Jennifer's card is shown to Katie. Michael's card is shown to Michael. 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: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:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Katie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Katie","Michael","Jennifer"],"index":19175,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989533424,"difficulty":0.0010466576}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that 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":"Selma can now know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Scott","Kristin","Selma","Michael"],"index":65548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973249435,"difficulty":0.0026750565}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Errol does not know whether Steve is thirsty. It is publicly announced that Steve does not know whether Daisy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Maria can now know whether Steve is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daisy","Maria","Steve","Errol"],"index":36293,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.5207304955,"difficulty":1.5207304955}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edie's forehead is muddy. It is publicly announced that Kristen does not know whether Kristen's forehead 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 (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Kristen can now know whether James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Edie","Kristen"],"index":49900,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9569419622,"difficulty":1.9569419622}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (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) ] [ ! ~(3) ] 0","hypothesis":"Dennis can now know that Grace can know that Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dennis","Grace","Deborah"],"index":23909,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975827932,"difficulty":0.0024172068}
+{"premise":"There are two persons. Everyone is visible 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 Aubrey's forehead is not muddy. It is publicly announced that Pasquale's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows that (Agenta knows that 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":"Aubrey can now know that Pasquale can know that Aubrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Pasquale","Aubrey"],"index":67605,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9671320915,"difficulty":0.0328679085}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Camille's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows whether 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":"Angela can now know whether Angela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Greg","Angela","Camille","Liza"],"index":26937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921646118,"difficulty":0.0078353882}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlotte does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether 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":"Charlotte can now know whether Warner can know whether Charlotte is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Warner","Charlotte"],"index":11139,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998904705,"difficulty":0.001095295}
+{"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 Kenneth is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows that 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":"Ronald can now know that Ginger can know that Ginger is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kenneth","Ronald","Ginger"],"index":57571,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9924699664,"difficulty":0.0075300336}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Henry can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donald","Henry","William"],"index":64744,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992838502,"difficulty":0.0007161498}
+{"premise":"There are three persons. Everyone is visible 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 Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Cynthia","Michael"],"index":56932,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992451668,"difficulty":0.0007548332}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damian does not know whether Damian's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Phyllis can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Damian","Phyllis"],"index":25991,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994899035,"difficulty":0.0005100965}
+{"premise":"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":"Nancy can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggie","Nancy","Raymond"],"index":5289,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919658899,"difficulty":0.0080341101}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"David can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["David","Donald","Christa"],"index":45260,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993101716,"difficulty":0.006898284}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roberta 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 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 Harold can know that Roberta's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harold","Roberta","Edward"],"index":40787,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979100823,"difficulty":0.0020899177}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donald's card is shown to Donald. Donald's card is shown to Meridith. Meridith's card is shown to Meridith. 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 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Donald can now know whether Meridith can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Donald","Meridith"],"index":2696,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994425178,"difficulty":0.0005574822}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley knows whether Shirley's forehead is muddy. It is publicly announced that Wesley knows whether 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 1) ] [ ! (Agentd knows whether 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) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Ronald can now know that Wesley can know that Shirley's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shirley","Irene","Ronald","Wesley"],"index":49028,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967809916,"difficulty":0.0032190084}
+{"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. Princess's card is shown to Princess. Clarissa's card is shown to Princess. Princess's card is shown to Clarissa. Clarissa's card is shown to Clarissa. It is publicly announced that someone picked a red card. It is publicly announced that Richard does not know whether Princess picked a red card. It is publicly announced that Clarissa knows whether Princess picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Princess can now know whether Richard can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Princess","Clarissa"],"index":26379,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992922544,"difficulty":0.0007077456}
+{"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. Latoya's card is shown to Latoya. Latoya's card is shown to Ida. Ida's card is shown to Ida. 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 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Latoya can now know whether Ida picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Latoya","Ida"],"index":54055,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5274021029,"difficulty":1.5274021029}
+{"premise":"There are four persons. Everyone is visible 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) ] [ ! (Agentd 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) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Norma can now know that Richard can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Juan","Larry","Richard"],"index":7579,"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 Jason 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 3)","n_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":"Jacqueline can now know whether Jacqueline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jason","Jennifer","Jacqueline"],"index":38532,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9952594638,"difficulty":0.0047405362}
+{"premise":"There are three persons. Everyone is visible 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 knows whether or not nobody's forehead is muddy. It is publicly announced that Alan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 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":"Alan can now know that Marilyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elias","Alan","Marilyn"],"index":64858,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972848892,"difficulty":0.0027151108}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 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":"Harriet can now know that Caroline can know that Alvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Caroline","Alvin","Harriet"],"index":335,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974433184,"difficulty":0.0025566816}
+{"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 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) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Edward can now know that Sarah can know that Alexa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","Shirley","Alexa","Edward"],"index":57120,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980329871,"difficulty":0.0019670129}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 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":"Annette can now know that Luis can know whether Annette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annette","Luis","James","Peter"],"index":65802,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987558126,"difficulty":0.0012441874}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Venetta does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Edward can now know that Edward is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Edward","Veronica","Venetta"],"index":31281,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.989266634,"difficulty":0.010733366}
+{"premise":"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's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW 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":"Christine can now know that Sandra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Randall","Christine","Lee","Sandra"],"index":36399,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8639273047,"difficulty":1.8639273047}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cristina does not know whether Cristina's forehead is 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) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"James can now know whether Steven can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Harry","Steven","Cristina"],"index":15299,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993168116,"difficulty":0.0006831884}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Marsha can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lisa","Michael","Marsha","Lawrence"],"index":55952,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989815354,"difficulty":0.0010184646}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jane can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Kenneth","Jane","Linda"],"index":5610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979397655,"difficulty":0.0020602345}
+{"premise":"There are 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 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":"Wilma can now know whether Michael can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Linda","Wilma","Michael"],"index":19274,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993834496,"difficulty":0.0006165504}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Vincent can now know that Sarah can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Vincent","David","Sarah"],"index":55387,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989441037,"difficulty":0.0010558963}
+{"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 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":"Edward can now know that Edgar can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edward","Edgar"],"index":48210,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989834428,"difficulty":0.0010165572}
+{"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":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":"Bonita can now know that Steven can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bonita","Mark","Paul","Steven"],"index":24997,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979836941,"difficulty":0.0020163059}
+{"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 Regina. Regina's card is shown to Stacy. Stacy's card is shown to Stacy. It is publicly announced that someone picked a red card. It is publicly announced that Stacy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Stacy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Regina","Stacy"],"index":45555,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7805351019,"difficulty":0.2194648981}
+{"premise":"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 (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kim can now know whether Steven can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Kim","Steven","Laura"],"index":24648,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991835952,"difficulty":0.0008164048}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Daniel can now know that Duane can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Daniel","Duane","Andre"],"index":47553,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989468455,"difficulty":0.0010531545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Dave can now know that Mark can know whether Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mark","Joseph","Dave"],"index":15249,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993745685,"difficulty":0.0006254315}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jared's card is shown to Jared. Aaron's card is shown to Aaron. Lisa'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 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jared can now know that Robert can know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jared","Aaron","Robert","Lisa"],"index":58929,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8332111239,"difficulty":0.1667888761}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kayla does not know whether or not everyone's forehead is muddy. It is publicly announced that Kayla does not know whether Kayla's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kayla can now know that Melody can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kayla","Melody"],"index":20293,"s-l":"forehead-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 Carol does not know whether or not everyone is thirsty. It is publicly announced that Christine knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agenta knows whether 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)) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Carol can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","James","Christine","Patricia"],"index":65333,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9945625663,"difficulty":0.0054374337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jillian knows whether Jacob's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Noah can now know that Jacob can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Jillian","Noah","Jacob"],"index":8789,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9793463945,"difficulty":0.0206536055}
+{"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 Philip. Andrea's card is shown to Philip. Barbara's card is shown to Andrea. Philip's card is shown to Barbara. Barbara's card is shown to Barbara. Laverne's card is shown to Barbara. Barbara's card is shown to Laverne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (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 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know that Andrea can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Philip","Andrea","Barbara","Laverne"],"index":35174,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992699027,"difficulty":0.0007300973}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"Virgil can now know whether Patricia can know that Edith's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edith","Virgil","Patricia"],"index":45291,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994319081,"difficulty":0.0005680919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Raymond can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Stella","Aaron","Raymond"],"index":43846,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979807734,"difficulty":0.0020192266}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Joseph can now know whether George can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Linda","George","Michael"],"index":17573,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993646741,"difficulty":0.0006353259}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Betty. Cheryl's card is shown to David. David's card is shown to Cheryl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Betty can now know that David can know that Cheryl picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","David","Cheryl"],"index":34910,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9970604777,"difficulty":0.0029395223}
+{"premise":"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)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Elisa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Elisa","James","Martha"],"index":1639,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974695444,"difficulty":0.0025304556}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dale does not know whether Dale's forehead is muddy. It is publicly announced that Dale does not know whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Dale","Kurt","Laura"],"index":29784,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989639521,"difficulty":0.0010360479}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emmy's card is shown to Clyde. Emmy's card is shown to Emmy. 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 Emmy knows whether Clyde 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":"Emmy can now know that Emmy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Clyde","Emmy"],"index":62320,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99132514,"difficulty":0.00867486}
+{"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 Joe. Joe's card is shown to Mary. Roger's card is shown to Mary. Randy's card is shown to Roger. Mary'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:4 Agentb:1,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Roger can now know that Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Mary","Roger","Randy"],"index":14461,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987491369,"difficulty":0.0012508631}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentb knows whether 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":"Sol can now know whether Heather is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Trisha","Sol","Heather"],"index":29610,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975118637,"difficulty":0.0024881363}
+{"premise":"There are three persons. Everyone is visible 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 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":"Jacqueline can now know that Larry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jacqueline","Larry","Regina"],"index":32674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980074763,"difficulty":0.0019925237}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 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":"Wonda can now know whether Victor can know that Sean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victor","Kay","Sean","Wonda"],"index":11657,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9777367711,"difficulty":0.0222632289}
+{"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)","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":"Chu can now know whether Sandra can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sandra","Denise","Aaron","Chu"],"index":4036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9910079837,"difficulty":0.0089920163}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gene knows whether Natasha's forehead is muddy.","smcdel_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 3)","n_announcements":1,"pbcheck":"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":"Gene can now know that Natasha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Gene","Natasha"],"index":53647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9921975732,"difficulty":0.0078024268}
+{"premise":"There are two persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Zoila can now know that Jeffery can know whether Zoila's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Zoila","Jeffery"],"index":151,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993898869,"difficulty":0.0006101131}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arnold's card is shown to Joyce. Travis's card is shown to Arnold. It is publicly announced that someone picked a red card. It is publicly announced that Joyce does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Arnold can now know that Joyce can know that Joyce picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joyce","Arnold","Travis"],"index":10442,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6694631577,"difficulty":0.3305368423}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Melissa does not know whether or not everyone is thirsty. It is publicly announced that Melissa knows whether Melissa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Melissa can now know that Suzanne can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Suzanne","Melissa","Olive"],"index":67669,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994730353,"difficulty":0.0005269647}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Rochelle can now know that Sarah's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rochelle","James","Mary","Sarah"],"index":51377,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976862669,"difficulty":0.0023137331}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Timothy can now know that Ann can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Ismael","Timothy","Ann"],"index":18888,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991639853,"difficulty":0.0008360147}
+{"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. Damien's card is shown to William. Brian's card is shown to William. Damien's card is shown to Damien. 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":"William can now know that Damien can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Damien","Brian"],"index":51534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993914366,"difficulty":0.0006085634}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether Steven is thirsty. It is publicly announced that Dorothy does not know whether Steven is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows 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":"Dorothy can now know that Steven can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dorothy","Steven"],"index":6876,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990727901,"difficulty":0.0009272099}
+{"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. Scott's card is shown to Louis. Louis's card is shown to Scott. Scott's card is shown to Scott. Scott's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Nancy can now know that Scott can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Scott","Nancy"],"index":62507,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993618131,"difficulty":0.0006381869}
+{"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 Ross. Ross's card is shown to Ross. 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:1,2 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 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joe can now know that Ross can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joe","Ross","Paul"],"index":3636,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967762828,"difficulty":0.0032237172}
+{"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 Erin. Erin's card is shown to Beverly. Beverly's card is shown to Beverly. Jennifer's card is shown to Beverly. Erin's card is shown to Jennifer. Beverly'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:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Erin can now know that Beverly can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Erin","Beverly","Jennifer"],"index":13802,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993232489,"difficulty":0.0006767511}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that Loretta knows whether Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Loretta can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","Jeremy","Loretta","Mike"],"index":64206,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994511008,"difficulty":0.0005488992}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agentd knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Michael can now know that Brian can know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Brian","Diane","Michael"],"index":59713,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9073625803,"difficulty":0.0926374197}
+{"premise":"There are 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 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":"Evangelina can now know whether Karen can know whether Evangelina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Micheal","Karen","Dale","Evangelina"],"index":19799,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993908405,"difficulty":0.0006091595}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie knows whether or not everyone's forehead is muddy. It is publicly announced that Kevin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know that Jackie can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Jackie","Paul","Kevin"],"index":52731,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988615513,"difficulty":0.0011384487}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Pauline can now know that Keith can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pauline","Clare","John","Keith"],"index":51348,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989336133,"difficulty":0.0010663867}
+{"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 4)","n_announcements":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":"Darren can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Adolph","Darren","James"],"index":55392,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964131713,"difficulty":0.0035868287}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor knows whether or 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) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Eleanor can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eleanor","Jessica"],"index":58861,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989238381,"difficulty":0.0010761619}
+{"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 Christine. Christine's card is shown to Michael. Kent's card is shown to Larry. Christine's card is shown to Kent. Michael's card is shown to Kent. It is publicly announced that someone picked a red card. It is publicly announced that Michael picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:4 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Kent can now know that Michael can know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christine","Michael","Larry","Kent"],"index":47753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7147619724,"difficulty":0.2852380276}
+{"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 Suzanne. Jennifer's card is shown to Mary. Suzanne'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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Suzanne can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Suzanne","Mary","Jennifer"],"index":61131,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.986372292,"difficulty":0.013627708}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 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":"Ricardo can now know that David can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Laura","Ricardo"],"index":26111,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991349578,"difficulty":0.0008650422}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that 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 Leo 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 whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marie","Mary","John","Leo"],"index":66784,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993274212,"difficulty":0.0006725788}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy. 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 (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) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Gerald can now know whether Roger can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Karen","Gerald","Roger"],"index":40145,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993740916,"difficulty":0.0006259084}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Trinh knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Trinh 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":["Trinh","Edward"],"index":23509,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993320107,"difficulty":0.0006679893}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jerome is not thirsty. It is publicly announced that James knows whether Jerome 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) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] Agentb knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! 1 ] 0","hypothesis":"Pricilla can now know that Vicki can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Pricilla","Vicki","Jerome"],"index":3669,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9863218069,"difficulty":1.9863218069}
+{"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 Estelle. Estelle's card is shown to Deborah. Mark's card is shown to Deborah. Estelle's card is shown to Mark. Deborah'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:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know that Mark picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Estelle","Deborah","Mark"],"index":64200,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982396364,"difficulty":0.0017603636}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Bridgette. Lauren's card is shown to Lauren. Lisa's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Bridgette can now know whether Lauren can know whether Jim picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jim","Bridgette","Lauren","Lisa"],"index":3758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986299276,"difficulty":0.0013700724}
+{"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 Barbara knows whether Barbara is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Terence can now know whether Barbara can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Terence","Barbara"],"index":17089,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993076324,"difficulty":0.0006923676}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether someone is thirsty. It is publicly announced that Janine does not know whether Linda is thirsty. It is publicly announced that Janine is thirsty. It is publicly announced that Eunice does not know whether Linda is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] (Agentc knows that 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Linda can now know that Eunice is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Janine","Linda","Eunice"],"index":28089,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9836753011,"difficulty":0.0163246989}
+{"premise":"There are four persons. Everyone is visible 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 Ruby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Dominick can now know that John can know that Dominick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruby","John","Dominick","Ruth"],"index":17339,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982113838,"difficulty":0.0017886162}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Willie. Geneva's card is shown to Willie. Ira's card is shown to Willie. Willie's card is shown to Geneva. Ira's card is shown to Geneva. Willie's card is shown to Ira. 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 whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Willie can now know whether Willie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willie","Helen","Geneva","Ira"],"index":15328,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9124081135,"difficulty":0.0875918865}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Earl's card is shown to Audrey. Audrey's card is shown to Stan. Stan's card is shown to Stan. Earl's card is shown to Stan. Earl's card is shown to Earl. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Stan can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Audrey","Stan","Earl"],"index":45947,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994101524,"difficulty":0.0005898476}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles knows whether or not nobody is thirsty. It is publicly announced that Lorraine does not know whether Charles is thirsty. It is publicly announced that Michael does not know whether Lorraine is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Michael can now know that Lorraine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lorraine","Charles","Michael"],"index":67183,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9948760867,"difficulty":0.0051239133}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melvin can now know whether Karen can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marc","Gregory","Karen","Melvin"],"index":6172,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994294047,"difficulty":0.0005705953}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. 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 Viola knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows 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":"Teresa can now know that Donna can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Viola","Scott","Teresa","Donna"],"index":47768,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987437129,"difficulty":0.0012562871}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Faith. Dawn's card is shown to Dawn. It is publicly announced that someone picked a red card. It is publicly announced that Faith does not know whether Faith picked a red card. It is publicly announced that Dawn does not know whether Faith picked a red card. It is publicly announced that Faith does not know whether or not everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1&2) ] 0","hypothesis":"Dawn can now know whether Faith can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Faith","Dawn"],"index":42632,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999417901,"difficulty":0.000582099}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandy'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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vivian","Sandy","John","Sylvia"],"index":58471,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994137287,"difficulty":0.0005862713}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (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":"Melva can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","Melva","Ruby"],"index":16918,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99899894,"difficulty":0.00100106}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Megan's card is shown to Megan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Megan can now know that Virginia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Virginia","Megan","Rickey"],"index":5954,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974752069,"difficulty":0.0025247931}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Desiree knows whether Desiree's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (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":"Desiree can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Desiree","John"],"index":16786,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993859529,"difficulty":0.0006140471}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hayley's card is shown to Hayley. Kevin's card is shown to Heather. Heather's card is shown to Michele. Kevin's card is shown to Michele. Michele's card is shown to Michele. It is publicly announced that someone picked a red card. It is publicly announced that Hayley picked a red card. It is publicly announced that Kevin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 3 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Heather can now know that Hayley picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Hayley","Heather","Kevin","Michele"],"index":44738,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6125419736,"difficulty":1.6125419736}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louis knows whether or not everyone's forehead is muddy. It is publicly announced that Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Frances can now know that Felix's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","Gregory","Louis","Felix"],"index":47381,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9947038293,"difficulty":0.0052961707}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Evelyn knows whether someone is thirsty. It is publicly announced that Toni knows whether or not nobody is thirsty. It is publicly announced that Lisa knows whether Lisa is thirsty. It is publicly announced that Toni 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Tracey can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Evelyn","Lisa","Toni","Tracey"],"index":8590,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954106212,"difficulty":0.0045893788}
+{"premise":"There are two persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Clifford can now know whether Frankie can know that Frankie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frankie","Clifford"],"index":9795,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993104935,"difficulty":0.0006895065}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 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) ] [ ! 2 ] 0","hypothesis":"Jason can now know whether James can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","James","David"],"index":21943,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994371533,"difficulty":0.0005628467}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 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":"Mary can now know that Mathew can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Mathew"],"index":43972,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994872808,"difficulty":0.0005127192}
+{"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 Christine. Sharon's card is shown to Christine. Christine's card is shown to April. April's card is shown to April. 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:1,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know whether Christine picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christine","April","Sharon","Tammy"],"index":62280,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9199154973,"difficulty":0.0800845027}
+{"premise":"There are three persons. Everyone is visible 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's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows 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":"Marisa can now know that Kim can know whether Marisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","David","Marisa"],"index":22707,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994533658,"difficulty":0.0005466342}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). John's card is shown to John. John's card is shown to Lucie. Lucie's card is shown to Lucie. Carol's card is shown to Carol. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lucie can now know whether Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Lucie","Carol"],"index":66646,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6022619605,"difficulty":0.3977380395}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charles does not know whether or not everyone is thirsty. It is publicly announced that Virgil 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 ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! 1 ] 0","hypothesis":"Susanna can now know whether Charles can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virgil","Susanna","Charles"],"index":57182,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994797111,"difficulty":0.0005202889}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kari's forehead is muddy. It is publicly announced that Cindy knows whether Kari's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agenta knows that (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) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Douglas can now know that Cindy can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Douglas","John","Kari","Cindy"],"index":6161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994371533,"difficulty":0.0005628467}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether Rosa's forehead is muddy. It is publicly announced that Gilbert knows whether Rosa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Rosa can now know that Kim can know whether Rosa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gilbert","Kim","Nicholas","Rosa"],"index":7800,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998771131,"difficulty":0.001228869}
+{"premise":"There are three persons. Everyone is visible 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 Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"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":"Jennifer can now know that Paris can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Paris","Gregory"],"index":33380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989401698,"difficulty":0.0010598302}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"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":"Mark can now know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Victor","John"],"index":58819,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983922839,"difficulty":0.0016077161}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to June. Martha's card is shown to Martha. Eugene's card is shown to Martha. Martha'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:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"June can now know whether Eugene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["June","Randy","Martha","Eugene"],"index":29521,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9117534757,"difficulty":0.0882465243}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 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":"Michael can now know that Charles can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Perry","Michael","Charles"],"index":51748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984947443,"difficulty":0.0015052557}
+{"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 Alan. Thomas's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Thomas does not know whether Thomas picked a red card. It is publicly announced that Thomas knows whether or not nobody 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) ] [ ! (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:3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Alan can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Alan","Kenneth"],"index":41261,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993997812,"difficulty":0.0006002188}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Angelica's card is shown to Fern. Richard's card is shown to Richard. Fern's card is shown to Teena. Fern's card is shown to Angelica. Richard's card is shown to Angelica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Fern can now know whether Richard can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Fern","Richard","Teena","Angelica"],"index":46143,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993908405,"difficulty":0.0006091595}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Clifton 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) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Clifton can now know that Quinn can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Quinn","Doris","Clifton"],"index":7390,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999509573,"difficulty":0.000490427}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Abbey's card is shown to Francis. Francis's card is shown to Abbey. Abbey's card is shown to Abbey. Francis's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Abbey knows whether Abbey picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Francis can now know whether Abbey can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francis","Abbey","Robert"],"index":62258,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994439483,"difficulty":0.0005560517}
+{"premise":"There are two persons. Everyone is visible 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 Luther'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":"Vanessa can now know that Luther can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Luther","Vanessa"],"index":8655,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989655018,"difficulty":0.0010344982}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gina knows whether Terry is thirsty. It is publicly announced that Gina knows whether Terry is thirsty. It is publicly announced that Terry knows whether Gina is thirsty. It is publicly announced that Gina knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows that (Agentb knows 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":"Gina can now know that Terry can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gina","Terry"],"index":49444,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999110043,"difficulty":0.000889957}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether Matthew's forehead is muddy. It is publicly announced that Josie knows whether or not everyone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Josie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Josie","Jose","Gary","Matthew"],"index":44707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994594455,"difficulty":0.0005405545}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcy's card is shown to John. Michael's card is shown to John. Marcy's card is shown to Marcy. Marcy's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Marcy does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"John can now know whether Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Marcy","Michael"],"index":54119,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9848785996,"difficulty":0.0151214004}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nola knows whether Nola is thirsty. It is publicly announced that Frances knows whether Frances is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Nola can now know that Frances can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Nola","Frances"],"index":66944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989299178,"difficulty":0.0010700822}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Kourtney can now know whether Michael can know whether Angela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Angela","Kourtney","Michael"],"index":30024,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990881681,"difficulty":0.0009118319}
+{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agenta knows 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":"Marguerite can now know that Dennis can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dennis","Marguerite","Loretta"],"index":3779,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994502664,"difficulty":0.0005497336}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Rhonda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (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) ] 0","hypothesis":"Doris can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rhonda","Timothy","Doris"],"index":23089,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990792274,"difficulty":0.0009207726}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elizabeth's card is shown to Elizabeth. Elizabeth's card is shown to James. James's card is shown to Delma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Elizabeth","James","Delma"],"index":54199,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993323684,"difficulty":0.0006676316}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Billy 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 (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":"Brendon can now know that Billy can know that Brendon is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brendon","Michelle","Fredrick","Billy"],"index":53539,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997641325,"difficulty":0.002358675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julie is not thirsty. It is publicly announced that Roberto 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) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Julie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Roberto","William","Julie"],"index":715,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.999057591,"difficulty":0.000942409}
+{"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 Sally is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] Agentc knows whether (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jeffery can now know whether Thomas can know that Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Sally","Jeffery","Robert"],"index":35723,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954283237,"difficulty":0.0045716763}
+{"premise":"There are three persons. Everyone is visible 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 David's forehead is muddy. It is publicly announced that Bonnie's forehead is not muddy. It is publicly announced that Bonnie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Beverly can now know whether Bonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Beverly","Bonnie","David"],"index":52709,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994698167,"difficulty":0.0005301833}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether or not nobody's forehead is muddy. It is publicly announced that Beulah's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agenta knows that (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that Linda can know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Beulah","Linda","Michael"],"index":41082,"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. Each person draws a card, face unrevealed (red or black). Charles's card is shown to Charles. Charles's card is shown to Illa. Charles's card is shown to Lewis. Tina's card is shown to Lewis. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card. It is publicly announced that Illa 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)) ] (Agentb knows that 2)","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":"Illa can now know that Illa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Illa","Lewis","Tina"],"index":14804,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9698939323,"difficulty":0.0301060677}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jo's card is shown to Jo. Michael's card is shown to Jo. Ida's card is shown to Jo. Michael's card is shown to Michael. Jeanne's card is shown to Michael. Ida's card is shown to Ida. Jeanne's card is shown to Ida. Michael'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:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 VALID? [ ! (1|2|3|4) ] (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:2,4 Agentc:3,4 Agentd:2 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":["Jo","Michael","Ida","Jeanne"],"index":25944,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999001205,"difficulty":0.000998795}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 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":"Jeff can now know that Raymond can know whether Raymond is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeff","Raymond","Marcia"],"index":66120,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8994215727,"difficulty":0.1005784273}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tanya's card is shown to Tanya. Lester's card is shown to Tanya. Tanya's card is shown to Lester. Lester's card is shown to Lester. 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 Tanya knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Lester can now know that Tanya can know that Lester picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tanya","Lester"],"index":7806,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.914490521,"difficulty":0.085509479}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether Larry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chester","James","Larry"],"index":4801,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993721843,"difficulty":0.0006278157}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether Susan is thirsty. It is publicly announced that Allen does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows 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":"Travis can now know that Susan can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Allen","Carol","Travis"],"index":67570,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994995594,"difficulty":0.0005004406}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clare knows whether Clare's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Clare can now know that Monica can know whether Monica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Monica","Cheryl","Edward","Clare"],"index":45442,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9912911654,"difficulty":1.9912911654}
+{"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 Maria is thirsty. It is publicly announced that Maria is not thirsty. It is publicly announced that Betty does not know whether Michael is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] (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 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Betty can now know whether Maria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Betty","Maria"],"index":3982,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5170457363,"difficulty":0.4829542637}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammie's card is shown to Tammie. Carla's card is shown to Tammie. Margaret's card is shown to Tammie. Margaret's card is shown to William. William's card is shown to Margaret. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tammie can now know that William picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammie","Carla","William","Margaret"],"index":12519,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997739315,"difficulty":0.002260685}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentc knows 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":"Ana can now know that Barbara can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ana","Valene","Barbara","Elisa"],"index":46262,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993008375,"difficulty":0.0006991625}
+{"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 Tommie. Tommie's card is shown to Tommie. It is publicly announced that someone picked a red card. It is publicly announced that Tommie 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:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1|2) ] (Agentb knows that 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)) ] [ ! (1|2) ] 0","hypothesis":"Tommie can now know that Tommie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mildred","Tommie"],"index":39375,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.947281003,"difficulty":0.052718997}
+{"premise":"There are four persons. Everyone is visible 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 Julia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Julia can now know that Denis can know that Tracey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Denis","Darlene","Julia","Tracey"],"index":25934,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978073239,"difficulty":0.0021926761}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Caroline can now know that Sheila can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irene","Dorothy","Sheila","Caroline"],"index":23970,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988268018,"difficulty":0.0011731982}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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":"Steven can now know that Lorna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorna","Blythe","Steven"],"index":45586,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9130086899,"difficulty":0.0869913101}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruth's card is shown to Ruth. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Ruth can now know whether Robert can know whether Ruth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ruth","Robert"],"index":45229,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985070825,"difficulty":0.0014929175}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows whether 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":"Chad can now know that John can know whether Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","John","Chad"],"index":15295,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992513061,"difficulty":0.0007486939}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Donna. Annie's card is shown to Donna. 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:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Annie 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":["Donna","Annie","William"],"index":45663,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993501306,"difficulty":0.0006498694}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laurena's card is shown to John. Laurena's card is shown to Kenneth. Kenneth's card is shown to Laurena. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb 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":"Laurena can now know whether Kenneth can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Kenneth","Laurena"],"index":6905,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993987083,"difficulty":0.0006012917}
+{"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 Ray. Ray's card is shown to Melvin. Melvin's card is shown to Melvin. Ray's card is shown to Dorothy. Melvin's card is shown to Dorothy. Dorothy's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentb knows that 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":"Melvin can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ray","Melvin","Dorothy"],"index":32307,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9925621152,"difficulty":0.0074378848}
+{"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 Robert is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (Agenta knows whether (~(1|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":"Rachel can now know that Robert can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Michael","Rachel"],"index":42770,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993128777,"difficulty":0.0006871223}
+{"premise":"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 Ramona knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"April can now know that Ramona can know that April's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ramona","Nancy","April","John"],"index":50940,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972443581,"difficulty":0.0027556419}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Anne's card is shown to Gary. Thomas's card is shown to Gary. Anne's card is shown to Anne. Thomas's card is shown to Anne. Gary's card is shown to Thomas. Anne's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Thomas picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Gary can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gary","Anne","Thomas"],"index":47400,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985851049,"difficulty":0.0014148951}
+{"premise":"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 Sidney knows whether Jimmy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] Agenta knows whether (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) ] [ ! 2 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jimmy can now know whether Thomas can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmy","Thomas","Sidney"],"index":47560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9108695984,"difficulty":0.0891304016}
+{"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. Steve's card is shown to Anna. Anna's card is shown to Anna. Steve's card is shown to Rita. Rita's card is shown to Rita. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether Steve picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anna can now know that Rita can know that Anna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steve","Anna","Rita"],"index":57112,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9854155183,"difficulty":0.0145844817}
+{"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 Diana. Rose's card is shown to Diana. Diana's card is shown to Amy. Amy's card is shown to Amy. Diana's card is shown to Rose. Rose's card is shown to Rose. It is publicly announced that someone picked a red card. It is publicly announced that Rose knows whether Amy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Amy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Diana","Amy","Rose"],"index":20478,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994408488,"difficulty":0.0005591512}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether someone's forehead is muddy.","smcdel_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)","n_announcements":1,"pbcheck":"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":"Louise can now know that Alicia can know whether Alicia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alicia","Louise","Brittany"],"index":50114,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993465543,"difficulty":0.0006534457}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony knows whether or not nobody is thirsty. It is publicly announced that Tony does not know whether Brandy is thirsty. It is publicly announced that Danny does not know whether or not everyone is thirsty. It is publicly announced that Tony does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Brandy can now know whether Tony can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brandy","Tony","Danny"],"index":2474,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9954079986,"difficulty":0.0045920014}
+{"premise":"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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Roger can now know whether Randall can know that Beau's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beau","Randall","John","Roger"],"index":19013,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9949059486,"difficulty":0.0050940514}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Barbara can now know that Kenneth can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Kenneth","Adrienne"],"index":16408,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989809394,"difficulty":0.0010190606}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dixie knows whether Dixie'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 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":"Dixie can now know that Dixie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Christine","Dixie"],"index":46122,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9950090647,"difficulty":0.0049909353}
+{"premise":"There are three persons. Everyone is visible 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 Chris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc 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&2&3)) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Yasmin","Michael","Chris"],"index":42912,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9663139582,"difficulty":0.0336860418}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edwin 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 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":"Martha can now know that Edwin can know whether Edwin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Edwin","Martha"],"index":25362,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9959006906,"difficulty":0.0040993094}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (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) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Willie can now know that Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Douglas","Jason","Myra"],"index":20167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974924326,"difficulty":0.0025075674}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patsy's card is shown to John. Patsy's card is shown to Patsy. It is publicly announced that someone picked a red card. It is publicly announced that Patsy 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)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"John can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Patsy"],"index":6207,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994509816,"difficulty":0.0005490184}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Richard knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Emily"],"index":19596,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.966702342,"difficulty":0.033297658}
+{"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 Lori. Sarah's card is shown to Sarah. 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))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Sarah can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lori","Sarah"],"index":4932,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9922733903,"difficulty":0.0077266097}
+{"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. Joseph's card is shown to Gertrude. Gertrude's card is shown to Joseph. Gertrude's card is shown to Ashley. Ashley's card is shown to Ashley. Gertrude's card is shown to Lenora. 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:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lenora can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gertrude","Joseph","Ashley","Lenora"],"index":61407,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989917874,"difficulty":0.0010082126}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwayne knows whether or not everyone's forehead is muddy. It is publicly announced that Dwayne does not know whether Dwayne's forehead is muddy. It is publicly announced that Edward knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Dwayne can now know that Edward can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dwayne","Joseph","Edward"],"index":52428,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994668365,"difficulty":0.0005331635}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Yoshiko's card is shown to Arnold. Yoshiko'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 Yoshiko knows whether someone picked a red card. It is publicly announced that Yoshiko 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 Yoshiko 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 2)","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":"Yoshiko can now know whether Yoshiko picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Arnold","Yoshiko","Robert"],"index":1051,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9853155613,"difficulty":0.0146844387}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ida's card is shown to Jorge. Andrea's card is shown to Ida. Jorge's card is shown to Andrea. Ida's card is shown to Andrea. Andrea's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Ida 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)) ] (Agenta 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":"Jorge can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jorge","Ida","Andrea"],"index":53352,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989702702,"difficulty":0.0010297298}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. Darlene's card is shown to Darlene. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Maria does not know whether Darlene picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Maria can now know that Darlene can know whether Maria picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maria","Darlene"],"index":34481,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6986938715,"difficulty":0.3013061285}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether Ernie's forehead is muddy. It is publicly announced that Joe does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows 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 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Joe can now know whether Ernie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joe","Ernie"],"index":50519,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994619489,"difficulty":0.0005380511}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Daniel can now know whether Phyllis can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Phyllis","Daniel","Jamel"],"index":60064,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993385673,"difficulty":0.0006614327}
+{"premise":"There are four persons. Everyone is visible 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 Gayle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Helen can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","James","Trevor","Gayle"],"index":47103,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992425442,"difficulty":0.0007574558}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows 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":"Ronald can now know whether Hector can know whether Hector's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Ronald","Hector","Keith"],"index":55250,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994069338,"difficulty":0.0005930662}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delphia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"Amy can now know that Stacey can know that Stacey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Delphia","Amy","Stacey"],"index":11235,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978590608,"difficulty":0.0021409392}
+{"premise":"There are three persons. Everyone is visible 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 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 (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Florence can now know that Chris can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","Thomas","Chris"],"index":13295,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989646673,"difficulty":0.0010353327}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caroline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Caroline can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephanie","Caroline"],"index":24811,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988872409,"difficulty":0.0011127591}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Blanche's card is shown to Blanche. Blanche's card is shown to Lillian. Lillian's card is shown to Lillian. Lillian's card is shown to Glenda. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","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":"Blanche can now know whether Glenda can know whether Blanche picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Blanche","Lillian","Glenda"],"index":10931,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9976183772,"difficulty":0.0023816228}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen does not know whether Maria is thirsty. It is publicly announced that Ernesto does not know whether or not everyone is thirsty. It is publicly announced that Ellen does not know whether Joyce is thirsty. It is publicly announced that Maria knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows that 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":"Ellen can now know whether Joyce can know that Ernesto is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maria","Ellen","Ernesto","Joyce"],"index":19958,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9860975742,"difficulty":0.0139024258}
+{"premise":"There are four persons. Everyone is visible 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 Jesse's forehead is muddy. It is publicly announced that Robert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] 0","hypothesis":"Beverly can now know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Angel","Robert","Beverly","Jesse"],"index":23350,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994714856,"difficulty":0.0005285144}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether Gerald's forehead is muddy. It is publicly announced that Joseph'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 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Joseph can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gerald","Joseph"],"index":32486,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6843591332,"difficulty":1.6843591332}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilfred knows whether Wilfred's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Miguel can now know that Wilfred can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Miguel","Wilfred"],"index":52561,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989053011,"difficulty":0.0010946989}
+{"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 Brian. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth knows whether Brian 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 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":"Kenneth can now know that Brian picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brian","Kenneth"],"index":38394,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9670385718,"difficulty":1.9670385718}
+{"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 John. Maria's card is shown to Sara. Sara'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:1 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:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sara can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maria","John","Sara","Robert"],"index":51463,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994043112,"difficulty":0.0005956888}
+{"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. John's card is shown to Anna. Anna's card is shown to John. Anna's card is shown to Joshua. Joshua's card is shown to Joshua. Anna's card is shown to Sheena. 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:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1,3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","John","Joshua","Sheena"],"index":16334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9943109751,"difficulty":0.0056890249}
+{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that Mary knows whether Ruben's forehead is muddy.","smcdel_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 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":"Mary can now know that Thomas can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ruben","Mary","Thomas"],"index":7676,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9965502024,"difficulty":0.0034497976}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jocelyn's card is shown to Jocelyn. Kevin's card is shown to Jocelyn. Kevin'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 or not everyone picked a red card. It is publicly announced that Kevin knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Kevin can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jocelyn","Kevin"],"index":24699,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981554151,"difficulty":0.0018445849}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Felicia's card is shown to Felicia. William's card is shown to Felicia. Charles's card is shown to Charles. William's card is shown to Charles. Charles's card is shown to Melissa. Melissa's card is shown to Melissa. Felicia's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Melissa does not know whether William picked a red card. It is publicly announced that Felicia does not know whether Charles 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) ] Agentc knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,4 Agentc:2,3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Melissa can now know whether William can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Felicia","Charles","Melissa","William"],"index":13767,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9757165909,"difficulty":0.0242834091}
+{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Felix's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Kevin","James","Felix"],"index":23675,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9981637597,"difficulty":0.0018362403}
+{"premise":"There are two persons. Everyone is visible 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 Edward'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 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":"Edward can now know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Edward","Peter"],"index":3132,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928576946,"difficulty":0.0071423054}
+{"premise":"There are four persons. Everyone is visible 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 Alicia knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Keith can now know whether Rebecca can know whether Rebecca's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Keith","Monica","Rebecca","Alicia"],"index":29954,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992980957,"difficulty":0.0007019043}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Michael"],"index":44676,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990488887,"difficulty":0.0009511113}
+{"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. Myrna's card is shown to Daniel. Myrna's card is shown to Kristin. Myrna's card is shown to Joseph. Joseph's card is shown to Myrna. Myrna's card is shown to Myrna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:4 Agentc:4 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Myrna can now know whether Daniel can know that Myrna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Kristin","Joseph","Myrna"],"index":55025,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9254053831,"difficulty":0.0745946169}
+{"premise":"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. It is publicly announced that Barbara 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 (1&2&3&4)) ] [ ! (Agenta knows whether 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:2,3,4 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":"Mary can now know that Virginia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Mary","Virginia","David"],"index":47908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989796281,"difficulty":0.0010203719}
+{"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 Sandra knows whether or not nobody is thirsty. It is publicly announced that Sandra 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 (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":"Sandra can now know that Natalie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sandra","Natalie"],"index":64092,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9546182752,"difficulty":1.9546182752}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agenta knows whether 1) ] 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) ] 0","hypothesis":"Rebecca can now know that James can know that Arden's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Susan","Arden","Rebecca","James"],"index":60494,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980493784,"difficulty":0.0019506216}
+{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Blythe knows whether Blythe's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Wendy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows that (1&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":"Blythe can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Blythe","Wendy"],"index":3463,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951811433,"difficulty":0.0048188567}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rebekah's card is shown to George. Joshua's card is shown to George. George's card is shown to Joshua. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"George can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Rebekah","Joshua"],"index":4743,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993773103,"difficulty":0.0006226897}
+{"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 Louis does not know whether Barbara is thirsty. It is publicly announced that Barbara does not know whether Louis is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether 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) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Bobby can now know that Barbara can know whether Louis is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Bobby","Louis","Barbara"],"index":49836,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9947350025,"difficulty":0.0052649975}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (~(1|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":"Walter can now know that Mary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Walter","Mary"],"index":49562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989696741,"difficulty":0.0010303259}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marie knows whether or not everyone's forehead is muddy. It is publicly announced that Grant does not know whether Grant's forehead is muddy. It is publicly announced that Marie does not know whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Laura can now know that Pedro can know whether Pedro's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Grant","Pedro","Marie"],"index":26925,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.954102993,"difficulty":1.954102993}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey does not know whether Tracey's forehead is muddy. It is publicly announced that Lori 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)))","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":"Lori can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tracey","Lori"],"index":45738,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993844032,"difficulty":0.0006155968}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lewis's card is shown to Bonnie. Lewis's card is shown to Lewis. It is publicly announced that someone picked a red card. It is publicly announced that Bonnie 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 whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Lewis can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bonnie","Lewis"],"index":62899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994288087,"difficulty":0.0005711913}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie does not know whether Debbie's forehead is muddy. It is publicly announced that Debbie's forehead is not muddy. It is publicly announced that Debbie 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)) ] (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Debbie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Debbie","Danny"],"index":61802,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994871616,"difficulty":0.0005128384}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brittney knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Chad","Brittney","Rita","Curtis"],"index":54693,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988952279,"difficulty":0.0011047721}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Robert. Nikki's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Nikki picked a red card. It is publicly announced that Patricia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! 1 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Patricia can now know that Patricia picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Robert","Nikki"],"index":48501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5458542705,"difficulty":0.4541457295}
+{"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.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 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":"Matthew can now know that Wayne can know that Matthew is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Wayne","Matthew","Michelle"],"index":538,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8648176789,"difficulty":1.8648176789}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lottie's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lottie can now know that Joann can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lottie","Joann"],"index":1803,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987524748,"difficulty":0.0012475252}
+{"premise":"There are three persons. Everyone is visible 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 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 2) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know whether Adam can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Adam","William","Betty"],"index":51323,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992085099,"difficulty":0.0007914901}
+{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that Eric knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Andrew can now know that Andrew's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Andrew","Eric","Odell"],"index":4677,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955073595,"difficulty":0.0044926405}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (1&2) ] 0","hypothesis":"Gerald can now know that Leanne can know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leanne","Gerald"],"index":26514,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9887728095,"difficulty":0.0112271905}
+{"premise":"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's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Barbara can now know that Annie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ramona","Annie","Barbara"],"index":10636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988364577,"difficulty":0.0011635423}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Eva. Phillip's card is shown to Eva. Phillip's card is shown to Phillip. Frank's card is shown to Phillip. Phillip's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank does not know whether Eva picked a red card. It is publicly announced that Eva does not know whether Frank picked a red card. It is publicly announced that Frank knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Eva can now know that Phillip can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Phillip","Frank"],"index":8087,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994632602,"difficulty":0.0005367398}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry does not know whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Amanda can now know that Bruce can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Georgia","Bruce","Henry","Amanda"],"index":9827,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9878419042,"difficulty":0.0121580958}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olga's card is shown to Betty. Olga's card is shown to Derek. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Olga can now know whether Betty picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Olga","Betty","Derek"],"index":45609,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975243211,"difficulty":0.0024756789}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Irene does not know whether Abby is thirsty. It is publicly announced that Abby does not know whether Leslie is thirsty. It is publicly announced that 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 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] (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) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Leslie can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Abby","Leslie","Irene"],"index":32296,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990454316,"difficulty":0.0009545684}
+{"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 Robert. Robert's card is shown to Larry. Terry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Terry knows whether Robert picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Terry can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Terry","Larry"],"index":2591,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9406301975,"difficulty":0.0593698025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald does not know whether or not everyone is thirsty.","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":"Rich can now know that Gerald can know whether Scott is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gerald","Rich","Scott"],"index":29118,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9804270267,"difficulty":0.0195729733}
+{"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)","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":"Ray can now know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ray","Eric","Mary"],"index":161,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953373671,"difficulty":0.0046626329}
+{"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 Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sara can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sara","Andria","Victor"],"index":2549,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993528724,"difficulty":0.0006471276}
+{"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 Rene is thirsty. It is publicly announced that Rene does not know whether Minnie is thirsty. It is publicly announced that Rene is thirsty. It is publicly announced that Rene knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentd knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 2 ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know whether William is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Teresa","Rene","Minnie","William"],"index":34918,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9974562526,"difficulty":0.0025437474}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phyllis knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Ida knows whether Ida's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Daryl can now know whether Fran's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Daryl","Phyllis","Fran"],"index":40310,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
+{"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 Althea. Althea's card is shown to Althea. Helen's card is shown to Althea. Althea's card is shown to Marlene. Helen's card is shown to Marlene. Althea's card is shown to Helen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christopher can now know whether Helen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Althea","Marlene","Helen"],"index":43277,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9510253072,"difficulty":0.0489746928}
+{"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 Eugene knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Sonya can now know that Eugene is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Sonya","Eugene","David"],"index":20036,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9937455654,"difficulty":0.0062544346}
+{"premise":"There are four persons. Everyone is visible 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's forehead is not muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 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) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Patricia can now know that Bernard can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patrick","Phillip","Bernard","Patricia"],"index":621,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989878535,"difficulty":0.0010121465}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew does not know whether Debra is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 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) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Raymond can now know that Debra can know that Debra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Raymond","Andrew","Christine","Debra"],"index":64069,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.992833972,"difficulty":0.007166028}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Trisha's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] Agenta knows whether (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 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Veronica can now know whether Trisha can know that Veronica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Veronica","Trisha","Linda"],"index":51192,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8251340389,"difficulty":1.8251340389}
+{"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 (1&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":"Sherry can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Danny","Sherry"],"index":61617,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.99361974,"difficulty":0.00638026}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Windy 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Johnny can now know whether Johnny's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darrell","Marvin","Windy","Johnny"],"index":46486,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955875874,"difficulty":0.0044124126}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maggie does not know whether Maggie's forehead is muddy. It is publicly announced that Omar knows whether Omar's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Omar can now know that Maggie can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Carlos","Omar","Maggie"],"index":63707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994270802,"difficulty":0.0005729198}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Duane knows whether Andrew's forehead is muddy. It is publicly announced that Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] 0","hypothesis":"Juanita can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Andrew","Cecilia","Duane"],"index":65572,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8164285421,"difficulty":0.1835714579}
+{"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 Stacy is thirsty. It is publicly announced that Stacy is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows 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) ] [ ! ~(3) ] 0","hypothesis":"Stacy can now know whether Martha can know that Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Evelyn","Martha","Stacy","Robert"],"index":56273,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.6106348634,"difficulty":1.6106348634}
+{"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. Candice's card is shown to Marie. Edward's card is shown to Candice. Marie's card is shown to Candice. It is publicly announced that someone picked a red card. It is publicly announced that Edward does not know whether Marie 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:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Marie can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Marie","Candice"],"index":8898,"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 Maryellen does not know whether Maryellen'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 whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Richard can now know whether Maryellen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Maryellen","Rosemary"],"index":8863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992415905,"difficulty":0.0007584095}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dawn does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that 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":"Lawrence can now know whether Lynda can know that Dawn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lawrence","Dawn","Lynda","James"],"index":2947,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9899297357,"difficulty":0.0100702643}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elna's card is shown to Elna. India's card is shown to Elna. Daniel's card is shown to Elna. India's card is shown to Miles. Daniel's card is shown to Miles. Miles's card is shown to India. Elna's card is shown to Daniel. Daniel's card is shown to Daniel. It is publicly announced that someone picked a red card. It is publicly announced that India does not know whether India 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) ] (Agentb knows whether 1)","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":"Miles can now know whether Elna picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elna","Miles","India","Daniel"],"index":36789,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.5659653544,"difficulty":1.5659653544}
+{"premise":"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 Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows 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 3) ] 0","hypothesis":"Jeannie can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Richard","Mary","Jeannie"],"index":34327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912125468,"difficulty":0.0087874532}
+{"premise":"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 knows whether Markus'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 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":"Brenda can now know whether Markus can know whether Markus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brenda","Markus"],"index":17353,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.986253202,"difficulty":1.986253202}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lilliana is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentb knows that (1|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":"Larry can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lillian","Larry","Lilliana"],"index":58757,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995250702,"difficulty":0.0004749298}
+{"premise":"There are four persons. Everyone is visible 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 Heidi's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentd knows that 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":"Joan can now know that Frank can know that Heidi's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joan","Heidi","Ella","Frank"],"index":28983,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980407357,"difficulty":0.0019592643}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Gerald can now know whether Thomas can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Kelly","Sharon","Gerald"],"index":64248,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.968875587,"difficulty":0.031124413}
+{"premise":"There are 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 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":"Philip can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tiffany","Philip","William"],"index":47570,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978880286,"difficulty":0.0021119714}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Octavio's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Anna can now know whether Ebony can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Anna","Octavio","Ebony"],"index":25172,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993000031,"difficulty":0.0006999969}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Prince's card is shown to Prince. Judith's card is shown to Judith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Judith can now know whether Prince can know that Judith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Prince","Judith"],"index":28467,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7818438411,"difficulty":1.7818438411}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laurie knows whether Laurie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 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:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Laurie can now know that Earl can know whether Earl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laurie","Earl"],"index":37268,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992899895,"difficulty":0.0007100105}
+{"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 Kory is thirsty. It is publicly announced that Joseph knows whether or not everyone is thirsty. It is publicly announced that Joseph does not know whether Carlos is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (~(1|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":"Carlos can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Kory","Carlos"],"index":42340,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990699887,"difficulty":0.0009300113}
+{"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 Jennefer. Jorge's card is shown to Jorge. Robert's card is shown to Jorge. Jennefer's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 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:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jorge can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jennefer","James","Jorge","Robert"],"index":47000,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999394536,"difficulty":0.000605464}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margie knows whether or not everyone's forehead is muddy. It is publicly announced that Sybil's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Sybil can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sybil","Margie","Betty"],"index":8252,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999037385,"difficulty":0.000962615}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Katy can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katy","June","Joseph","Corey"],"index":63602,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994754195,"difficulty":0.0005245805}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Shirley can now know that Irene can know that Nicholas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicholas","Irene","Frances","Shirley"],"index":29085,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.979522109,"difficulty":0.020477891}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vincent's card is shown to Kirk. Vincent's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Kirk picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Kirk can now know that Vincent can know whether Tracy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kirk","Vincent","Tracy"],"index":59139,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9427662492,"difficulty":0.0572337508}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosina's card is shown to Vernon. Linda's card is shown to Rosina. Linda's card is shown to Linda. Vernon's card is shown to Troy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Linda can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Vernon","Rosina","Linda","Troy"],"index":62645,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993025064,"difficulty":0.0006974936}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leila does not know whether or not everyone is thirsty. It is publicly announced that Anthony knows whether Anthony 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 that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Leila can now know that Catherine is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leila","Anthony","Michael","Catherine"],"index":51338,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955997467,"difficulty":0.0044002533}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Meghan does not know whether William 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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentd 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) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"William can now know that Meghan can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Meghan","William","Paulette","John"],"index":40229,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994105101,"difficulty":0.0005894899}
+{"premise":"There are four persons. Everyone is visible 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 Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Dawn can now know that Ruth can know that Karyn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karyn","Dawn","Ruth","Erin"],"index":61428,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983021021,"difficulty":0.0016978979}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Peggy can now know that Beth's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beth","Patricia","Cathleen","Peggy"],"index":60013,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.6020208001,"difficulty":0.3979791999}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (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":"Cathy can now know whether Anna can know that Anna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Cathy","John"],"index":58731,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7917394638,"difficulty":0.2082605362}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheila does not know whether Sheila's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Leroy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Sheila can now know whether Leroy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sheila","Leroy"],"index":16099,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9832487106,"difficulty":0.0167512894}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert knows whether Robert is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Clarence can now know that Edward can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Sandra","Edward","Clarence"],"index":27165,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8247678876,"difficulty":1.8247678876}
+{"premise":"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 (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that Edward can know that Francis's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","Francis","Edward","Thomas"],"index":63630,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9949413538,"difficulty":0.0050586462}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ruby knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":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":"Clarence can now know that Carmen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ruby","Clarence","Carmen","Sung"],"index":34351,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990314245,"difficulty":0.0009685755}
+{"premise":"There are four persons. Everyone is visible 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 Alicia's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (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":"Dennis can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dennis","James","Alicia","Robert"],"index":62388,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988107681,"difficulty":0.0011892319}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ada knows whether Ada's forehead is muddy. It is publicly announced that Katrina 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) ] [ ! (Agentc knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Neva can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Ada","Katrina","Neva"],"index":26536,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998798728,"difficulty":0.001201272}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tammy knows whether or not everyone is thirsty. It is publicly announced that Michael knows whether Tammy 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 (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Michael can now know that Mary can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Tammy","Mary"],"index":29621,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9713026881,"difficulty":0.0286973119}
+{"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 Joanne. Tony's card is shown to Tony. Tony's card is shown to Kenneth. 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 Rachel knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Tony can now know that Rachel can know that Joanne picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joanne","Tony","Rachel","Kenneth"],"index":25256,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9651242495,"difficulty":0.0348757505}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. 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 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Arturo can now know whether Arturo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bonnie","Arturo","Patricia"],"index":20783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993979931,"difficulty":0.0006020069}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc 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) ] [ ! 3 ] 0","hypothesis":"Edward can now know that Craig can know whether Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alan","Marshall","Edward","Craig"],"index":53948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993514419,"difficulty":0.0006485581}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rosa does not know whether Nancy is thirsty. It is publicly announced that Rosa knows whether Rosa is thirsty. It is publicly announced that Nancy does not know whether Rosa is thirsty. It is publicly announced that Judith does not know whether Rosa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows 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) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Rosa can now know that Nancy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Rosa","Judith"],"index":37607,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994758964,"difficulty":0.0005241036}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lena knows whether Lena'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)","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":"Mara can now know that Lena can know that Lena's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lena","Mara"],"index":46770,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9941382408,"difficulty":0.0058617592}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Derick's card is shown to Margaret. Florence's card is shown to Derick. Florence's card is shown to Florence. It is publicly announced that someone picked a red card. It is publicly announced that Florence knows whether someone picked a red card. It is publicly announced that Derick does not know whether Margaret 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) ] Agentc knows whether (Agentb knows that (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":"Florence can now know whether Derick can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","Derick","Florence"],"index":9578,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993989468,"difficulty":0.0006010532}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Simon's card is shown to Simon. Simon's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that Simon picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Michael can now know whether Simon can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Simon","Michael"],"index":56793,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994582534,"difficulty":0.0005417466}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Rene can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rene","Gary","Kyle","Angelina"],"index":57684,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994564652,"difficulty":0.0005435348}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randy knows whether Randy is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Randy can now know that Albert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Albert","Randy"],"index":29319,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9932844639,"difficulty":0.0067155361}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wade does not know whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] Agentc knows that (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":"Dawn can now know that Wade can know that Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Wade","Dawn","Michael"],"index":4265,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977827668,"difficulty":0.0022172332}
+{"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. Luciano's card is shown to Jeffrey. Nancy's card is shown to Luciano. Jeffrey'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 or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jeffrey can now know whether Nancy can know that Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeffrey","Luciano","Nancy"],"index":26433,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9135208726,"difficulty":0.0864791274}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (~(1|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":"Willie can now know whether Kirsten can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Kirsten","Willie"],"index":49761,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993190765,"difficulty":0.0006809235}
+{"premise":"There are three persons. Everyone is visible 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 Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Hee can now know that Linda can know whether Hee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Hee","Linda","Ronald"],"index":18868,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994117022,"difficulty":0.0005882978}
+{"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 Nancy. Brandon's card is shown to Brandon. Dan's card is shown to Brandon. Nancy's card is shown to Dan. Barbara's card is shown to Dan. Barbara's card is shown to Barbara. 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 knows whether or not nobody picked a red card. It is publicly announced that Dan does not know whether Brandon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,3 Agentc:1,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Brandon can now know that Nancy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Brandon","Dan","Barbara"],"index":46782,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994059801,"difficulty":0.0005940199}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd knows whether Marie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marie can now know that Alejandro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alejandro","Todd","Marie","Nicole"],"index":58385,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976565838,"difficulty":0.0023434162}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brant's card is shown to Charlotte. Charlotte's card is shown to Charlotte. Jessica's card is shown to Charlotte. Karen's card is shown to Jessica. Jessica's card is shown to Jessica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Brant can now know that Karen can know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brant","Karen","Charlotte","Jessica"],"index":27784,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982142448,"difficulty":0.0017857552}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Thomas. Susan's card is shown to Johnny. Johnny's card is shown to Johnny. Thomas's card is shown to James. Johnny's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Johnny can now know that James picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Thomas","Johnny","James"],"index":5481,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9984423518,"difficulty":0.0015576482}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monique's card is shown to Monique. Philip's card is shown to Monique. Bessie's card is shown to Philip. Philip's card is shown to Bessie. Bessie's card is shown to Bessie. 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:2,3 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:1,2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Philip can now know that Bessie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Monique","Philip","Bessie"],"index":38314,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9863685966,"difficulty":0.0136314034}
+{"premise":"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 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Kenneth can now know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Walter","Kim","Kenneth","Ann"],"index":21179,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977300763,"difficulty":0.0022699237}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lauren's card is shown to Shawn. Shawn's card is shown to Shawn. Lauren's card is shown to Holly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 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 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lauren can now know that Shawn can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lauren","Shawn","Holly"],"index":21758,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993444085,"difficulty":0.0006555915}
+{"premise":"There are two persons. Everyone is visible 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.","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":"Heriberto can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Andrew","Heriberto"],"index":57698,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992444515,"difficulty":0.0007555485}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roslyn knows whether Roslyn is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Roslyn can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Everett","Anthony","Roslyn"],"index":2906,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994787574,"difficulty":0.0005212426}
+{"premise":"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 Tracy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Tracy can now know whether Mandi can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mandi","Tracy"],"index":22132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993848801,"difficulty":0.0006151199}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patricia's card is shown to Patricia. Patricia's card is shown to Gary. Gary's card is shown to Gary. It is publicly announced that someone picked a red card. It is publicly announced that Gary knows whether Gary picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Gary can now know whether Patricia can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Gary"],"index":9206,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994462132,"difficulty":0.0005537868}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ollie's card is shown to Mary. Mary's card is shown to Ollie. Ollie's card is shown to Ollie. Mary's card is shown to Luis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Mary can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Ollie","Luis"],"index":9973,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994032383,"difficulty":0.0005967617}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether William's forehead is muddy. It is publicly announced that Terry's forehead is not muddy. It is publicly announced that Terry knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jose can now know that Terry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jose","Terry","William"],"index":51593,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.924038589,"difficulty":0.075961411}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that James 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":"Edna can now know that James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roger","James","Joseph","Edna"],"index":11696,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995199442,"difficulty":0.0004800558}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that Gene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gene","Jeffrey","Randolph","Christine"],"index":13458,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977873564,"difficulty":0.0022126436}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nannie does not know whether Don is thirsty. It is publicly announced that Katherine is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] Agentb knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Katherine can now know whether Don can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nannie","Katherine","Don","Scott"],"index":484,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994474053,"difficulty":0.0005525947}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Terry's card is shown to Terry. Mike's card is shown to Terry. Betty's card is shown to Terry. Juanita's card is shown to Mike. Betty's card is shown to Mike. Mike'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 Terry does not know whether Terry picked a red card. It is publicly announced that Terry does not know whether Terry picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Terry can now know that Mike can know that Terry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juanita","Terry","Mike","Betty"],"index":44334,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9838472009,"difficulty":0.0161527991}
+{"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 Amber is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Amber does not know whether Della is thirsty. It is publicly announced that Della does not know whether Amber is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Amber can now know that John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Della","John","Amber"],"index":30008,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9963678122,"difficulty":0.0036321878}
+{"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. Hien's card is shown to Stephen. Stephen's card is shown to Hien. It is publicly announced that someone picked a red card. It is publicly announced that Michelle 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) ] [ ! ~(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:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michelle can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michelle","Stephen","Hien"],"index":42337,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998300612,"difficulty":0.001699388}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorraine's card is shown to Lorraine. Teresa's card is shown to Teresa. Lorraine's card is shown to Megan. Teresa's card is shown to Megan. Megan's card is shown to Megan. It is publicly announced that someone picked a red card. It is publicly announced that Lorraine does not know whether or not everyone picked a red card. It is publicly announced that Teresa knows whether Teresa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Teresa can now know whether Lorraine can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorraine","Teresa","Megan"],"index":30004,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9873792529,"difficulty":0.0126207471}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leon is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Leon can now know that Leon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carie","Leon"],"index":51843,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9479135275,"difficulty":0.0520864725}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brianne's card is shown to Sharon. Johnny's card is shown to Johnny. Sharon's card is shown to Brianne. Brianne's card is shown to Brianne. It is publicly announced that someone picked a red card. It is publicly announced that Brianne does not know whether Johnny picked a red card. It is publicly announced that Brianne knows whether Sharon picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Johnny can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Johnny","Brianne"],"index":56601,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989160299,"difficulty":0.0010839701}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elaine does not know whether Doris is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Patricia can now know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Elaine","Enrique","Doris"],"index":12817,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6356931329,"difficulty":0.3643068671}
+{"premise":"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) ] [ ! ~(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":"James can now know that Nicholas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicholas","Jennifer","James"],"index":24559,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994689822,"difficulty":0.0005310178}
+{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 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":"Mark can now know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jason","Mark","William","Jaime"],"index":2614,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9961159229,"difficulty":0.0038840771}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Odessa's card is shown to Odessa. Odessa's card is shown to Maria. It is publicly announced that someone picked a red card. It is publicly announced that Odessa does not know whether Maria picked a red card. It is publicly announced that Odessa knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Maria can now know that Odessa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Odessa","Maria"],"index":36578,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9705159664,"difficulty":1.9705159664}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Tom's card is shown to Andrea. Donna's card is shown to Tom. Tom's card is shown to Ruby. Ruby's card is shown to Donna. Donna's card is shown to Donna. It is publicly announced that someone picked a red card. It is publicly announced that Tom does not know whether Ruby picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Donna can now know that Ruby can know that Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrea","Tom","Ruby","Donna"],"index":34753,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979502559,"difficulty":0.0020497441}
+{"premise":"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)) ] 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Priscilla can know that Priscilla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susanne","James","Priscilla"],"index":29972,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9032694101,"difficulty":0.0967305899}
+{"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 Mary does not know whether Frieda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Rosetta can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rosetta","Mary","Frieda"],"index":60314,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9965458512,"difficulty":0.0034541488}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda knows whether or not 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 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":"Susie can now know that Brenda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Susie","Brenda","Lindsey"],"index":59261,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9432735443,"difficulty":0.0567264557}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Loretta does not know whether Loretta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 1)","n_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":"Loretta can now know whether Loretta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Loretta","Eric","Virginia"],"index":41786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993293047,"difficulty":0.006706953}
+{"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. Patricia's card is shown to Michelle. Mark's card is shown to Michelle. Mark's card is shown to Patricia. Mark'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:3 Agentc:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Patricia can now know that Mark can know whether Mark picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Patricia","Mark"],"index":37823,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6694284081,"difficulty":0.3305715919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Donald can now know whether Christopher can know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Donald","Elizabeth","Christopher"],"index":65557,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9765360951,"difficulty":0.0234639049}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Everett knows whether Sheila's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether 1)","n_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":"Everett can now know whether Everett's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Everett","Aaron","Sheila"],"index":34121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9935541153,"difficulty":0.0064458847}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willard's card is shown to Willard. Michael's card is shown to Willard. Willard's card is shown to Valerie. Michael's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Michael can now know that Willard can know whether Willard picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Willard","Valerie","Michael"],"index":30692,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7136279345,"difficulty":0.2863720655}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Hal can now know whether Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Hal","Jonathan","Gladys"],"index":27260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993675351,"difficulty":0.0006324649}
+{"premise":"There are two persons. Everyone is visible 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 John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Edward"],"index":32370,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999435246,"difficulty":0.000564754}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike knows whether Mike's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Andres can now know that Daniel can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mike","Andres","Daniel","Edward"],"index":4497,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981957078,"difficulty":0.0018042922}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal does not know whether Crystal's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Hazel can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Crystal","Jennifer","Hazel"],"index":5580,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
+{"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. Wanda's card is shown to Paul. Paul's card is shown to Henry. Henry's card is shown to Henry. Vivian's card is shown to Henry. Wanda's card is shown to Henry. Paul's card is shown to Vivian. Henry'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:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2,3,4 Agentc:1 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Henry can now know that Vivian can know that Wanda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paul","Henry","Vivian","Wanda"],"index":54628,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9981529117,"difficulty":0.0018470883}
+{"premise":"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 Debra'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 whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Lucila can now know whether Debra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lucila","Debra"],"index":11122,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9968807697,"difficulty":0.0031192303}
+{"premise":"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 Linda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentc knows that 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) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Doug can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Jesus","Doug","Ernie"],"index":45318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972398281,"difficulty":0.0027601719}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 1)","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":"Janice can now know that Terrell can know that Julia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Julia","Terrell","Janice","Julie"],"index":8711,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978685379,"difficulty":0.0021314621}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mindy knows whether Mindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] Agentc knows that (Agentb knows that 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":"April can now know that Deanna can know that Deanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mindy","Deanna","April"],"index":39099,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981143475,"difficulty":0.0018856525}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dorothy does not know whether Bernadette is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Dorothy can now know that Bernadette can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Bernadette","Chong"],"index":22932,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992572665,"difficulty":0.0007427335}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Darrell does not know whether or not everyone is thirsty. It is publicly announced that Robert does not know whether Steven is thirsty. It is publicly announced that Robert does not know whether Steven is thirsty. It is publicly announced that Robert 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Robert can now know whether Christopher can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Christopher","Robert","Darrell","Steven"],"index":40262,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994848967,"difficulty":0.0005151033}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonita's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows whether (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Mabel can now know whether Leslie can know whether Bonita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Randy","Mabel","Bonita","Leslie"],"index":16292,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992311001,"difficulty":0.0007688999}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dina's card is shown to Alberta. Kevin's card is shown to Kevin. Dina's card is shown to Dina. Dina's card is shown to Brandon. Brandon's card is shown to Brandon. It is publicly announced that someone picked a red card. It is publicly announced that Brandon does not know whether Alberta picked a red card. It is publicly announced that Alberta does not know whether Alberta picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:3 Agentd:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Alberta can now know whether Kevin can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alberta","Kevin","Dina","Brandon"],"index":43900,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993849993,"difficulty":0.0006150007}
+{"premise":"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 Joyce's forehead is muddy. It is publicly announced that Karma's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Karma can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rolando","Karma","Joyce","Shirley"],"index":26492,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"premise":"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's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Laura knows whether Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agenta knows that (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 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Laura can now know that Matthew can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Laura","Matthew","Carrie"],"index":61595,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9381406903,"difficulty":1.9381406903}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton does not know whether Milton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 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":"Al can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Milton","Al","Sadie"],"index":11012,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"premise":"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 Lilian does not know whether Lilian's forehead 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 (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lilian can now know that Merle can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Merle","Lilian"],"index":9184,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993054867,"difficulty":0.0006945133}
+{"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. Alice's card is shown to Jesse. John's card is shown to John. John's card is shown to Alice. 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 whether 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":"John can now know whether Alice picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesse","John","Alice"],"index":8003,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.892147541,"difficulty":1.892147541}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Rosa can now know whether Kate can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosa","Kate"],"index":31655,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993245602,"difficulty":0.0006754398}
+{"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 Kimberly. Mary's card is shown to Paul. It is publicly announced that someone picked a red card. It is publicly announced that Louise picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Louise can now know that Kimberly can know whether Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","Louise","Paul","Mary"],"index":51031,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8350791335,"difficulty":0.1649208665}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lynne's card is shown to John. Robert's card is shown to Robert. Robert's card is shown to Lynne. 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 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Lynne can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Robert","Lynne"],"index":1358,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6437190175,"difficulty":0.3562809825}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mellissa does not know whether Adrian is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Adrian knows whether Mellissa 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) ] 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) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mellissa can now know that Adrian can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Adrian","Mellissa"],"index":27748,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989846349,"difficulty":0.0010153651}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows 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":"John can now know whether Brad can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Brad","Jennifer","Joseph"],"index":21214,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9777145386,"difficulty":0.0222854614}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera knows whether Ellen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Ellen can now know that Vera can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ellen","Vera"],"index":64928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993933439,"difficulty":0.0006066561}
+{"premise":"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 Sarah's forehead is muddy.","smcdel_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&2&3))","n_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":"Dianne can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sarah","Dianne","Christopher"],"index":59928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9543781877,"difficulty":0.0456218123}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Oliver's card is shown to Jessica. Kathy's card is shown to Oliver. Kenneth's card is shown to Kenneth. Jessica's card is shown to Kathy. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Oliver can now know whether Kathy can know whether Oliver picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Oliver","Kenneth","Kathy"],"index":47870,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9982774258,"difficulty":0.0017225742}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Gabriel can now know whether Cindy can know that Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cindy","Beverly","John","Gabriel"],"index":12793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994245708,"difficulty":0.005754292}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). James's card is shown to Patricia. David's card is shown to David. Patricia's card is shown to Carmen. David's card is shown to Carmen. Carmen's card is shown to Carmen. 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:3 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"David can now know whether Carmen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","David","James","Carmen"],"index":21595,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9531538486,"difficulty":1.9531538486}
+{"premise":"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 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) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (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: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":"David can now know whether Leroy can know that Barry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barry","Leroy","David","Brian"],"index":271,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9847352505,"difficulty":0.0152647495}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew 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) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Patricia can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Matthew","Betty","Robert"],"index":14269,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989061356,"difficulty":0.0010938644}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether Ella is thirsty.","smcdel_problem":"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 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 4) ] 0","hypothesis":"James can now know that Kevin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Michael","Kevin","Ella"],"index":4581,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957933426,"difficulty":0.0042066574}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Daniel can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marilyn","Eric","Daniel"],"index":27766,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9930152893,"difficulty":0.0069847107}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adam does not know whether Erin is thirsty. It is publicly announced that Erin does not know whether Rob is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (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 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Erin can now know that Rob is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rob","Erin","Adam"],"index":9830,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975250363,"difficulty":0.0024749637}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Derrick knows whether 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) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Derrick can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patricia","Shirley","Derrick","Nicole"],"index":29809,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993705153,"difficulty":0.0006294847}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald does not know whether 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 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":"Gerald can now know that Patricia can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Patricia","Gerald"],"index":12262,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8778366446,"difficulty":0.1221633554}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kelly does not know whether Dawn is thirsty. It is publicly announced that Dawn knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Dawn can now know whether Virgil is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kelly","Virgil","Dawn","Mary"],"index":65972,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982030392,"difficulty":0.0017969608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeff does not know whether Jennifer is thirsty. It is publicly announced that John does not know whether Jeff is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jeff can now know whether Curt can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeff","John","Jennifer","Curt"],"index":26455,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954118133,"difficulty":0.0045881867}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Barbara can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Donna","Barbara"],"index":39562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987518787,"difficulty":0.0012481213}
+{"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 Susan. Susan's card is shown to Emily. Emily's card is shown to Kevin. Melissa's card is shown to Kevin. Kevin'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:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Emily can now know whether Melissa can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Emily","Kevin","Melissa"],"index":37893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993964434,"difficulty":0.0006035566}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to Holly. Douglas's card is shown to Holly. Holly's card is shown to Douglas. Holly's card is shown to Warren. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 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:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Holly can now know whether Douglas can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Holly","Douglas","Warren"],"index":64060,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99933213,"difficulty":0.00066787}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elmo knows whether Verna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Elmo can now know whether Judith can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elmo","Judith","William","Verna"],"index":42199,"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 is thirsty. It is publicly announced that Debra does not know whether Amy is thirsty. It is publicly announced that Peggy is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Amy can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amy","Peggy","Debra"],"index":16679,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.6652836204,"difficulty":1.6652836204}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delores's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether Francisco's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Shawn can now know that Delores can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francisco","Delores","Shawn"],"index":63117,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988158941,"difficulty":0.0011841059}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy. It is publicly announced that Susan knows whether someone's forehead is muddy. It is publicly announced that Susan knows whether Susan's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 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":"Susan can now know that Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Susan","Jeffrey"],"index":38275,"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 not everyone'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) ] [ ! (~(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) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"John can now know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Daniel","John","Stephanie"],"index":43941,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996720612,"difficulty":0.003279388}
+{"premise":"There are three persons. Everyone is visible 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 Amanda's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Francis can now know whether Francis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Amanda","Bobby","Francis"],"index":56928,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993969202,"difficulty":0.0006030798}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Winston's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"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":"Cathy can now know that Carol can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Winston","Cathy"],"index":35488,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988578558,"difficulty":0.0011421442}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"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":"Paul can now know that Fannie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ida","Paul","Fannie"],"index":62011,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999402523,"difficulty":0.000597477}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Maria's card is shown to Maria. 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 Cheryl 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 whether 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":"Cheryl can now know whether Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cheryl","Maria"],"index":12624,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9532756209,"difficulty":0.0467243791}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Robbie. Robbie's card is shown to Deborah. Deborah's card is shown to Deborah. Lucille's card is shown to Richard. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robbie can now know that Richard can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robbie","Deborah","Richard","Lucille"],"index":42492,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987529516,"difficulty":0.0012470484}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Katrina is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Casey can now know whether Lois can know whether Katrina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katrina","Lois","Casey"],"index":20018,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992231131,"difficulty":0.0007768869}
+{"premise":"There are two persons. Everyone is visible 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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Rosa can now know that Peter can know that Peter's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Peter","Rosa"],"index":61910,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980260134,"difficulty":0.0019739866}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francis does not know whether Tanya is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] (Agenta knows that (~(1|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":"Michael can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Tanya","Francis"],"index":33295,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987320304,"difficulty":0.0012679696}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Maud knows whether Maud's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Pam can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Maud","Sandra","Ronald","Pam"],"index":53717,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9936774373,"difficulty":0.0063225627}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Geraldine's card is shown to Geraldine. Debbie's card is shown to Geraldine. Geraldine's card is shown to Tony. Dean's card is shown to Debbie. Dean's card is shown to Dean. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Tony can now know that Debbie can know whether Dean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Geraldine","Tony","Debbie","Dean"],"index":22784,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.5351498723,"difficulty":1.5351498723}
+{"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) ] [ ! 3 ] (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) ] [ ! 3 ] 0","hypothesis":"Brock can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Brock","Michael","Tina"],"index":9532,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9869744778,"difficulty":0.0130255222}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Keith. Paige's card is shown to Paige. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Keith can now know whether Paige can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Keith","Paige"],"index":61721,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993946552,"difficulty":0.0006053448}
+{"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 Cathy. Wayne's card is shown to Cathy. Cathy's card is shown to Jonathan. Wayne's card is shown to Wayne. Wayne's card is shown to Hae. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cathy can now know that Wayne picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cathy","Jonathan","Wayne","Hae"],"index":7865,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961777925,"difficulty":0.0038222075}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Miguel does not know whether Gerald is thirsty. It is publicly announced that Gerald 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) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Miguel can now know whether Gerald can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Miguel","Craig","Gerald"],"index":10988,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.994446516,"difficulty":0.005553484}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tara knows whether Tara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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":"Tracy can now know that Tara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tracy","Tara","William","Frederick"],"index":58909,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9610216618,"difficulty":1.9610216618}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Diana's card is shown to Felton. Felton's card is shown to Diana. It is publicly announced that someone picked a red card. It is publicly announced that Felton picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Diana can now know whether Felton can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Felton","Diana"],"index":15485,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992755055,"difficulty":0.0007244945}
+{"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 Eric. Dale's card is shown to Dale. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Eric can now know whether Dale can know whether Dale picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Dale"],"index":1558,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9973332882,"difficulty":0.0026667118}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Edward. Leslie's card is shown to Leslie. Lillian's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lila can now know whether Leslie can know whether Lillian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lila","Edward","Leslie","Lillian"],"index":15389,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981597066,"difficulty":0.0018402934}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether or not nobody's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon'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":"Dorsey can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorsey","Sharon"],"index":24615,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989411235,"difficulty":0.0010588765}
+{"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. Michael's card is shown to Eileen. Eileen's card is shown to Eileen. Michael's card is shown to Samuel. Eileen's card is shown to Samuel. It is publicly announced that someone picked a red card. It is publicly announced that Eileen does not know whether Samuel picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Jay can now know that Eileen can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Eileen","Jay","Samuel"],"index":37433,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999358356,"difficulty":0.000641644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kevin does not know whether or not everyone is thirsty. It is publicly announced that Kevin knows whether Kevin is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Karen can now know that Robert can know that Karen is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Kevin","Robert"],"index":27170,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9492551684,"difficulty":0.0507448316}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jose does not know whether or not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Josephine can now know whether Jose can know whether Leeann is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Josephine","Leeann","Jose"],"index":53759,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991544485,"difficulty":0.0008455515}
+{"premise":"There are three persons. Everyone is visible 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 3)","n_announcements":1,"pbcheck":"VARS 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":"Stanley can now know that Linda can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Harry","Stanley","Linda"],"index":62430,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9935334921,"difficulty":0.0064665079}
+{"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 Joyce is thirsty. It is publicly announced that Jose 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|2|3|4)))","n_announcements":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":"Jose can now know that Charles can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joyce","Jose","Michael","Charles"],"index":56207,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994669557,"difficulty":0.0005330443}
+{"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 Kenneth. Tammy's card is shown to Kenneth. Queen's card is shown to Kenneth. Tammy's card is shown to Tammy. Queen's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Kenneth can now know whether Queen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kenneth","Jon","Tammy","Queen"],"index":28444,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8691626787,"difficulty":0.1308373213}
+{"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":"Daniel can now know whether Helen can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Helen","Daniel","Paul"],"index":7460,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999414444,"difficulty":0.000585556}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentb knows that (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Otis can now know that Jim can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paula","Otis","Francis","Jim"],"index":9176,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99941957,"difficulty":0.00058043}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Raul is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Monica is thirsty. It is publicly announced that Stephen knows 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) ] [ ! ~(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":"Raul can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Monica","Stephen","Raul"],"index":65388,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999479115,"difficulty":0.000520885}
+{"premise":"There are two 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 LAW Top OBS Agenta:1 Agentb:2 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:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Hillary can now know whether Sandra can know whether Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hillary","Sandra"],"index":10471,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987952709,"difficulty":0.0012047291}
+{"premise":"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 William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(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) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"William can now know that Damon can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Damon","William"],"index":29527,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9928255081,"difficulty":0.0071744919}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether or not everyone's forehead is muddy. It is publicly announced that Ellen does not know whether Ellen's forehead is muddy.","smcdel_problem":"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 (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)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Irene can now know that Crystal can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Crystal","Irene"],"index":43193,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994414449,"difficulty":0.0005585551}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jacqueline 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|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":"Mable can now know that Jacqueline can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mable","Jacqueline","Kenneth"],"index":15882,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995181561,"difficulty":0.0004818439}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon knows whether Ramon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that 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":"Dominique can now know that Charles can know that Dominique's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dominique","Charles","Ramon"],"index":37747,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982885718,"difficulty":0.0017114282}
+{"premise":"There are three persons. Everyone is visible 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 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":"Harry can now know that Rebecca can know whether Patricia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Patricia","Rebecca"],"index":57319,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vera 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 (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Micheal can now know that Vera can know that Leigh's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Micheal","Leigh","Brian","Vera"],"index":59438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970165491,"difficulty":0.0029834509}
+{"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 Genevive. Genevive's card is shown to Victoria. Genevive's card is shown to Courtney. Victoria's card is shown to Courtney. Courtney's card is shown to Courtney. It is publicly announced that someone picked a red card. It is publicly announced that Courtney knows whether Victoria picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] (Agentc knows whether 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":"Courtney can now know whether Courtney picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Genevive","Victoria","Courtney"],"index":66652,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8269620538,"difficulty":0.1730379462}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Geneva can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Geneva","Justin","James","Tracey"],"index":49985,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988464117,"difficulty":0.0011535883}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence knows whether or not everyone's forehead is muddy. It is publicly announced that Florence knows whether Mark's forehead is muddy. It is publicly announced that Florence 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 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":"Mark can now know that Florence can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Florence","Mark"],"index":20592,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963418841,"difficulty":0.0036581159}
+{"premise":"There are two persons. Everyone is visible 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 Heidi knows whether Rita'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 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":"Heidi can now know whether Rita can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Heidi","Rita"],"index":26452,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994364381,"difficulty":0.0005635619}
+{"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 Theodore. Rodney's card is shown to Reginald. Rodney's card is shown to Rodney. It is publicly announced that someone picked a red card. It is publicly announced that Rodney does not know whether Reginald 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 2) ] (Agentb 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) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Reginald can now know that Theodore picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theodore","Reginald","Rodney"],"index":25327,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998065412,"difficulty":0.001934588}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Carlos knows whether Carlos is thirsty.","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 (~(1|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":"Ron can now know that Linda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Ron","Linda","Carlos"],"index":2497,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990372658,"difficulty":0.0009627342}
+{"premise":"There are four persons. Everyone is visible 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 Tyrone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(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:1,2,3,4 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":"Tyrone can now know whether Julia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Julia","Tyrone","Michel"],"index":17279,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994037151,"difficulty":0.0005962849}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! 3 ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Ashley can now know whether Paul can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brandi","Paul","Ashley","Nell"],"index":9447,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995160103,"difficulty":0.0004839897}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe knows whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Wendy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guadalupe","Wendy","Daniel","Stanley"],"index":17762,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987131357,"difficulty":0.0012868643}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Janice. Lillian's card is shown to Janice. Bertha's card is shown to Janice. Bertha's card is shown to Jennifer. Janice's card is shown to Lillian. Janice's card is shown to Bertha. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 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)) ] Agentb knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jennifer can now know whether Lillian can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janice","Jennifer","Lillian","Bertha"],"index":24510,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.990695715,"difficulty":0.009304285}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (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":"Mary can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Joseph","Matthew","Mary"],"index":4050,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998716712,"difficulty":0.001283288}
+{"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. Briana's card is shown to Roy. Roy's card is shown to Briana. It is publicly announced that someone picked a red card. It is publicly announced that Roy knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Roy can now know that Briana picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Roy","Briana"],"index":15592,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9940654039,"difficulty":0.0059345961}
+{"premise":"There are four persons. Everyone is visible 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. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Daniel can now know that Lisa can know that Daniel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Daniel","Jose","Mary"],"index":27522,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.989151001,"difficulty":0.010848999}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Darryl's card is shown to Darryl. Kenneth's card is shown to Darryl. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Kenneth picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Darryl can now know whether Kenneth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Darryl","Kenneth"],"index":19439,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9826642871,"difficulty":0.0173357129}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sean knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Lamar can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lamar","Sean","Mollie"],"index":53227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994060993,"difficulty":0.0005939007}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether Kimberely's forehead is muddy. It is publicly announced that Kimberely's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] Agentb knows whether (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"Jessica can now know whether Kenneth can know that Kimberely's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Jessica","Kimberely"],"index":24812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994864464,"difficulty":0.0005135536}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandy knows whether someone's forehead is muddy. It is publicly announced that Brandy 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 (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brandy can now know whether Marie can know that Brandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brandy","Marie"],"index":28997,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.821416378,"difficulty":0.178583622}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Monika's card is shown to Monika. Barbara's card is shown to Henry. Monika's card is shown to Barbara. Katherine's card is shown to Barbara. Barbara's card is shown to Katherine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,4 Agentd:3 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:3 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Henry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Monika","Henry","Barbara","Katherine"],"index":66200,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9979751706,"difficulty":0.0020248294}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vaughn does not know whether Vaughn'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 that (Agentd knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Patsy can now know that Vaughn can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patsy","Sandy","James","Vaughn"],"index":3926,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994115829,"difficulty":0.0005884171}
+{"premise":"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 Annalee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Annalee can now know whether John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Annalee","Sharon","John","Melissa"],"index":36394,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9207553864,"difficulty":0.0792446136}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Anthony can now know that Bryan can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Evelyn","Anthony","Bryan","Jose"],"index":16979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989699125,"difficulty":0.0010300875}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Arnold can now know whether Darren can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darren","Jenna","Arnold","Jonathan"],"index":2352,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993189573,"difficulty":0.0006810427}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Forrest's card is shown to Forrest. Pablo's card is shown to Forrest. Earl's card is shown to Pablo. Pablo'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 Earl 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 (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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Forrest can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Forrest","Pablo","Earl"],"index":65382,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994373918,"difficulty":0.0005626082}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jon does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"James can now know whether Carl can know that Carl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jon","James","Marilyn","Carl"],"index":9040,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9934072495,"difficulty":0.0065927505}
+{"premise":"There are four persons. Everyone is visible 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 ] 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":"Susan can now know that George can know that Susan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Fannie","Heather","Susan"],"index":35951,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.8731274009,"difficulty":1.8731274009}
+{"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. Rachel's card is shown to Helen. Sarah's card is shown to Helen. Helen's card is shown to Robbie. Robbie'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:1,3,4 Agentb:1 Agentc:2,4 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:1,3,4 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robbie can now know that Rachel can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Robbie","Rachel","Sarah"],"index":53012,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992728829,"difficulty":0.0007271171}
+{"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 Joanne. Robert's card is shown to Joanne. Teresa's card is shown to Teresa. Joanne's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc: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:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Teresa can now know whether Joanne can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joanne","Teresa","Robert"],"index":50020,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9611361623,"difficulty":0.0388638377}
+{"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 Hazel. Joyce's card is shown to Hazel. Paul's card is shown to Paul. Paul'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:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Paul can now know that Hazel can know that Hazel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hazel","Paul","Joyce"],"index":44844,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.997451365,"difficulty":0.002548635}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Simone 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 (~(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":"Charles can now know that Simone can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Simone","Charles"],"index":59904,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989889264,"difficulty":0.0010110736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Marissa is thirsty. It is publicly announced that Robert does not know whether Lucille is thirsty. It is publicly announced that Marissa knows whether Marissa is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Lucille can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Robert","Marissa"],"index":26684,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994570613,"difficulty":0.0005429387}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Laurena knows whether Laurena 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 (~(1|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":"Diana can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diana","Debra","Laurena"],"index":36776,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989352822,"difficulty":0.0010647178}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Margo knows whether Margo's forehead is muddy. It is publicly announced that Edith 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) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"James can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Margo","Edith","Richard","James"],"index":12647,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975086451,"difficulty":0.0024913549}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Evan can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Evan","Frederick","Robert"],"index":34605,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992497563,"difficulty":0.0007502437}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Melissa'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 (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) ] 0","hypothesis":"Melissa can now know whether Mary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Melissa","Laverne"],"index":26809,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994786382,"difficulty":0.0005213618}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Pauline's card is shown to Pauline. Pauline's card is shown to Bradley. Marvin's card is shown to Marvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bradley can now know whether Pauline picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","David","Bradley","Marvin"],"index":4049,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8945398927,"difficulty":1.8945398927}
+{"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 Cathy is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Walter can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Walter","James","Cathy","George"],"index":21589,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993396401,"difficulty":0.0006603599}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy knows whether Ayesha's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Martin can now know whether Martin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Martin","Linda","Randy","Ayesha"],"index":61331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993904829,"difficulty":0.0006095171}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Larry can now know whether James can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ettie","Ricardo","Larry","James"],"index":52133,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993678927,"difficulty":0.0006321073}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Galen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"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":"Christine can now know that Galen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Douglas","Galen","Christine"],"index":36887,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986330867,"difficulty":0.0013669133}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anita knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that 1)","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":"Irene can now know that Anita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Anita","Irene"],"index":36998,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9966854453,"difficulty":0.0033145547}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosalie does not know whether Rosalie's forehead is muddy. It is publicly announced that Johnny does not know whether Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(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":"Rosalie can now know that Johnny can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnny","Vinita","Rosalie"],"index":10079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994338155,"difficulty":0.0005661845}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ginny's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agentb knows 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":"Clyde can now know whether Ginny can know that Clyde's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laverne","Ginny","Anthony","Clyde"],"index":42578,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993636012,"difficulty":0.0006363988}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jana knows whether or not nobody's forehead is muddy. It is publicly announced that Helen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(2) ] Agentb knows that (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))) ] [ ! ~(2) ] 0","hypothesis":"Helen can now know that Jana can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Helen","Jana","Phillip"],"index":38592,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989479184,"difficulty":0.0010520816}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michael's card is shown to Lisa. Lisa's card is shown to Mary. Lisa's card is shown to Michael. Mary's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lisa can now know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lisa","Mary","Michael"],"index":60386,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9961054921,"difficulty":0.0038945079}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuel does not know whether Roxane is thirsty. It is publicly announced that Manuel does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Roxane can now know whether Marion can know that Marion is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marion","Manuel","Michael","Roxane"],"index":26531,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.840749383,"difficulty":0.159250617}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 that Joshua can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elizabeth","Joshua","Dorthy","Edward"],"index":10259,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989375472,"difficulty":0.0010624528}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor knows whether Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Samuel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Eleanor","Samuel"],"index":32488,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998660326,"difficulty":0.001339674}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Renita does not know whether Jason is thirsty. It is publicly announced that Renita knows whether or not nobody is thirsty. It is publicly announced that Renita does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Jason can now know whether Barrie can know whether Barrie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barrie","Renita","Jason"],"index":31750,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9851759672,"difficulty":0.0148240328}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sallie's card is shown to Alan. Alan's card is shown to Beulah. Juanita's card is shown to Beulah. Sallie's card is shown to Juanita. Beulah's card is shown to Juanita. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Alan can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Alan","Sallie","Beulah","Juanita"],"index":2621,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993614554,"difficulty":0.0006385446}
+{"premise":"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 Linda's forehead is muddy. It is publicly announced that Kelly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know whether Linda can know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Linda","Steven","Kelly"],"index":28812,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9785232544,"difficulty":0.0214767456}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark knows whether Mario is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mario knows whether Mario is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Mario can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mark","Mario"],"index":41068,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990179539,"difficulty":0.0009820461}
+{"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 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) ] [ ! (1&2&3&4) ] [ ! 2 ] (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) ] [ ! (1&2&3&4) ] [ ! 2 ] 0","hypothesis":"Angie can now know that Angie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Francesca","Rick","Griselda","Angie"],"index":43989,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9943998456,"difficulty":0.0056001544}
+{"premise":"There are three persons. Everyone is visible 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 (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":"Roberta can now know whether Marvin can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marvin","Janice","Roberta"],"index":20404,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993740916,"difficulty":0.0006259084}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Burl's card is shown to Jessica. Jessica's card is shown to Justin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Burl can now know that Jessica can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessica","Burl","Justin"],"index":65858,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9908413887,"difficulty":0.0091586113}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nathan does not know whether Barbara is thirsty. It is publicly announced that Diane does not know whether Flora is thirsty. It is publicly announced that Diane does not know whether Barbara is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Diane can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Barbara","Flora","Nathan"],"index":63671,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9961729646,"difficulty":0.0038270354}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Misty knows whether Santos's forehead is muddy. It is publicly announced that Santos's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows whether 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":"Misty can now know whether Santos's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Misty","Santos"],"index":39276,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994693398,"difficulty":0.0005306602}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Melissa can now know that Imogene can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Imogene","Melissa"],"index":62535,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994302392,"difficulty":0.0005697608}
+{"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 David. Sharon's card is shown to David. Betty's card is shown to Betty. Sharon's card is shown to Betty. Sharon's card is shown to Sharon. Katie's card is shown to Sharon. Katie's card is shown to Katie. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:2,3 Agentc:3,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Sharon can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["David","Betty","Sharon","Katie"],"index":46686,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9865474701,"difficulty":0.0134525299}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Betty knows whether Betty is thirsty. It is publicly announced that Richard does not know whether Betty is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Betty can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Betty","Richard"],"index":61254,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989597797,"difficulty":0.0010402203}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ruby's card is shown to Ruby. Ruby's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary knows whether someone picked a red card. It is publicly announced that Mary does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3 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 whether (~(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":"Ruby can now know that Mary can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Mary","Aretha"],"index":22077,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether Virginia is thirsty. It is publicly announced that Rose does not know whether Virginia is thirsty. It is publicly announced that Rose 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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 3) ] (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Shirley can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shirley","Josephine","Virginia","Rose"],"index":5787,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994593263,"difficulty":0.0005406737}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Louisa's card is shown to Louisa. Bertha's card is shown to Louisa. Louisa's card is shown to Bertha. Bertha's card is shown to Bertha. Lyman's card is shown to Bertha. Bertha's card is shown to Lyman. Lyman's card is shown to Gustavo. 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) ] (Agentb 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":"Bertha can now know that Gustavo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Louisa","Bertha","Lyman","Gustavo"],"index":10494,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9985246062,"difficulty":0.0014753938}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan knows whether Milagros is thirsty. It is publicly announced that Milagros is thirsty. It is publicly announced that Milagros knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Susan can now know that Milagros can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susan","Milagros"],"index":37676,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.5928502679,"difficulty":0.4071497321}
+{"premise":"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 does not know whether Stanley's forehead is muddy. It is publicly announced that Micheal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Janice can now know whether Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janice","Micheal","Stanley","Anna"],"index":18983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9788726568,"difficulty":0.0211273432}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows 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":"Heather can now know that Sheryl can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Heather","Sheryl","Delia"],"index":2229,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998837173,"difficulty":0.001162827}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Isaac does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Peter can now know whether Delia can know whether Delia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Isaac","Delia","Elba"],"index":57463,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9758349657,"difficulty":0.0241650343}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 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":"Darlene 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":["Michael","Berta","Darlene"],"index":55610,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988636971,"difficulty":0.0011363029}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (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":"Francisco can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["George","Francisco"],"index":66323,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99887079,"difficulty":0.00112921}
+{"premise":"There are 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 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":"Alison can now know that Quinn can know that Quinn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelvin","Quinn","Alison"],"index":13705,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984192848,"difficulty":0.0015807152}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elsie's card is shown to David. Elsie's card is shown to Elsie. Joseph's card is shown to Joseph. Elsie'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:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 Agentc:3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Elsie can now know whether Lawrence can know that Lawrence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Elsie","Joseph","Lawrence"],"index":15916,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9254245758,"difficulty":1.9254245758}
+{"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 Justin. Gerald's card is shown to Gerald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Barbara can now know that Justin can know whether Justin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Justin","Barbara","Gerald"],"index":27119,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8617475033,"difficulty":0.1382524967}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not nobody's forehead is muddy. It is publicly announced that Kenneth knows whether Kenneth's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that Verna 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 (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 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) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Kenneth can now know whether Brenda can know whether Verna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","Kenneth","Verna","Hazel"],"index":51333,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994495511,"difficulty":0.0005504489}
+{"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 Jamie. Jamie's card is shown to Michael. Michael's card is shown to Michael. Jamie's card is shown to James. Michael's card is shown to Ethel. Ethel's card is shown to Ethel. It is publicly announced that someone picked a red card. It is publicly announced that Ethel does not know whether James picked a red card. It is publicly announced that Jamie knows whether James 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) ] Agentb knows that (Agentd knows that 2)","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":"Michael can now know that Ethel can know that Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamie","Michael","James","Ethel"],"index":57950,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9897219539,"difficulty":0.0102780461}
+{"premise":"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 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 (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alicia can now know that William can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Alicia","Caridad","Jose"],"index":18791,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9961367249,"difficulty":0.0038632751}
+{"premise":"There are three persons. Everyone is visible 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 everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 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":"Paul can now know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Isabel","Brenda","Paul"],"index":743,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993948936,"difficulty":0.0006051064}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows 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":"Raymond can now know that Keith can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Keith"],"index":10643,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992156029,"difficulty":0.0007843971}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Rosie's forehead is muddy. It is publicly announced that Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 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) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rosie","Robert","Sandra"],"index":22217,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986276627,"difficulty":0.0013723373}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorene knows whether someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Lorene can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Michael","Lorene"],"index":46628,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7131379843,"difficulty":1.7131379843}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Jonathan. Andrea's card is shown to Jonathan. Nancy's card is shown to Daniel. Daniel's card is shown to Daniel. Daniel's card is shown to Andrea. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2,3 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daniel can now know that Jonathan can know that Andrea picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jonathan","Nancy","Daniel","Andrea"],"index":11303,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982262254,"difficulty":0.0017737746}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Audrey. Sarah's card is shown to Audrey. Sarah's card is shown to Vickie. Audrey's card is shown to Ashley. Vickie's card is shown to Sarah. Sarah's card is shown to Sarah. It is publicly announced that someone picked a red card. It is publicly announced that Vickie does not know whether Audrey 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 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:4 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Vickie can now know that Sarah can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Audrey","Vickie","Ashley","Sarah"],"index":19581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9790936112,"difficulty":0.0209063888}
+{"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 Jose. Randy's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether or not everyone picked a red card. It is publicly announced that Jose does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jose can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jose","Randy"],"index":43462,"s-l":"explicit-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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know that Joe can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joe","Laura","Robert","Frank"],"index":42709,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9659634233,"difficulty":0.0340365767}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard is not thirsty. It is publicly announced that Mildred does not know whether Jason is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] Agenta 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) ] [ ! ~(3) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Jason can now know whether Hannah can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jason","Hannah","Richard","Mildred"],"index":48914,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992858768,"difficulty":0.0007141232}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Julia does not know whether John 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 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Julia can now know whether Christopher can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julia","John","Christopher","Kimberly"],"index":54134,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994814992,"difficulty":0.0005185008}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica's forehead is not muddy. It is publicly announced that Anthony 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) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know that James can know that Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Anthony","Monica"],"index":63391,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975376129,"difficulty":0.0024623871}
+{"premise":"There are 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 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Timothy","Juan","Robert","David"],"index":23772,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994034767,"difficulty":0.0005965233}
+{"premise":"There are three persons. Everyone is visible to others. 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 David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Danielle can now know whether David can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Danielle","Michael"],"index":25344,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994556308,"difficulty":0.0005443692}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rey does not know whether Rey's forehead is muddy. It is publicly announced that 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 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":"Alvin can now know whether Rey can know that Rey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rey","Alvin"],"index":1061,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5063548684,"difficulty":0.4936451316}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eli's card is shown to Eli. Danilo's card is shown to Eli. Charlotte's card is shown to Danilo. Eli's card is shown to Charlotte. 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 that 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":"Charlotte can now know that Charlotte picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eli","Danilo","Charlotte"],"index":7497,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9949856997,"difficulty":0.0050143003}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martin knows whether someone is thirsty. It is publicly announced that Armand does not know whether Martin is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agentd knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Lisa can now know whether Alison is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Armand","Alison","Martin","Lisa"],"index":34370,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979647398,"difficulty":0.0020352602}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine knows whether Dolly's forehead is muddy. It is publicly announced that Katherine'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":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":"Dolly can now know that Katherine can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dolly","Katherine"],"index":59599,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990241528,"difficulty":0.0009758472}
+{"premise":"There are four 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. It is publicly announced that Stanley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Stanley can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rita","Patricia","Stanley","Charles"],"index":39922,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9769226313,"difficulty":0.0230773687}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Peter. Peter's card is shown to Leonard. Daniel'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 Leonard picked a red card. It is publicly announced that Peter does not know whether Peter picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Daniel can now know whether Leonard can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Peter","Leonard","Daniel"],"index":35862,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999161005,"difficulty":0.000838995}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffery knows whether Christine's forehead is muddy. It is publicly announced that Christine knows whether Christine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 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 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Jeffery can now know that Christine can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronny","Christine","Jeffery","Helen"],"index":6027,"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 James does not know whether Ron is thirsty.","smcdel_problem":"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 (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Ron can now know that Ashley can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","James","Paul","Ron"],"index":8867,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993934631,"difficulty":0.0006065369}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roman knows whether Roman is thirsty.","smcdel_problem":"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 (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 2) ] 0","hypothesis":"Marissa can now know whether Carlton can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Roman","Carlton","Marissa"],"index":5751,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992511868,"difficulty":0.0007488132}
+{"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 Carmen. Carmen's card is shown to Michael. Carmen's card is shown to Eva. 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) ] Agentb knows that (Agenta knows whether (~(1|2|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":"Michael can now know that Carmen can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmen","Michael","Eva"],"index":59097,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999352634,"difficulty":0.000647366}
+{"premise":"There are four persons. Everyone is visible 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 Debra's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agentd knows that 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 2) ] 0","hypothesis":"James can now know that William can know that Debra's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Debra","James","William"],"index":64145,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979786277,"difficulty":0.0020213723}
+{"premise":"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 does not know whether Cecilia's forehead is muddy. It is publicly announced that Cecilia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Cecilia can now know that Dave can know that Cecilia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Dave","Cecilia","Morris"],"index":47241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946680069,"difficulty":0.0053319931}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samuel's card is shown to Johnny. Chad's card is shown to Chad. Johnny's card is shown to Nicole. Samuel's card is shown to Nicole. Johnny's card is shown to Samuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:1,4 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:4 Agentb:2 Agentc:1,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Samuel can now know that Samuel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Johnny","Chad","Nicole","Samuel"],"index":23802,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9941138625,"difficulty":0.0058861375}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Leatrice does not know whether Stacey is thirsty. It is publicly announced that Albert does not know whether Stacey is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Leatrice can now know that Stacey is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leatrice","Jamie","Albert","Stacey"],"index":27801,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9938318729,"difficulty":0.0061681271}
+{"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 or not everyone is thirsty. It is publicly announced that Brian knows whether or not nobody is thirsty. It is publicly announced that Rhonda does not know whether Keesha is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Keesha can now know whether Brian can know whether Keesha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Keesha","Rhonda"],"index":21685,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988717437,"difficulty":0.0011282563}
+{"premise":"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 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 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":"Daniel can now know that Jesse can know that Jesse's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edward","Jesse","Daniel"],"index":56650,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9682372212,"difficulty":0.0317627788}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Rebecca can now know that Martha can know whether Jeff's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeff","Willie","Rebecca","Martha"],"index":42838,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990854263,"difficulty":0.0009145737}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not nobody's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Clarissa can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Clarissa","Laura"],"index":12083,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983381033,"difficulty":0.0016618967}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sandra does not know whether Florence is thirsty. It is publicly announced that Florence knows whether Florence is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether 3) ] (Agentc knows that 1)","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":"Florence can now know that Sandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Gary","Florence"],"index":42719,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9848182797,"difficulty":0.0151817203}
+{"premise":"There are 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 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":"Joan can now know whether Jennifer can know whether Katherine's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Bradley","Jennifer","Katherine","Joan"],"index":15070,"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. It is publicly announced that someone is thirsty. It is publicly announced that Owen does not know whether Kelly is thirsty. It is publicly announced that Owen 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) ] [ ! ~(Agentd 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Thomas can now know whether John can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Thomas","John","Owen"],"index":54873,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994189739,"difficulty":0.0005810261}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Debroah can now know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Debroah","Thomas","Anna"],"index":39624,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982368946,"difficulty":0.0017631054}
+{"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 Donald is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether Donald is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 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 3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Donald can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Carl","Donald"],"index":6628,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9957564473,"difficulty":0.0042435527}
+{"premise":"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 or not everyone'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 (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Donald can now know that Michael can know that Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lynda","Reba","Donald","Michael"],"index":51428,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9720478654,"difficulty":0.0279521346}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Patrick is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentc knows whether (1&2&3&4))","n_announcements":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":"Antonio can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patrick","Raymond","Antonio","Alison"],"index":22813,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.962898612,"difficulty":0.037101388}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nancy is not thirsty. It is publicly announced that Cornelius is not thirsty. It is publicly announced that Nancy does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Angela can now know that Cornelius can know that Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Angela","Nancy","Cindy","Cornelius"],"index":43469,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9748986363,"difficulty":0.0251013637}
+{"premise":"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 (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Danny can now know that Anthony can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Anthony","Danny","June"],"index":17854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988926053,"difficulty":0.0011073947}
+{"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 Mary. Joseph's card is shown to Mary. Joseph's card is shown to Janet. Anthony's card is shown to Janet. Mary's card is shown to Joseph. Joseph's card is shown to Joseph. Anthony'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:2,3 Agentb:3,4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 Agentc:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Mary can know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Janet","Joseph","Anthony"],"index":62669,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986496568,"difficulty":0.0013503432}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Randi can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Robert","Mary","Randi"],"index":45433,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7305128574,"difficulty":0.2694871426}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Allen does not know whether Lindsey is thirsty. It is publicly announced that Lindsey does not know whether Allen 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) ] (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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Lindsey can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allen","Lindsey","Norman"],"index":6491,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959523678,"difficulty":0.0040476322}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ryan knows whether Ryan's forehead is muddy. It is publicly announced that Ivonne knows whether Alberta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentd knows whether 1) ] (Agentd knows that 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":"Ivonne can now know that Ivonne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alberta","Ryan","Edward","Ivonne"],"index":34961,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995455265,"difficulty":0.004544735}
+{"premise":"There are four persons. Everyone is visible 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 Sarah's forehead is muddy. It is publicly announced that Francis knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that 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":"Sarah can now know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sarah","Billie","Francis","David"],"index":23233,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9973015785,"difficulty":0.0026984215}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerold knows whether Charles's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agentd knows that (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 2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Terry can now know that Charles can know whether Jerold's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucille","Charles","Jerold","Terry"],"index":21824,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993895292,"difficulty":0.0006104708}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corey's card is shown to Viola. Michael's card is shown to Corey. Corey'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:2 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Corey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Viola","Corey","Michael","Matthew"],"index":55742,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7361698747,"difficulty":1.7361698747}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eric is thirsty. It is publicly announced that Eric knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 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) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gloria can now know whether Eric can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gloria","Eric"],"index":52504,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9709818363,"difficulty":0.0290181637}
+{"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":"Joanna can now know that Mary can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andre","Joanna","Mary","Andrew"],"index":32476,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987555742,"difficulty":0.0012444258}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Barbara. Emma's card is shown to Barbara. Emma's card is shown to Kourtney. Kourtney's card is shown to Kourtney. It is publicly announced that someone picked a red card. It is publicly announced that Emma does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb: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:1,2 Agentb:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Emma can now know whether Barbara can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Emma","Kourtney"],"index":13169,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994480014,"difficulty":0.0005519986}
+{"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 Christina. Tia's card is shown to Christina. Christina's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Tia picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Christina can now know whether Mary can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christina","Mary","Tia"],"index":12491,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9897152781,"difficulty":0.0102847219}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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":"Everett can now know that Janice can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Janice","Bradford","Everett","Carolyn"],"index":49266,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984355569,"difficulty":0.0015644431}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laverne's card is shown to Laverne. Emily's card is shown to Laverne. Laverne's card is shown to Emily. 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 Emily picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Laverne can now know that Emily can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Laverne","Emily"],"index":56056,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994046688,"difficulty":0.0005953312}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Francis can now know that Zachary can know that Zachary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juanita","Francis","Justin","Zachary"],"index":39612,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912159443,"difficulty":0.0087840557}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Martha does not know whether Lisa is thirsty. It is publicly announced that Martha does not know whether Lisa is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Lisa can now know that Martha can know that Martha is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Martha","Lisa"],"index":5503,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9815065861,"difficulty":1.9815065861}
+{"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 Deborah. Berta's card is shown to Deborah. Deborah's card is shown to Patricia. Patricia's card is shown to Robert. Robert's card is shown to Robert. Patricia's card is shown to Berta. Robert's card is shown to Berta. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 Agentc:2,3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Robert can now know whether Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Patricia","Robert","Berta"],"index":50798,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9379478693,"difficulty":0.0620521307}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that 1)","n_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":"Joshua can now know whether Jennifer can know that Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jennifer","Helen","Joshua"],"index":57355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9916252494,"difficulty":0.0083747506}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Houston 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 3)","n_announcements":1,"pbcheck":"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":"Teresa can now know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sandra","Houston","Teresa"],"index":5139,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994134903,"difficulty":0.0005865097}
+{"premise":"There are three persons. Everyone is visible 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 not everyone's forehead is muddy. It is publicly announced that Norma 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) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 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) ] [ ! ~(3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Alan can now know that Kevin can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Norma","Alan","Kevin"],"index":48561,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993515611,"difficulty":0.0006484389}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney 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":"Courtney can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Courtney","Ricky","Joseph"],"index":52783,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987485409,"difficulty":0.0012514591}
+{"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 Benjamin. Miquel's card is shown to Miquel. Mary's card is shown to Miquel. Miquel's card is shown to Lauren. Lauren's card is shown to Lauren. 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:4 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2,4 Agentc:2,3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Benjamin can now know whether Miquel picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Miquel","Lauren","Mary"],"index":35813,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.7521073818,"difficulty":1.7521073818}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 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":"Dorothy can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dorothy","Jack"],"index":31993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990206957,"difficulty":0.0009793043}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mary's card is shown to Mary. Mary's card is shown to Shu. Mary's card is shown to Eileen. Shu's card is shown to Eileen. It is publicly announced that someone picked a red card. It is publicly announced that Shu does not know whether Kyle picked a red card. It is publicly announced that Shu does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Mary can now know whether Kyle picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Kyle","Shu","Eileen"],"index":4,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9747561216,"difficulty":0.0252438784}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nora knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Nora can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Nora","David","Ophelia"],"index":12128,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988956451,"difficulty":0.0011043549}
+{"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 Jose. Jennifer's card is shown to Jose. Jennifer's card is shown to James. Jose's card is shown to Maryann. Maryann's card is shown to Maryann. It is publicly announced that someone picked a red card. It is publicly announced that Maryann does not know whether Jennifer picked a red card. It is publicly announced that James does not know whether Maryann 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":"James can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","James","Maryann","Jennifer"],"index":60501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993591905,"difficulty":0.0006408095}
+{"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 Manuel 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 (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) ] [ ! (~(1&2&3)) ] [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Melba can now know whether Manuel can know that Melba is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Manuel","Annette","Melba"],"index":63644,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9194056988,"difficulty":0.0805943012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Everette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Maria can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Maria","Everette"],"index":59708,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954427481,"difficulty":0.0045572519}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tabatha's card is shown to Ronald. Ronald's card is shown to Tabatha. Tabatha's card is shown to Elsie. Tabatha's card is shown to Charles. It is publicly announced that someone picked a red card. It is publicly announced that Elsie knows whether or not everyone picked a red card. It is publicly announced that Charles does not know whether Elsie picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:2 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Charles can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Tabatha","Elsie","Charles"],"index":31115,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987481833,"difficulty":0.0012518167}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dee knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":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":"Tim can now know that Frederick can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessie","Tim","Frederick","Dee"],"index":36556,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992626309,"difficulty":0.0007373691}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Monica does not know whether Sandra is thirsty.","smcdel_problem":"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 that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Melinda can now know whether Monica can know that Melinda is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melinda","Monica","Rebecca","Sandra"],"index":51231,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9524573684,"difficulty":0.0475426316}
+{"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 Barbara. Robert's card is shown to Alan. Barbara's card is shown to Robert. Alan's card is shown to Jack. Jack's card is shown to Jack. It is publicly announced that someone picked a red card. It is publicly announced that Alan does not know whether Barbara picked a red card. It is publicly announced that Jack does not know whether Barbara picked a red card. It is publicly announced that Robert does not know whether Alan picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:3 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc 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 Agentb:3 Agentc:1 Agentd:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Barbara can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Alan","Robert","Jack"],"index":11931,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990183115,"difficulty":0.0009816885}
+{"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 Christine. Debra's card is shown to Debra. Christine's card is shown to Deborah. Debra's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Christine does not know whether or not everyone picked a red card. It is publicly announced that Debra knows whether Debra picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Debra can now know whether Deborah can know whether Debra picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christine","Debra","Deborah"],"index":56815,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.997961998,"difficulty":0.002038002}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randy does not know whether Randy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 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) ] 0","hypothesis":"John can now know that Robert can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Randy","Robert","John"],"index":56126,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993470311,"difficulty":0.0006529689}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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) ] [ ! 3 ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Cristine can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Todd","Cristine","Bobby"],"index":31159,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998891294,"difficulty":0.001108706}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows 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":"Marian can now know whether Deborah can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marian","Vicky","Deborah","Edgar"],"index":13396,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992284775,"difficulty":0.0007715225}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Travis does not know whether Denise is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Travis can now know that Michael can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Travis","Michael","Denise"],"index":36944,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989430308,"difficulty":0.0010569692}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William'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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"William can now know whether Allen picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Allen"],"index":24672,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9767285585,"difficulty":0.0232714415}
+{"premise":"There are two persons. Everyone is visible 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 Frances'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 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":"Frances can now know whether Viviana can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Viviana","Frances"],"index":5318,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Paula 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 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":"Steven can now know whether Paula can know whether Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Paula","Deborah","Steven"],"index":35525,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991014004,"difficulty":0.0008985996}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stuart knows whether Stuart's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Stuart can now know that Stuart's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stuart","Jeffery","Debra","Belinda"],"index":33321,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9576666355,"difficulty":1.9576666355}
+{"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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Danielle can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Danielle","Dorthy"],"index":49641,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989445806,"difficulty":0.0010554194}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ronald's card is shown to Ronald. Kevin's card is shown to Ronald. Pamela's card is shown to Ronald. Ronald's card is shown to Thomas. Pamela's card is shown to Thomas. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,4 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kevin can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Kevin","Thomas","Pamela"],"index":66827,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917008281,"difficulty":0.0082991719}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Viola does not know whether Viola's forehead is muddy. It is publicly announced that Viola knows whether or not nobody's forehead is muddy. It is publicly announced that Viola does not know whether Viola'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 whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Viola can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Viola","Julian"],"index":51022,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994431138,"difficulty":0.0005568862}
+{"premise":"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 Jason does not know whether or not everyone's forehead is muddy. It is publicly announced that Isabella knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] Agentc 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) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Kathryn can now know that Isabella can know that Isabella's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jason","Isabella","Kathryn"],"index":51105,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6452077031,"difficulty":1.6452077031}
+{"premise":"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 William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(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) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Yang","John","William"],"index":40098,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909676909,"difficulty":0.0090323091}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarice knows whether someone's forehead is muddy. It is publicly announced that Clarice 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|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agenta knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Dennis can now know whether Clarice can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Albert","Christopher","Clarice"],"index":14360,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994053841,"difficulty":0.0005946159}
+{"premise":"There are three persons. Everyone is visible 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 Lester's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lester","Anthony","Thomas"],"index":14257,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993849993,"difficulty":0.0006150007}
+{"premise":"There are four persons. Everyone is visible 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 Adrian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Adrian can now know whether Louis can know whether Adrian's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Ora","Michell","Adrian"],"index":38009,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994051456,"difficulty":0.0005948544}
+{"premise":"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 Alexander does not know whether or not everyone's forehead is muddy. It is publicly announced that Earlie knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Earlie can now know whether Alexander can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alexander","Earlie","Mary"],"index":62330,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993625283,"difficulty":0.0006374717}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Regina knows whether Luke's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Matthew can now know that Luke's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Daniel","Luke","Matthew","Regina"],"index":520,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958309531,"difficulty":0.0041690469}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Emily's card is shown to Emily. Lisa's card is shown to Emily. Lamar's card is shown to Lamar. Ned's card is shown to Lamar. Lisa's card is shown to Lamar. Emily's card is shown to Ned. Ned's card is shown to Lisa. It is publicly announced that someone picked a red card. It is publicly announced that Lisa knows whether or not nobody picked a red card. It is publicly announced that Lisa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] Agentc knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3,4 Agentc:1 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! 4 ] 0","hypothesis":"Ned can now know whether Lisa can know that Ned picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emily","Lamar","Ned","Lisa"],"index":30957,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9313575625,"difficulty":1.9313575625}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nettie does not know whether Frank is thirsty. It is publicly announced that Frank does not know whether Nettie 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) ] (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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Nettie can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Frank","Michael","Nettie"],"index":5657,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990000129,"difficulty":0.0009999871}
+{"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 Naomi does not know whether Claudia is thirsty. It is publicly announced that Claudia 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))) ] (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&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Naomi can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Johanna","Claudia","Naomi"],"index":47574,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993745685,"difficulty":0.0006254315}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Norman can now know whether Ellen can know whether Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norman","Ellen","Charles","Edward"],"index":37217,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994133711,"difficulty":0.0005866289}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher does not know whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Eric can now know whether Robert can know whether Robert is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrew","Christopher","Eric","Robert"],"index":35020,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9936289191,"difficulty":0.0063710809}
+{"premise":"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 Noel's forehead is muddy. It is publicly announced that Noel knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Noel can now know whether Leslie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Mary","Noel","Leslie"],"index":9451,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9613759518,"difficulty":0.0386240482}
+{"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. Alexander's card is shown to David. Alexander's card is shown to Alexander. 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 Alexander does not know whether or not everyone picked a red card. It is publicly announced that Alexander does not know whether David picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Alexander can now know that David can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Alexander"],"index":40646,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994525313,"difficulty":0.0005474687}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willie's card is shown to Willie. Willie's card is shown to Hugh. Hugh's card is shown to Carol. Kenneth's card is shown to Carol. Kenneth's card is shown to Kenneth. It is publicly announced that someone picked a red card. It is publicly announced that Hugh knows whether or not nobody picked a red card. It is publicly announced that Carol picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agenta knows that (Agentb knows that 4)","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":"Willie can now know that Hugh can know that Kenneth picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Willie","Hugh","Carol","Kenneth"],"index":53608,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9927371144,"difficulty":0.0072628856}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dena's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Harry can now know whether Dena can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dena","John","Raymond","Harry"],"index":51721,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994906187,"difficulty":0.0005093813}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie knows whether or not nobody's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that Connie can know whether Connie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Robert","Connie"],"index":66302,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9915804267,"difficulty":1.9915804267}
+{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that Joyce knows whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Donald can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Joyce","Donald"],"index":5843,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994250536,"difficulty":0.0005749464}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Norma knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 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":"Leonard can now know that Leonard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Viola","Norma","Leonard"],"index":20022,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.870656848,"difficulty":0.129343152}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan is thirsty. It is publicly announced that Sharon knows whether someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Susan can now know whether Sharon is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sharon","Susan","Jason"],"index":31325,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8221434355,"difficulty":1.8221434355}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gussie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows 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":"Rosemarie can now know that Gussie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Gussie","Rosemarie","Johnny"],"index":16154,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981770515,"difficulty":0.0018229485}
+{"premise":"There are four persons. Everyone is visible 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 Mike knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] Agenta knows that (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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Carlos can now know that Michael can know whether Paul's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carlos","Paul","Michael","Mike"],"index":28239,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993392825,"difficulty":0.0006607175}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether Kathy's forehead is muddy. It is publicly announced that Kristin knows whether Kristin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Kristin can now know that Maria can know that Kristin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Kristin","Kathy","Vanessa"],"index":10184,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966367483,"difficulty":0.0033632517}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jan is not thirsty. It is publicly announced that Rosemarie knows whether or not everyone is thirsty. It is publicly announced that Todd is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 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) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Todd can now know whether Jan can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosemarie","Jan","Todd"],"index":66065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9973069429,"difficulty":0.0026930571}
+{"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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joey can now know whether Carla can know whether Joey is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roger","Joey","Lorraine","Carla"],"index":63244,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998847723,"difficulty":0.001152277}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether William is thirsty. It is publicly announced that Corrie does not know whether Dorthy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 3) ] Agentb knows that (Agentc knows 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 2) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"William can now know that Dorthy can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corrie","William","Dorthy"],"index":27546,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994300008,"difficulty":0.0005699992}
+{"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 Tony. Tony's card is shown to Tony. David's card is shown to Judith. Judith's card is shown to Judith. It is publicly announced that someone picked a red card. It is publicly announced that Judith does not know whether Tony picked a red card. It is publicly announced that Judith does not know whether Tony picked a red card. It is publicly announced that Tony knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["David","Tony","Judith"],"index":38720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994383454,"difficulty":0.0005616546}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine does not know whether Geraldine's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 that (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jewel can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Geraldine","Jewel","Frank"],"index":32126,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gregory is not thirsty. It is publicly announced that Ann knows whether Gregory is thirsty. It is publicly announced that Gregory does not know whether Teresa is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Gregory can now know whether Jamie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ann","Jamie","Teresa","Gregory"],"index":56017,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970755577,"difficulty":0.0029244423}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nancy's card is shown to Charlene. Charlene's card is shown to Maria. Justin's card is shown to Maria. Justin's card is shown to Nancy. Nancy's card is shown to Nancy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1,2 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:4 Agentb:1,2 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Justin can now know whether Maria picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charlene","Justin","Maria","Nancy"],"index":26567,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9967646599,"difficulty":0.0032353401}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eva's card is shown to Eva. Lavonne's card is shown to Eva. Eva's card is shown to Lavonne. Lavonne's card is shown to Lavonne. Robert's card is shown to Lavonne. Eva's card is shown to Robert. Lavonne's card is shown to Robert. Robert's card is shown to Robert. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eva","Lavonne","Robert"],"index":64292,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993565679,"difficulty":0.0006434321}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eva does not know whether Edna is thirsty. It is publicly announced that Ronald 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":"Edna can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eva","Ronald","Edna"],"index":63808,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999427855,"difficulty":0.000572145}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann's forehead is muddy. It is publicly announced that Gregory 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) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Gregory can now know that Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shirley","Ann","Nicole","Gregory"],"index":52966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6167799234,"difficulty":0.3832200766}
+{"premise":"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 Brenda'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":"Brenda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cynthia","Brenda"],"index":38050,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979789853,"difficulty":0.0020210147}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse knows whether Jesse is thirsty. It is publicly announced that Janet knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 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 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Janet can now know that Cynthia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Janet","Cynthia","Jesse"],"index":32563,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9977814555,"difficulty":0.0022185445}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rufus knows whether Rufus'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 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":"Rufus can now know that Barbara can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Barbara","Rufus"],"index":20296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989689589,"difficulty":0.0010310411}
+{"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 Nancy does not know whether Michael is thirsty. It is publicly announced that Patrica knows whether or not everyone is thirsty. It is publicly announced that Patrica does not know whether Nancy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] Agenta knows that (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Michael can now know that Patrica can know whether Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Nancy","Patrica"],"index":6565,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7067986131,"difficulty":1.7067986131}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen does not know whether Martha is thirsty. It is publicly announced that Charles 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(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:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Martha can now know that Ellen can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellen","Charles","Martha"],"index":13742,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993057251,"difficulty":0.0006942749}
+{"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 Daniel. Carrie's card is shown to Willie. Rebecca's card is shown to Willie. Daniel's card is shown to Carrie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Carrie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(3) ] 0","hypothesis":"Carrie can now know whether Willie can know that Carrie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Willie","Carrie","Rebecca"],"index":18513,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9284430146,"difficulty":0.0715569854}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Phillip does not know whether Betty is thirsty. It is publicly announced that Phillip 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)","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":"Betty can now know that Phillip can know whether Betty is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Betty","Phillip"],"index":42037,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.500459969,"difficulty":0.499540031}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shawna's card is shown to James. Lucas's card is shown to James. Shawna's card is shown to Shawna. Shawna's card is shown to Lucas. It is publicly announced that someone picked a red card. It is publicly announced that Shawna knows whether Shawna picked a red card. It is publicly announced that Shawna does not know whether or not everyone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 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)) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"James can now know that Lucas can know that Lucas picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Shawna","Lucas"],"index":51636,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9088039994,"difficulty":1.9088039994}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ronald knows whether Ronald is thirsty. It is publicly announced that Ronald is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Ronald can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patricia","Pedro","Ronald"],"index":40298,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995338917,"difficulty":0.0004661083}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wade does not know whether Patricia is thirsty. It is publicly announced that Wade does not know whether or not everyone is thirsty. It is publicly announced that Wade does not know whether or not everyone is thirsty. It is publicly announced that 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&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 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) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Wade can now know whether Patricia can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","Wade"],"index":59037,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979654551,"difficulty":0.0020345449}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Jesus can now know whether Krystle can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesus","Donald","Diane","Krystle"],"index":23164,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993651509,"difficulty":0.0006348491}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Penny does not know whether Sarah is thirsty. It is publicly announced that Sarah does not know whether Suzanne is thirsty.","smcdel_problem":"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) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Sarah can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Penny","Roberta","Sarah","Suzanne"],"index":17373,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993695617,"difficulty":0.0006304383}
+{"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 Carrie. Charles's card is shown to Carrie. Carrie's card is shown to Charles. Jon's card is shown to Alan. Alan's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Charles knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:2,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Carrie can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carrie","Jon","Charles","Alan"],"index":22973,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988827109,"difficulty":0.0011172891}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty. It is publicly announced that Helen does not know whether or not everyone is thirsty. It is publicly announced that Helen does not know whether Karen 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 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 (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Helen can now know whether Karen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Karen"],"index":24535,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992439747,"difficulty":0.0007560253}
+{"premise":"There are 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 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":"Dwight can now know whether Dwight's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Aimee","Nancy","Freeman","Dwight"],"index":51871,"s-l":"forehead_mirror-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 Cornelius does not know whether or not everyone is thirsty. It is publicly announced that Cornelius knows whether or not nobody is thirsty. It is publicly announced that Edmund does not know whether Pamela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Edmund can now know that Cornelius can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cornelius","Pamela","Edmund"],"index":11268,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994968176,"difficulty":0.0005031824}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanne does not know whether or not everyone is thirsty. It is publicly announced that Jeanne does not know whether Alonzo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] Agentd knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Jeanne can now know that Alonzo can know whether Alonzo is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lewis","Alonzo","Iris","Jeanne"],"index":48622,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8154901862,"difficulty":0.1845098138}
+{"premise":"There are four persons. Everyone is visible 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 that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Robert can now know whether Roy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Dana","Roy","Kelley"],"index":16331,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993207455,"difficulty":0.0006792545}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Willis's card is shown to Debra. Willis's card is shown to William. Gregory's card is shown to Gregory. Gregory's card is shown to Willis. 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) ] Agenta knows whether (Agentc knows whether 3)","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":"Debra can now know whether Gregory can know whether Gregory picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Debra","William","Gregory","Willis"],"index":8519,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970701933,"difficulty":0.0029298067}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Charlie does not know whether or not everyone is thirsty. It is publicly announced that Charlie does not know whether Eula is thirsty. It is publicly announced that Eula does not know whether Lois is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Lois can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lois","Charlie","Eula"],"index":54050,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9953705668,"difficulty":0.0046294332}
+{"premise":"There are four persons. Everyone is visible 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 Brett's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (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":"Paul can now know whether Nelson's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carole","Nelson","Paul","Brett"],"index":25896,"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. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stewart 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)","n_announcements":1,"pbcheck":"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":"Tara can now know that Stewart can know whether Tara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tara","Stewart","Daniel"],"index":55562,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994227886,"difficulty":0.0005772114}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Regina can now know whether Carla can know whether Regina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Regina","Thomas","Carla"],"index":49541,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994152784,"difficulty":0.0005847216}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gary does not know whether Juanita is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Juanita can now know whether Brian can know that Juanita is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Martha","Juanita","Gary"],"index":1926,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9523829222,"difficulty":0.0476170778}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Erika knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tonya can now know whether Mary can know that Tonya is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lauren","Mary","Tonya","Erika"],"index":63969,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8926600814,"difficulty":0.1073399186}
+{"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 Kaylene. Michael's card is shown to Michael. Michael's card is shown to Deana. Deana's card is shown to Deana. 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 Deana picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! 3 ] 0","hypothesis":"Michael can now know whether Deana can know that Deana picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kaylene","Michael","Deana"],"index":15564,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9725791812,"difficulty":0.0274208188}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Mario can now know that Kelly can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kelly","Betty","Mario","George"],"index":27660,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993793964,"difficulty":0.0006206036}
+{"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 someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Jessica can now know whether Gaynelle can know whether Gaynelle is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cecil","Gaynelle","Jessica"],"index":67426,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9886084795,"difficulty":0.0113915205}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wallace 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) ] [ ! (Agentd knows whether 1) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Donald can now know that Wallace's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Laura","Brandy","Wallace"],"index":878,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983793497,"difficulty":0.0016206503}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marsha can now know that Robert can know that Marsha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Marsha","Robert"],"index":38355,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998118937,"difficulty":0.001881063}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathy knows whether or not nobody's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy. It is publicly announced that Charles's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Kathy can now know whether Charles can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kathy","Charles"],"index":37783,"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 Grace does not know whether Carol is thirsty. It is publicly announced that Grace does not know whether Theresa is thirsty. It is publicly announced that Carol is thirsty. It is publicly announced that Theresa does not know whether Grace is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Theresa can now know whether Grace can know whether Theresa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carol","Theresa","Grace"],"index":66656,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9986234903,"difficulty":0.0013765097}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawrence knows whether someone is thirsty. It is publicly announced that Lawrence knows whether Lawrence is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that 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)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lawrence can now know whether Leticia can know that Sandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leticia","Sandra","Lawrence"],"index":13592,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9948143959,"difficulty":0.0051856041}
+{"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 Jerry. Jerry's card is shown to Larry. It is publicly announced that someone picked a red card. It is publicly announced that Larry picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Jerry can now know whether Larry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jerry","Larry"],"index":28271,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9733038545,"difficulty":0.0266961455}
+{"premise":"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 Ashley 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) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ashley can now know that Mark can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Ashley","Mark"],"index":13715,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9852390289,"difficulty":0.0147609711}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ignacio's card is shown to Margot. Reginald's card is shown to Ignacio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 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 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Reginald can now know whether Margot can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margot","Reginald","Ignacio","Audrey"],"index":31744,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9938409328,"difficulty":0.0061590672}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ruth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Ruth can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Mark","Ruth"],"index":54882,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993112087,"difficulty":0.0006887913}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Anthony can now know that Jana can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jana","Jerrie","Anthony"],"index":20468,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9720034003,"difficulty":0.0279965997}
+{"premise":"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 Jaime's forehead is muddy. It is publicly announced that Brittany knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jaime can now know that Jaime's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carol","John","Brittany","Jaime"],"index":63983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9933179617,"difficulty":0.0066820383}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows 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) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know whether Harlan can know whether Harlan is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Harlan","Eddie","Susan"],"index":65732,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9837405086,"difficulty":0.0162594914}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (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":"Richard can now know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Melissa","Richard","Alan"],"index":45679,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8719962835,"difficulty":0.1280037165}
+{"premise":"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 Jessica's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christina","Jessica","John"],"index":33848,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7277472019,"difficulty":1.7277472019}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Griselda does not know whether or not everyone's forehead is muddy. It is publicly announced that Marjorie knows whether Griselda's forehead is muddy. It is publicly announced that Griselda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows 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)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Griselda can now know whether Marjorie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Griselda","Marjorie"],"index":35111,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8895205855,"difficulty":0.1104794145}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agentc knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Angela can now know that James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","James","Angela"],"index":8861,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9196515679,"difficulty":0.0803484321}
+{"premise":"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 Ashley knows whether James's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Kay does not know whether Kay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! 4 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kay 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":["Kay","Paul","Ashley","James"],"index":2535,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9585688114,"difficulty":0.0414311886}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether Horace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Horace can now know that Jessica can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Rachel","Horace","Jessica"],"index":7504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988868833,"difficulty":0.0011131167}
+{"premise":"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's forehead is not muddy. It is publicly announced that Lisa knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Lisa can now know that Hortencia can know that Hortencia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tara","Hortencia","Lisa"],"index":17241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960526228,"difficulty":0.0039473772}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tessa knows whether or not nobody's forehead is muddy. It is publicly announced that Peggy knows whether Tessa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","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":"Tessa can now know that Tessa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tessa","Peggy"],"index":31174,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9951869845,"difficulty":0.0048130155}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carmen's card is shown to Marianne. Carmen's card is shown to Carmen. Teresa's card is shown to Carmen. Marianne's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Carmen does not know whether Marianne picked a red card. It is publicly announced that Carmen does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carmen can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marianne","Carmen","Teresa"],"index":44432,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983427525,"difficulty":0.0016572475}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows that (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 that Dale can know that Arthur's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dale","Jesus","Rebecca","Arthur"],"index":21906,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974420071,"difficulty":0.0025579929}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sherry's card is shown to Michel. Michel's card is shown to Sherry. Cristina's card is shown to Sara. Michel's card is shown to Sara. Sara's card is shown to Sara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,2,4 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:3 Agentb:2 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sherry can now know that Michel can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cristina","Michel","Sherry","Sara"],"index":2066,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993361831,"difficulty":0.0006638169}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Scott is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Eileen can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kathryn","Sarah","Scott","Eileen"],"index":65468,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995013475,"difficulty":0.0004986525}
+{"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. Scott's card is shown to Miranda. Miranda's card is shown to Leah. Walter's card is shown to Scott. Leah'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:4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:2 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Walter can now know that Leah can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Miranda","Leah","Scott"],"index":19224,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987630844,"difficulty":0.0012369156}
+{"premise":"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":"Jessica can now know whether Angela can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","Angela","Jill"],"index":30321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993294477,"difficulty":0.0006705523}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 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":"David can now know whether William can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Phyllis","William","Shane"],"index":37529,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992322922,"difficulty":0.0007677078}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Tammy can now know that Zachary can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Zachary","Roxanne","Tammy"],"index":27435,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988817573,"difficulty":0.0011182427}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"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":"Lawrence can now know that Richard can know that Lawrence's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lawrence","Richard","Kristin"],"index":1668,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978268743,"difficulty":0.0021731257}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nicole's card is shown to Nicole. Terry's card is shown to Nicole. Nicole's card is shown to Lynn. Nicole's card is shown to Terry. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lynn can now know that Nicole can know whether Terry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicole","Lynn","Terry"],"index":63886,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8026020527,"difficulty":1.8026020527}
+{"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 Michael is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Melinda can now know that Michael can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Melinda","Michael"],"index":5459,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999430716,"difficulty":0.000569284}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mercedes does not know whether or not everyone is thirsty. It is publicly announced that Kristin does not know whether William is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Kristin can now know that Kristin is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristin","William","Mercedes"],"index":42874,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7965439558,"difficulty":0.2034560442}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Michael can now know whether Linda can know whether Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Michael"],"index":11952,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994016886,"difficulty":0.0005983114}
+{"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 Marjorie. Marjorie's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Marjorie 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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Linda can now know that Marjorie can know that Linda picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marjorie","Linda"],"index":41515,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.8307185173,"difficulty":0.1692814827}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debby does not know whether Debby's forehead is muddy. It is publicly announced that Stephanie knows whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentb knows that 1)","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":"Debby can now know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Stephanie","Debby"],"index":57745,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.947312355,"difficulty":1.947312355}
+{"premise":"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 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) ] [ ! (Agentb knows whether 3) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Marilyn can now know that Lisa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marilyn","Terry","Angela","Lisa"],"index":65397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973394275,"difficulty":0.0026605725}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tomas knows whether someone is thirsty. It is publicly announced that Tomas knows whether Tomas is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jill can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nancy","Jill","Tomas"],"index":23006,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989190102,"difficulty":0.0010809898}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agenta knows that (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Ethel can now know that Carlos can know whether Steven is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ethel","Steven","Mary","Carlos"],"index":15975,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976508021,"difficulty":0.0023491979}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Federico knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":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":"Kenneth can now know that Federico is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jill","Kenneth","Dewayne","Federico"],"index":23555,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9245357513,"difficulty":0.0754642487}
+{"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 Judy does not know whether Margaret is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Margaret can now know that James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Judy","Margaret"],"index":55432,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983285069,"difficulty":0.0016714931}
+{"premise":"There are four persons. Everyone is visible 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 Deborah's forehead is muddy. It is publicly announced that George knows whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"George can now know that Deborah can know whether George's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["George","Deborah","Kimberly","Susan"],"index":62257,"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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristin's forehead is not muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Lauren can now know whether Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kristin","Lauren","Cynthia"],"index":11466,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9955501556,"difficulty":1.9955501556}
+{"premise":"There are two 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 knows whether Linda 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) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that John can know whether John is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","John"],"index":2846,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7793993354,"difficulty":0.2206006646}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Christopher knows whether or not everyone is thirsty.","smcdel_problem":"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":"Jonah can now know that Macie can know that Jonah is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Jonah","William","Macie"],"index":6812,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9874252677,"difficulty":0.0125747323}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randolph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (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":"Randolph can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Randolph","Theo"],"index":30042,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975929856,"difficulty":0.0024070144}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Amanda knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Alice can now know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amanda","Alice"],"index":12153,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9986477494,"difficulty":0.0013522506}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sarah does not know whether Doug is thirsty. It is publicly announced that Sara does not know whether Doug is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Sara can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Doug","Sarah","Sara","Elaine"],"index":43431,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994155169,"difficulty":0.0005844831}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee knows whether Shaniqua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Shaniqua can now know that Renee can know whether Renee's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Renee","Raul","Shaniqua"],"index":25618,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grady's card is shown to Grady. Pearl's card is shown to Grady. John's card is shown to Pearl. John's card is shown to Darryl. Pearl's card is shown to John. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:4 Agentd:2 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:4 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Darryl can now know whether John picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Grady","Pearl","Darryl","John"],"index":15482,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6383714676,"difficulty":1.6383714676}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Earline does not know whether Shirley is thirsty. It is publicly announced that Earline does not know whether Kendrick is thirsty. It is publicly announced that Earline is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] Agentc knows 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) ] [ ! ~(Agenta knows whether 3) ] [ ! 1 ] 0","hypothesis":"Kendrick can now know that Shirley can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Earline","Shirley","Kendrick"],"index":2577,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9986561537,"difficulty":0.0013438463}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Latonya does not know whether or not everyone is thirsty. It is publicly announced that Jean 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) ] Agenta knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(4) ] 0","hypothesis":"Latonya can now know whether Jean can know that Virginia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Latonya","Pearl","Virginia","Jean"],"index":42636,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9890844226,"difficulty":0.0109155774}
+{"premise":"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 Lisa's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Lisa can now know that Brandy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Brandy","Lisa"],"index":23379,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988613129,"difficulty":0.0011386871}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Jacob. Jacob's card is shown to Theodore. It is publicly announced that someone picked a red card. It is publicly announced that Jacob picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Jacob can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jacob","Theodore"],"index":27467,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994756579,"difficulty":0.0005243421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Francis knows whether or not nobody is thirsty. It is publicly announced that Francis does not know whether Claire is thirsty.","smcdel_problem":"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 (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Troy can now know whether Francis can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sally","Troy","Claire","Francis"],"index":23999,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993757606,"difficulty":0.0006242394}
+{"premise":"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 does not know whether Doris's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy. It is publicly announced that Doris's forehead is not muddy. It is publicly announced that Darlene does not know whether Darlene's forehead is muddy.","smcdel_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":"Darlene can now know that Brenda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brenda","Doris","Darlene"],"index":27841,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990482926,"difficulty":0.0009517074}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows whether (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":"Gladys can now know whether Jana can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gladys","Dennis","Jana","Bobby"],"index":47729,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9890079498,"difficulty":0.0109920502}
+{"premise":"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) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Tonya can now know whether Mary can know whether Heather's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Heather","Lynne","Mary","Tonya"],"index":67120,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991244674,"difficulty":0.0008755326}
+{"premise":"There are two persons. Everyone is visible 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 Maureen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether Maureen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Maureen","Elizabeth"],"index":54106,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993483424,"difficulty":0.0006516576}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Katrina can now know that Stephen can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katrina","Stephen","Luke","Joseph"],"index":48851,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998881042,"difficulty":0.001118958}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Shirley can now know that Jay can know that Jay's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jay","Shirley","William"],"index":35279,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9715803266,"difficulty":0.0284196734}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Deborah's card is shown to Deborah. Clark's card is shown to Deborah. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta: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:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bruce can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bruce","Deborah","Clark","Sandra"],"index":24780,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993354678,"difficulty":0.0006645322}
+{"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 Bernice. Roy's card is shown to Bernice. Roy's card is shown to Ryan. Ryan's card is shown to Ryan. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bernice can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernice","Patrick","Roy","Ryan"],"index":38251,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989319444,"difficulty":0.0010680556}
+{"premise":"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 (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":"Mary can now know whether Otis can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Otis","Thomas","Mary"],"index":35468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
+{"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. Antoinette's card is shown to Jody. Andrea's card is shown to Antoinette. Karen's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Karen knows whether Karen picked a red card. It is publicly announced that Karen does not know whether or not everyone picked a red card. It is publicly announced that Jody does not know whether Jody picked a red card. It is publicly announced that Antoinette does not know whether Jody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jody can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Karen","Jody","Antoinette","Andrea"],"index":66503,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982963204,"difficulty":0.0017036796}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Audrey's card is shown to Nathaniel. Shannon's card is shown to Shannon. Robbie's card is shown to Audrey. It is publicly announced that someone picked a red card. It is publicly announced that Shannon does not know whether Audrey picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Shannon does not know whether Shannon picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nathaniel can now know that Robbie can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nathaniel","Robbie","Shannon","Audrey"],"index":53648,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993867874,"difficulty":0.0006132126}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Catherine knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (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":"Catherine can now know that Nathaniel can know that Christopher is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Catherine","Nathaniel"],"index":10891,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9883667827,"difficulty":0.0116332173}
+{"premise":"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.","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 whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nancy can now know whether Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eldon","Mary","Nancy"],"index":63887,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993299246,"difficulty":0.0006700754}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marguerita's card is shown to Jerry. Terrance's card is shown to Terrance. Terrance's card is shown to Marguerita. It is publicly announced that someone picked a red card. It is publicly announced that Terrance does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Terrance can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jerry","Terrance","Marguerita"],"index":18309,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994369149,"difficulty":0.0005630851}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 1)","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":"Regina can now know that Natalie can know whether Natalie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Natalie","Regina"],"index":9363,"s-l":"forehead_mirror-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 Melissa does not know whether David is thirsty. It is publicly announced that Melissa 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) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd 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) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"David can now know that Sarah is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Sarah","Ethel","Melissa"],"index":48657,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982755184,"difficulty":0.0017244816}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kelvin's card is shown to Kelvin. Juan's card is shown to Delois. Kimberly's card is shown to Delois. Juan's card is shown to Kimberly. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 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:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Kelvin can now know whether Kimberly picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Kelvin","Delois","Kimberly"],"index":55862,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9826338887,"difficulty":1.9826338887}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcus's card is shown to Marcus. Michael'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 Michael does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Marcus","Robert"],"index":55685,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8349075317,"difficulty":1.8349075317}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether Claude's forehead is muddy. It is publicly announced that Lynne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (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) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Claude can now know that Judith can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Claude","Judith","Lynne"],"index":43845,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994718432,"difficulty":0.0005281568}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lonnie does not know whether Danny is thirsty. It is publicly announced that Lonnie does not know whether 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) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Danny can now know that Lonnie can know whether Lonnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Danny","Lonnie"],"index":59240,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9571940899,"difficulty":0.0428059101}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Bernard's card is shown to Viola. 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)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bernard can now know that Bernard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bernard","Viola","William","Amy"],"index":56429,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9608923197,"difficulty":0.0391076803}
+{"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 Constance. Constance'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 Matthew picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Constance can now know whether Matthew can know that Constance picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Constance","Matthew"],"index":30262,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9092800021,"difficulty":0.0907199979}
+{"premise":"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 Eugene's forehead is muddy. It is publicly announced that Gretchen knows whether Eugene's forehead is muddy. It is publicly announced that Eugene 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)) ] (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) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Gretchen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eugene","Gretchen","Tiffany"],"index":53298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980599284,"difficulty":0.0019400716}
+{"premise":"There are 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 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":"Joseph can now know that Barbara can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Cory","Barbara","Joseph"],"index":14711,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985820055,"difficulty":0.0014179945}
+{"premise":"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 knows whether Rachel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 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) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Nadine can now know whether Maureen can know that Maureen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nadine","Andrew","Rachel","Maureen"],"index":30938,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.976439476,"difficulty":0.023560524}
+{"premise":"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 knows whether or not nobody'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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Ira can now know whether Dorothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ira","Dorothy"],"index":25325,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9933350086,"difficulty":0.0066649914}
+{"premise":"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) ] [ ! ~(3) ] 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) ] [ ! ~(3) ] 0","hypothesis":"Margaret can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Robert","Jim","Shane"],"index":15655,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903964996,"difficulty":0.0096035004}
+{"premise":"There are three persons. Everyone is visible 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 (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":"Alton can now know whether Ruby can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruby","Jeffrey","Alton"],"index":5659,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991440773,"difficulty":0.0008559227}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 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":"Dianne can now know that Dianne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dianne","Kathryn","Linda"],"index":63678,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980059266,"difficulty":0.0019940734}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hazel's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Hazel can now know that Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Hazel","Joseph"],"index":56198,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999473989,"difficulty":0.000526011}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia's forehead is muddy. It is publicly announced that Jimmy'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) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Jimmy can now know whether Kathleen can know whether Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathleen","Patricia","Jimmy","James"],"index":50429,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991756082,"difficulty":0.0008243918}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brett's forehead is 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 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":"Brett can now know that Amanda can know that Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Amanda","Patrick","Brett","Vera"],"index":20567,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978833795,"difficulty":0.0021166205}
+{"premise":"There are four persons. Everyone is visible 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 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 (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Thomas can now know that Margaret can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","Natalie","Margaret","Amanda"],"index":64581,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989503026,"difficulty":0.0010496974}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Juanita. Theresa's card is shown to Juanita. Juanita's card is shown to Theresa. Theresa's card is shown to Theresa. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agentb knows 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":"Theresa can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Juanita","Theresa"],"index":20272,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994109869,"difficulty":0.0005890131}
+{"premise":"There are three persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3 LAW 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 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW 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":"Mike can now know that Lois can know that Mike's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lois","Michelle","Mike"],"index":44062,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978479147,"difficulty":0.0021520853}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Muriel knows whether Muriel's forehead is muddy. It is publicly announced that Muriel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] Agenta knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Muriel can now know whether Harvey can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Phillip","Harvey","Kevin"],"index":32812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999443233,"difficulty":0.000556767}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Johnny does not know whether Eddie is thirsty. It is publicly announced that Eddie does not know whether Harold is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Eddie can now know that Johnny can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","Johnny","Andrew","Harold"],"index":7436,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989890456,"difficulty":0.0010109544}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rita is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Miles can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Erin","Rita","Miles"],"index":45328,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995342493,"difficulty":0.0004657507}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Delores knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] Agenta knows that (Agentc knows whether 1)","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":"Delores can now know that Charlotte can know whether Delores is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Delores","Joseph","Charlotte"],"index":46252,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9122067094,"difficulty":0.0877932906}
+{"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 Quinn. Harold's card is shown to Jeffrey. Quinn's card is shown to Harold. Jeffrey's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Jeffrey knows whether or not nobody picked a red card. It is publicly announced that Jeffrey does not know whether Quinn picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that 2)","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":"Jeffrey can now know that Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Quinn","Jeffrey","Harold"],"index":11927,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9848751426,"difficulty":0.0151248574}
+{"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. Clifford's card is shown to Susan. Clifford's card is shown to Clifford. It is publicly announced that someone picked a red card. It is publicly announced that Susan does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Clifford can now know whether Susan can know that Robert picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Susan","Clifford","Robert"],"index":9924,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.942409873,"difficulty":0.057590127}
+{"premise":"There are two persons. Everyone is visible 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 that (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"John can now know that Lily can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lily","John"],"index":38406,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.985617578,"difficulty":0.014382422}
+{"premise":"There are 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 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":"Chad can now know that Chad's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Pedro","Chad","Kayla"],"index":16153,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9983068705,"difficulty":0.0016931295}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maggie 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) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Robert can now know that Stephanie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephanie","Alfredo","Robert","Maggie"],"index":63378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994878769,"difficulty":0.0005121231}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentd knows that 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":"Amber can now know whether Hugo can know that Joshua is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joshua","Paul","Amber","Hugo"],"index":32313,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9898793697,"difficulty":0.0101206303}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Jerome does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":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 that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Olivia","Michael","David","Jerome"],"index":1034,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999537468,"difficulty":0.000462532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Don is thirsty. It is publicly announced that Jodi 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 (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) ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ruth can now know whether Melinda can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Don","Melinda","Jodi"],"index":53127,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993521571,"difficulty":0.0006478429}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corey knows whether Judith's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nick can now know whether Corey can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Corey","Judith","Nick"],"index":57378,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993607402,"difficulty":0.0006392598}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Henry's card is shown to Henry. Henry's card is shown to Hermelinda. It is publicly announced that someone picked a red card. It is publicly announced that Hermelinda knows whether Hermelinda picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Henry can now know whether Hermelinda can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Henry","Hermelinda"],"index":15966,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7421025038,"difficulty":0.2578974962}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mildred knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows that (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":"Mildred can now know whether Don can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Don","Mildred"],"index":51444,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994063377,"difficulty":0.0005936623}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jeff's card is shown to Jeff. Harold's card is shown to Jeff. Jeff's card is shown to Harold. Harold's card is shown to Delma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Delma can now know whether Jeff can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jeff","Harold","Delma"],"index":65868,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994090796,"difficulty":0.0005909204}
+{"premise":"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) ] [ ! ~(Agentc 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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gerald can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathryn","Gerald","John"],"index":57521,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989227653,"difficulty":0.0010772347}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Ronald can now know that Carolyn can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ronald","Carolyn"],"index":16457,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992282391,"difficulty":0.0007717609}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether Barbara's forehead is muddy. It is publicly announced that Katrina's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! ~(2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Barbara can now know whether Gary can know whether Katrina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Katrina","Barbara"],"index":10343,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999147892,"difficulty":0.000852108}
+{"premise":"There are four persons. Everyone is visible 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 Pamela'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:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] Agentd knows that (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) ] [ ! (Agentb knows whether 3) ] [ ! ~(1) ] 0","hypothesis":"Lonnie can now know that Eric can know whether Lonnie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Duane","Pamela","Lonnie"],"index":6348,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994280934,"difficulty":0.0005719066}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know whether John can know whether Frank's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Frank","James","John"],"index":37188,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998052597,"difficulty":0.001947403}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lewis knows whether Dinah's forehead is muddy. It is publicly announced that Lewis knows whether Dinah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (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":"Lewis can now know whether Kimberly can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lewis","Dinah","Kimberly","Ryan"],"index":6945,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993630052,"difficulty":0.0006369948}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentd knows whether 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":"Adrian can now know whether Jared's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christine","Jared","Anita","Adrian"],"index":1237,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992967844,"difficulty":0.0007032156}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is muddy. It is publicly announced that Matthew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] Agenta knows that (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Hubert can now know that Jean can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hubert","Carol","Matthew","Jean"],"index":54312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8714450002,"difficulty":0.1285549998}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Madeline knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 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":"Dewayne can now know whether Dewayne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Madeline","Diane","James","Dewayne"],"index":9542,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8220277429,"difficulty":0.1779722571}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sergio does not know whether Sergio's forehead is muddy. It is publicly announced that Frances does not know whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Frances can now know whether Donald can know that Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sergio","Frances","Donald"],"index":57475,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859579206,"difficulty":0.0140420794}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Valarie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Richard","Russell","Jan","Valarie"],"index":47635,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988105297,"difficulty":0.0011894703}
+{"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 Rick 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 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":"James can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Russell","Rick","James"],"index":36506,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971639514,"difficulty":0.0028360486}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Blaine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agenta knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Megan can now know that Blaine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Megan","Blaine","John","Calvin"],"index":10383,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993829727,"difficulty":0.0006170273}
+{"premise":"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 (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":"Martin can now know whether Lucille can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lucille","Clark","Martin"],"index":8244,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994107485,"difficulty":0.0005892515}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Russell can now know that Sylvia can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sylvia","Russell"],"index":22689,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994522929,"difficulty":0.0005477071}
+{"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 Grace 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) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Helen can now know that Russell can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Grace","Helen","Russell"],"index":41681,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990131855,"difficulty":0.0009868145}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kyle's card is shown to Kyle. Dorothy's card is shown to Kyle. Kyle's card is shown to Steven. Kyle's card is shown to Dorothy. Steven's card is shown to Dorothy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Steven can now know that Kyle can know that Kyle picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kyle","Steven","Dorothy"],"index":67252,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9972116351,"difficulty":0.0027883649}
+{"premise":"There are two 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 or not everyone's forehead is muddy. It is publicly announced that Samuel 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 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":"Samuel can now know whether William can know that Samuel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Samuel"],"index":14420,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9713799357,"difficulty":0.0286200643}
+{"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 David. George's card is shown to George. Deborah's card is shown to George. George's card is shown to Deborah. Deborah's card is shown to Deborah. It is publicly announced that someone picked a red card. It is publicly announced that Deborah does not know whether or not everyone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"George can now know that Deborah can know that Deborah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","George","Deborah"],"index":39334,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.7721922398,"difficulty":1.7721922398}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lester does not know whether or not everyone is thirsty. It is publicly announced that Lester does not know whether or not everyone is thirsty. It is publicly announced that Leroy knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Leroy can now know that Lester is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leroy","Lester"],"index":47189,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9525883198,"difficulty":1.9525883198}
+{"premise":"There are four persons. Everyone is visible 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'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 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Josie can now know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Yvonne","Lisa","Josie","Myra"],"index":54209,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981535077,"difficulty":0.0018464923}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ernest's card is shown to Ernest. Minnie's card is shown to Ricky. Minnie's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Minnie picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agenta knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Ernest can now know that Richard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ernest","Minnie","Ricky","Richard"],"index":30978,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9956282377,"difficulty":0.0043717623}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether or not everyone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 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) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Robert can now know that Haley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ralph","Robert","Kenneth","Haley"],"index":5808,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994219542,"difficulty":0.0005780458}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victor is thirsty. It is publicly announced that Michele knows whether Victor 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 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":"Victor can now know whether Jonathan is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michele","Jonathan","Victor"],"index":20333,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9976194501,"difficulty":0.0023805499}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bernard does not know whether Douglas is thirsty. It is publicly announced that Bernard does not know whether Douglas is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (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 2) ] 0","hypothesis":"Douglas can now know that Bernard can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bernard","Douglas"],"index":10459,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994168282,"difficulty":0.0005831718}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wilmer does not know whether or not everyone is thirsty. It is publicly announced that Eric does not know whether Terrance is thirsty. It is publicly announced that Wilmer does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Eric can now know whether Eric is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Terrance","Wilmer","Eric"],"index":36167,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968500733,"difficulty":0.0031499267}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Susan can now know that Leticia can know that Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Leticia","Christine","Susan"],"index":56442,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9904530048,"difficulty":0.0095469952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether (1|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":"John can now know whether Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","John","Joseph","Mark"],"index":48925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999381423,"difficulty":0.000618577}
+{"premise":"There are two persons. Everyone is visible 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 knows whether or not everyone's forehead is muddy. It is publicly announced that Angelina knows whether someone's forehead is muddy. It is publicly announced that Angelina knows whether Angelina's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agenta knows whether 1) ] (Agenta knows that 1)","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":"Angelina can now know that Angelina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Angelina","Elizabeth"],"index":17603,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9940270185,"difficulty":0.0059729815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know whether Jacquelyn can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Betty","Jacquelyn","William","Charles"],"index":19018,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9880135059,"difficulty":0.0119864941}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows whether (~(1|2|3)))","n_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":"Cassandra can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cassandra","Larry","Donald"],"index":13658,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994302392,"difficulty":0.0005697608}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joan's card is shown to Joan. Jody's card is shown to Joan. Jody's card is shown to Jody. Kathryn'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:1,2 Agentb:2 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Kathryn can now know that Joan can know that Kathryn picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joan","Jody","Kathryn"],"index":28837,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962651134,"difficulty":0.0037348866}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Luther's card is shown to James. James's card is shown to Luther. Luther's card is shown to Luther. Lynette's card is shown to Luther. Luther's card is shown to Eileen. 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) ] (Agentc knows that 2)","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":"Eileen can now know that Luther picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Luther","Eileen","Lynette"],"index":44346,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9905160069,"difficulty":0.0094839931}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shanna does not know whether Grayce is thirsty. It is publicly announced that Shanna does not know whether Cindy is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] (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 2) ] 0","hypothesis":"Cindy can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Shanna","Cindy","Grayce"],"index":58917,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994365573,"difficulty":0.0005634427}
+{"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 Laura. Laura's card is shown to Carolyn. John's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether Carolyn picked a red card. It is publicly announced that Laura does not know whether Laura picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Laura can now know whether John can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Laura","Carolyn","John"],"index":1540,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999181807,"difficulty":0.000818193}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Melissa can now know that Kimberly can know whether Betty's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Melissa","Betty","Rebecca"],"index":49929,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993433356,"difficulty":0.0006566644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Latosha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_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":"Brandon can now know whether Jeanette can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Latosha","Brandon","Jeanette"],"index":65784,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8771925569,"difficulty":0.1228074431}
+{"premise":"There are three persons. Everyone is visible 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 (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":"Nancy can now know whether Ronald can know that Ollie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ronald","Ollie","Nancy"],"index":38775,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993264675,"difficulty":0.0006735325}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Victoria's card is shown to Victoria. Victoria's card is shown to Sonja. Sonja's card is shown to Sonja. It is publicly announced that someone picked a red card. It is publicly announced that Victoria knows whether Victoria picked a red card. It is publicly announced that Victoria does not know whether Sonja picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether 2) ] Agentb knows whether (Agenta 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) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Sonja can now know whether Victoria can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Victoria","Sonja"],"index":15398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9756761789,"difficulty":0.0243238211}
+{"premise":"There are three persons. Everyone is visible 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 or not everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy. It is publicly announced that Tom's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! 1 ] [ ! 3 ] 0","hypothesis":"Alice can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alice","Nina","Tom"],"index":46952,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982873797,"difficulty":0.0017126203}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"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":"Mark can now know whether Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mark","Lori","Norma"],"index":60633,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994078875,"difficulty":0.0005921125}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Philip's card is shown to Philip. Corinna's card is shown to Philip. Sonya's card is shown to Philip. Corinna's card is shown to Corinna. Philip's card is shown to Sonya. Corinna's card is shown to Sonya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sonya can now know whether Corinna can know whether Corinna picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Philip","Corinna","Sonya"],"index":13319,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970423579,"difficulty":0.0029576421}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tina 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 (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know whether Tina can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tina","Paul","Robert","Antonio"],"index":18948,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993932247,"difficulty":0.0006067753}
+{"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 Sherry. Sherry's card is shown to Scott. Scott's card is shown to Scott. Scott's card is shown to Socorro. Socorro's card is shown to Socorro. 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 that (~(1|2|3|4)))","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":"Yung can now know whether Scott can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yung","Sherry","Scott","Socorro"],"index":15899,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992726445,"difficulty":0.0007273555}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sam knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Sam can now know that Ida's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Ida","Sam","George"],"index":35248,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982066154,"difficulty":0.0017933846}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lori's card is shown to Lyle. Lyle's card is shown to Ted. Lori's card is shown to Ted. It is publicly announced that someone picked a red card. It is publicly announced that Ted knows whether Lyle 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) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ted can now know whether Lyle can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lyle","Ted","Lori"],"index":112,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993149042,"difficulty":0.0006850958}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edith knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows 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":"Edith can now know whether Brian can know that Edith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edith","Brian"],"index":15214,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968488812,"difficulty":0.0031511188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (1|2|3|4) ] (Agentc knows whether (1&2&3&4))","n_announcements":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":"Ann can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Francesco","Ann","Alba"],"index":21381,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9706121683,"difficulty":0.0293878317}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Larry's card is shown to John. George's card is shown to John. Larry's card is shown to George. George's card is shown to George. It is publicly announced that someone picked a red card. It is publicly announced that Larry picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"John can now know that Larry can know that John picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Larry","John","George"],"index":36090,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9283643961,"difficulty":0.0716356039}
+{"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 Regina. Regina's card is shown to Regina. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Regina can now know whether David can know that David picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Regina"],"index":39663,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9350215197,"difficulty":0.0649784803}
+{"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. Dominick's card is shown to Michael. Michael's card is shown to Dominick. Michael's card is shown to Nora. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 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:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dominick can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Dominick","Nora","Delores"],"index":45055,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993989468,"difficulty":0.0006010532}
+{"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 Joyce. Joyce's card is shown to Joyce. Charles's card is shown to George. Joyce's card is shown to George. George's card is shown to Anna. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Anna can now know whether George picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Joyce","George","Anna"],"index":4218,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8792080879,"difficulty":0.1207919121}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janice's forehead 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 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":"Susan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Janice","Daniel","Susan"],"index":58194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995126724,"difficulty":0.0004873276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvester does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know whether Lance can know that Sylvester is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sylvester","Brian","Lance","Richard"],"index":14982,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9902448654,"difficulty":0.0097551346}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sonya's card is shown to Cathy. Cathy's card is shown to Judy. Cathy's card is shown to Sonya. 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 whether (Agentb knows whether (1|2|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":"Sonya can now know whether Judy can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cathy","Judy","Sonya"],"index":37521,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993821383,"difficulty":0.0006178617}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michael does not know whether Myra is thirsty.","smcdel_problem":"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)","n_announcements":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":"Myra can now know whether Victoria is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Marlo","Myra","Victoria"],"index":47073,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980565906,"difficulty":0.0019434094}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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 (1&2&3))","n_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":"Edward can now know that Bessie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Bessie","Edward"],"index":22216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928200841,"difficulty":0.0071799159}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"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":"Scott can now know whether Dina's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dina","Scott","Bruce"],"index":22693,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993932247,"difficulty":0.0006067753}
+{"premise":"There are four persons. Everyone is visible 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 Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Sarah can now know that George can know that Lisa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sarah","George","Jesse","Lisa"],"index":16789,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978747368,"difficulty":0.0021252632}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Thu's card is shown to Thu. Robert's card is shown to Thu. Ronald's card is shown to Thu. Thu's card is shown to Calvin. Robert's card is shown to Calvin. Ronald's card is shown to Robert. Thu's card is shown to Ronald. Robert'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:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentc knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that Robert can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thu","Calvin","Robert","Ronald"],"index":34976,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993773103,"difficulty":0.0006226897}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Chester","Brandy","Valeria"],"index":36264,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994594455,"difficulty":0.0005405545}
+{"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 Kyle is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(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) ] [ ! (~(1&2)) ] [ ! ~(1) ] 0","hypothesis":"John can now know whether Kyle is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Kyle","John"],"index":45456,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9949476719,"difficulty":0.0050523281}
+{"premise":"There are four persons. Everyone is visible 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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Sara can now know that Carie can know that Sara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Herman","Sara","Carie"],"index":61353,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975063205,"difficulty":0.0024936795}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether or not everyone is thirsty. It is publicly announced that Larry does not know whether Kenneth is thirsty. It is publicly announced that Marc does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marc can now know that Kenneth is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marc","Larry","Eddie","Kenneth"],"index":37819,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9905762672,"difficulty":0.0094237328}
+{"premise":"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 3)","n_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":"Nellie can now know whether Erma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nellie","Sharon","Erma"],"index":2602,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986225367,"difficulty":0.0013774633}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jamie is not thirsty. It is publicly announced that Deanna knows whether or not everyone is thirsty. It is publicly announced that Rosalba is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 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) ] [ ! ~(2) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Rosalba can now know that Deanna can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deanna","Jamie","Rosalba"],"index":28903,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999486804,"difficulty":0.000513196}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Charley's card is shown to Charley. Charley's card is shown to Gloria. Samantha's card is shown to Gloria. It is publicly announced that someone picked a red card. It is publicly announced that Charley does not know whether Cathy picked a red card. It is publicly announced that Charley does not know whether Gloria picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Gloria can now know that Charley can know whether Cathy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charley","Gloria","Cathy","Samantha"],"index":22105,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9917460084,"difficulty":0.0082539916}
+{"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 Dora 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Patricia can now know whether Thomas is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Patricia","Dora"],"index":928,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.969891727,"difficulty":0.030108273}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anna knows whether Christy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows that (Agenta knows 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":"Jean can now know that Diana can know that Anna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Diana","Anna","Christy","Jean"],"index":856,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998239398,"difficulty":0.001760602}
+{"premise":"There are three persons. Everyone is visible 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 John knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (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":["Robert","John","Annie"],"index":29158,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988987446,"difficulty":0.0011012554}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Eric's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Eric can now know whether Thelma can know that Eric's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Thelma"],"index":25342,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Sylvia is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agenta knows 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) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jesse can now know whether Lydia can know whether Sylvia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jesse","Gregory","Sylvia","Lydia"],"index":47902,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989497066,"difficulty":0.0010502934}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (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":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Glenn","Jeffery"],"index":63180,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998559773,"difficulty":0.001440227}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cleveland knows whether Merry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Merry can now know whether Manuel can know that Merry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Merry","Alyssa","Manuel","Cleveland"],"index":52619,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994279742,"difficulty":0.0005720258}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert is thirsty. It is publicly announced that Kate knows whether Kate is 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 whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Sandra can now know whether Kate is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kate","Gloria","Sandra","Robert"],"index":18448,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9945061803,"difficulty":1.9945061803}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows that 1)","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":"Ira can now know that Kimberly can know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Kimberly","Ira"],"index":1247,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996080339,"difficulty":0.003919661}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Dean. James's card is shown to Ebony. Dean's card is shown to James. Josephine's card is shown to James. James's card is shown to Josephine. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:1,4 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:3 Agentc:1,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ebony can now know whether Dean picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dean","Ebony","James","Josephine"],"index":20127,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.926068604,"difficulty":0.073931396}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brad is thirsty. It is publicly announced that Brad knows whether Brad is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brad","Robert"],"index":45705,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9972986579,"difficulty":0.0027013421}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Krystal's card is shown to Krystal. Jan's card is shown to Jan. Veronica's card is shown to Veronica. It is publicly announced that someone picked a red card. It is publicly announced that Veronica does not know whether Krystal picked a red card. It is publicly announced that Jan picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 1)","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":"Veronica can now know that Krystal can know that Krystal picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Krystal","Jan","Veronica","Jonathan"],"index":64598,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9457263947,"difficulty":0.0542736053}
+{"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 Marvis is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] Agenta knows whether (Agentc knows whether 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":"Joseph can now know whether Marvis can know whether Bernadette is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Bernadette","Marvis"],"index":33326,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998788178,"difficulty":0.001211822}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). William's card is shown to William. Sheila's card is shown to Sheila. It is publicly announced that someone picked a red card. It is publicly announced that Sheila knows whether Sheila picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"William can now know that Sheila can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Sheila"],"index":44902,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994200468,"difficulty":0.0005799532}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lupe's forehead is not 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) ] [ ! ~(2) ] [ ! ~(4) ] Agenta knows whether (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) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Frances can now know whether Lupe can know whether Frances's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frances","Lupe","Michael","Scott"],"index":14194,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994543195,"difficulty":0.0005456805}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc 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) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Barbara can now know that Neil's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Neil","John"],"index":41104,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980738163,"difficulty":0.0019261837}
+{"premise":"There are four 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 or not everyone's forehead is muddy. It is publicly announced that Earl knows whether Nancy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Nancy can now know whether Raymond can know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Raymond","Willie","Nancy"],"index":45035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9857031703,"difficulty":0.0142968297}
+{"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 (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Mary can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mirna","Elisha","Mary","Jennifer"],"index":32148,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994474053,"difficulty":0.0005525947}
+{"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. Olive's card is shown to Roy. Olive's card is shown to Olive. Roy's card is shown to Angel. Olive's card is shown to Angel. Angel's card is shown to Angel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Roy can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roy","Olive","Angel"],"index":56499,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994080067,"difficulty":0.0005919933}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Justin's card is shown to Harold. Harold's card is shown to Justin. Warren's card is shown to Justin. It is publicly announced that someone picked a red card. It is publicly announced that Warren knows whether Harold picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Warren can now know whether Warren picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Harold","Warren","Justin"],"index":716,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6377430558,"difficulty":0.3622569442}
+{"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 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":"Amy can now know that Julio is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Danielle","Julio","Amy"],"index":60755,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9980739355,"difficulty":0.0019260645}
+{"premise":"There are 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 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":"Joaquin can now know whether Antonio's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joaquin","John","Antonio"],"index":19159,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994087219,"difficulty":0.0005912781}
+{"premise":"There are three persons. Everyone is visible 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 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":"Michael can now know whether Dorothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Danelle","Dorothy"],"index":43659,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993129969,"difficulty":0.0006870031}
+{"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 Anita is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] 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) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Eric can now know whether John can know that Eric is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anita","John","Eric","Anne"],"index":38898,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9801887274,"difficulty":0.0198112726}
+{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that James knows whether Juan's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] Agentb knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(1) ] 0","hypothesis":"Juan can now know that James can know that Juan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Juan"],"index":16757,"s-l":"forehead_mirror-1","deberta_pred":0,"deberta_confidence":0.9907671809,"difficulty":1.9907671809}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Brandi can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Corina","John","Brandi"],"index":17542,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999461472,"difficulty":0.000538528}
+{"premise":"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 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":"Muriel can now know whether Nancy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Muriel","Nancy","Paul","Betty"],"index":52446,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990972281,"difficulty":0.0009027719}
+{"premise":"There are three persons. Everyone is visible 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 Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Edward can now know that Richie can know that Edward's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Edward","Richie"],"index":55227,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998046279,"difficulty":0.001953721}
+{"premise":"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 someone's forehead is muddy. It is publicly announced that Robert knows whether Alison's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta 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: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":"Alison can now know whether Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Sylvester","Alison"],"index":28052,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9745853543,"difficulty":0.0254146457}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Naomi's card is shown to Jesse. Tim's card is shown to Tim. Jesse's card is shown to Naomi. Naomi's card is shown to Naomi. It is publicly announced that someone picked a red card. It is publicly announced that Naomi knows whether Jesse picked a red card. It is publicly announced that Tim does not know whether Jesse picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jesse can now know that Tim picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jesse","Tim","Naomi"],"index":25640,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9868856668,"difficulty":0.0131143332}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Livia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows 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":"Tom can now know that Steven can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Livia","Tom","Steven"],"index":34419,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983585477,"difficulty":0.0016414523}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether Kevin is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Richard can now know whether Kevin can know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Richard"],"index":36490,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.998989284,"difficulty":0.001010716}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Douglas does not know whether Thomas is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Michele knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Michele can now know that Douglas can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Thomas","Douglas","Michele"],"index":38967,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998881042,"difficulty":0.001118958}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tracy knows whether or not nobody is thirsty. It is publicly announced that Steven does not know whether or not everyone is thirsty. It is publicly announced that Sandra knows whether Sandra is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (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":"Steven can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Steven","Sandra"],"index":66297,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9621032476,"difficulty":0.0378967524}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows 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":"Warren can now know that Derrick can know that Warren's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Derrick","Brian","Lillian","Warren"],"index":12606,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984971285,"difficulty":0.0015028715}
+{"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. Gregory's card is shown to Debbie. Gail's card is shown to Gregory. Debbie's card is shown to Gail. It is publicly announced that someone picked a red card. It is publicly announced that Gail does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gail can now know whether Gregory can know that Gail picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Debbie","Gregory","Gail"],"index":18713,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.758664012,"difficulty":1.758664012}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony knows whether or not nobody is thirsty. It is publicly announced that Cynthia does not know whether Anthony is thirsty. It is publicly announced that Bradley does not know whether Cynthia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Anthony can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Cynthia","Anthony","Bradley"],"index":3514,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993085861,"difficulty":0.0006914139}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ivy knows whether 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) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Stanley can now know that Ivy can know whether Ivy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ivy","Stanley","Greg"],"index":67086,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994015694,"difficulty":0.0005984306}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Traci does not know whether or not everyone is thirsty. It is publicly announced that Traci does not know whether April is thirsty. It is publicly announced that April knows whether or not everyone is thirsty. It is publicly announced that Traci does not know whether April is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"April can now know that April is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["April","Traci"],"index":56446,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8925008178,"difficulty":0.1074991822}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma 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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta: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":"Kim can now know whether Michelle can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kim","Michelle","Thelma"],"index":48486,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994274378,"difficulty":0.0005725622}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] (Agenta knows that (1&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":"Angela can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Sal","Donald"],"index":20832,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989375472,"difficulty":0.0010624528}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Mark can now know that Carl can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mark","Willie","Carl"],"index":26807,"s-l":"forehead-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. 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 that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Hollis can now know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Hollis"],"index":20033,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9885411263,"difficulty":0.0114588737}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Victor can now know that Reginald can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Victor","Ester","Reginald","David"],"index":31311,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992524981,"difficulty":0.0007475019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Consuelo knows whether Consuelo's forehead is muddy. It is publicly announced that Consuelo knows whether Consuelo's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Karen can now know whether Consuelo can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Khalilah","Christopher","Consuelo","Karen"],"index":4504,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
+{"premise":"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 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) ] [ ! (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":"Laurie can now know that Franklin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Franklin","William","Laurie"],"index":53426,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9957244396,"difficulty":0.0042755604}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows 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":"Ronnie can now know that Joan can know that Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maribel","Joan","Ronnie","Steven"],"index":3778,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996096909,"difficulty":0.003903091}
+{"premise":"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 knows whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that John can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Margaret","John","Jose"],"index":12192,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859461188,"difficulty":0.0140538812}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carlo's card is shown to Charles. Charles's card is shown to Carlo. Carlo's card is shown to Carlo. Joe's card is shown to Carlo. Carlo's card is shown to Dollie. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,2,4 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows that 2)","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":"Carlo can now know that Carlo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Carlo","Dollie","Joe"],"index":25771,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9809298515,"difficulty":0.0190701485}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that George can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michelle","George","John","Richard"],"index":5342,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989106655,"difficulty":0.0010893345}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rhonda's card is shown to Billy. Rhonda's card is shown to Rhonda. It is publicly announced that someone picked a red card. It is publicly announced that Billy knows whether or not everyone picked a red card. It is publicly announced that Rhonda knows whether someone picked a red card. It is publicly announced that not everyone picked a red card. It is publicly announced that Billy knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (~(1&2)) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Rhonda can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Billy","Rhonda"],"index":61420,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994213581,"difficulty":0.0005786419}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether or not everyone's forehead is muddy. It is publicly announced that Michael knows whether Brandon's forehead is muddy. It is publicly announced that Michael knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Brandon can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Brandon"],"index":26543,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993721843,"difficulty":0.0006278157}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Edgar can now know that Elizabeth can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Debby","Edgar","Elizabeth"],"index":8390,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993770719,"difficulty":0.0006229281}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deanna 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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that Reinaldo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Deanna","Mary","Reinaldo"],"index":60288,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9975639582,"difficulty":0.0024360418}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tara knows whether Tara's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Margaret can now know that Tara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tara","Margaret","Richard","Lynda"],"index":8406,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.995773375,"difficulty":0.004226625}
+{"premise":"There are four persons. Everyone is visible 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 Maude's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentb knows that (Agentc knows whether 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) ] [ ! 3 ] 0","hypothesis":"Gonzalo can now know that Maude can know whether Maude's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leann","Gonzalo","Maude","Joshua"],"index":24407,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994671941,"difficulty":0.0005328059}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Allyson's card is shown to Allyson. Jeffery's card is shown to Allyson. Laura's card is shown to Allen. Allen's card is shown to Jeffery. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc: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:1,4 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Allyson can now know whether Laura can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allyson","Laura","Allen","Jeffery"],"index":6306,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993748069,"difficulty":0.0006251931}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows that (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":"Anderson can now know that Edgar can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lupe","Edgar","Mark","Anderson"],"index":54472,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994667172,"difficulty":0.0005332828}
+{"premise":"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 Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glenda can now know that Paul can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Paul","Glenda","Debra"],"index":67141,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997744441,"difficulty":0.002255559}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy. It is publicly announced that Maribel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agenta knows that (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":"Linda can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Mac","Maribel","Rachel"],"index":14045,"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. 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 Carol is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"James can now know that Lauren can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Lauren","Carol"],"index":21958,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994592071,"difficulty":0.0005407929}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (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":"Doris can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Janet","Doris"],"index":43779,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986513257,"difficulty":0.0013486743}
+{"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 (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":"Hector can now know that Misty can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Hector","Rhonda","Misty"],"index":67560,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9987754226,"difficulty":0.0012245774}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"George can now know whether Jeremy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeremy","Sandra","George","Thomas"],"index":17574,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993801117,"difficulty":0.0006198883}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Violet's card is shown to Latonia. Latonia's card is shown to Latonia. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Andrea can now know whether Lonnie can know that Lonnie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Andrea","Lonnie","Violet","Latonia"],"index":12363,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9957336783,"difficulty":1.9957336783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca does not know whether Fred is thirsty. It is publicly announced that Fred is thirsty. It is publicly announced that Fred 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))) ] 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 2) ] [ ! 2 ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Fred can now know that Rebecca can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rebecca","Fred","Susan"],"index":14917,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995030165,"difficulty":0.0004969835}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sylvia's card is shown to Sylvia. Amber's card is shown to Sylvia. Sylvia's card is shown to Peter. Sylvia's card is shown to Amber. Peter's card is shown to Amber. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia does not know whether Peter picked a red card. It is publicly announced that Peter knows whether or not everyone picked a red card. It is publicly announced that Amber 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)) ] Agentc knows that (Agentb 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":"Amber can now know that Peter can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sylvia","Peter","Amber"],"index":28745,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994283319,"difficulty":0.0005716681}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Sharon can now know whether Janice can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janice","Sharon"],"index":40552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9875692725,"difficulty":0.0124307275}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy. It is publicly announced that Gregory's forehead is muddy. It is publicly announced that Sandra 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)) ] 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) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Gregory can now know that Sandra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Doris","Sandra","Gregory"],"index":29090,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990463853,"difficulty":0.0009536147}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Juanita's card is shown to Daryl. Daryl's card is shown to Juanita. Juanita's card is shown to Juanita. It is publicly announced that someone picked a red card. It is publicly announced that Daryl picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Daryl can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Daryl","Juanita"],"index":54189,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980159998,"difficulty":0.0019840002}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Vonda does not know whether 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) ] 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":"Vonda can now know whether Mack can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lisa","Vonda","Mack","Shirley"],"index":32373,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964834452,"difficulty":0.0035165548}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Velma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows that (Agenta knows that (1&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":"Velma can now know that Karen can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Karen","Velma"],"index":26113,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989244342,"difficulty":0.0010755658}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Danny knows whether or not nobody is thirsty.","smcdel_problem":"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 (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Faye can now know that James can know whether Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Faye","Jennifer","James","Danny"],"index":5476,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983748198,"difficulty":0.0016251802}
+{"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 Stacy. Donald's card is shown to Stacy. Charles's card is shown to Daniel. Donald's card is shown to Donald. It is publicly announced that someone picked a red card. It is publicly announced that Charles picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Stacy can now know that Donald can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Stacy","Daniel","Donald","Charles"],"index":7388,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6831745505,"difficulty":0.3168254495}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Johnny's card is shown to Johnny. Louise's card is shown to Johnny. Andrew's card is shown to Johnny. Johnny's card is shown to Louise. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows whether 1)","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":"Andrew can now know that Louise can know whether Johnny picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Johnny","Louise","Andrew"],"index":63249,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5245844722,"difficulty":0.4754155278}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Mark can now know that Michael can know that Clyde's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clyde","Harvey","Michael","Mark"],"index":50665,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9925588369,"difficulty":0.0074411631}
+{"premise":"There are four persons. Everyone is visible 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 Cathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"David can now know whether Kerry can know that Kerry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kerry","Terry","David","Cathy"],"index":60340,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992483258,"difficulty":0.0007516742}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Warner can now know that Richard can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Warner","Richard","Margaret"],"index":43299,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989153147,"difficulty":0.0010846853}
+{"premise":"There are four persons. Everyone is visible 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 Nancy knows whether 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) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Bradley can now know that Robert can know that Kathryn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bradley","Kathryn","Nancy","Robert"],"index":37673,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9869454503,"difficulty":0.0130545497}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patsy does not know whether Patsy's forehead is muddy. It is publicly announced that Frank knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Kirk can now know whether Patsy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patsy","Kirk","Frank","Julius"],"index":65913,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990727901,"difficulty":0.0009272099}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jason can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jason","Kathleen"],"index":62838,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991390705,"difficulty":0.0008609295}
+{"premise":"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. It is publicly announced that Tina knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tina can now know that Cassandra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Aaron","Tina","Cassandra"],"index":66194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.811308682,"difficulty":0.188691318}
+{"premise":"There are four persons. Everyone is visible 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 Gregory's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (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) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mildred can now know whether Susan can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Susan","David","Mildred"],"index":42589,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993739724,"difficulty":0.0006260276}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amanda does not know whether Willie is thirsty. It is publicly announced that Willie knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Willie can now know whether Quinton is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Quinton","Roxanna","Willie","Amanda"],"index":16026,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982104301,"difficulty":0.0017895699}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 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":"Matthew can now know whether Samantha can know whether Lorenzo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lorenzo","Samantha","Matthew"],"index":2246,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999396801,"difficulty":0.000603199}
+{"premise":"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 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)) ] (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) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ray can now know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ray","Michael","John"],"index":12147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9517096877,"difficulty":0.0482903123}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Deja. Deja's card is shown to Barbara. Barbara's card is shown to Barbara. Matthew's card is shown to Barbara. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 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:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deja can now know whether Barbara picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deja","Barbara","Matthew"],"index":61951,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8585796356,"difficulty":0.1414203644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jose can now know whether Jennifer can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jose","John","Jennifer"],"index":26935,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9738767147,"difficulty":0.0261232853}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Katherine knows whether 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) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lindsay can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Katherine","Lindsay","Melissa"],"index":22340,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9955080748,"difficulty":0.0044919252}
+{"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 James. Dorothy's card is shown to James. Ronald's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carole can now know that Dorothy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Carole","Ronald","Dorothy"],"index":67345,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976698756,"difficulty":0.0023301244}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laurie's card is shown to Pamela. Pamela's card is shown to Laurie. It is publicly announced that someone picked a red card. It is publicly announced that Laurie 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 that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Laurie can now know that Pamela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pamela","Laurie"],"index":26337,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9945376515,"difficulty":0.0054623485}
+{"premise":"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 knows whether or not nobody's forehead is muddy. It is publicly announced that Louise does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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&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":"Robert can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["George","Robert","Louise"],"index":7731,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974628687,"difficulty":0.0025371313}
+{"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. Jerry's card is shown to Jerry. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Lisa can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lisa","Jerry"],"index":26545,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9950107336,"difficulty":0.0049892664}
+{"premise":"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's forehead is muddy. It is publicly announced that Gordon knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Gordon can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Gordon","George"],"index":40848,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7976820469,"difficulty":0.2023179531}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Herbert knows whether Cindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Cindy can now know that Adrian can know whether Cindy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herbert","Cindy","Adrian"],"index":6676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998581171,"difficulty":0.001418829}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marcia does not know whether Julee is thirsty. It is publicly announced that Julee 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 3) ] [ ! ~(Agentc knows whether 1) ] Agentd knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Marcia can now know whether Ceola can know that Joseph is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Ceola","Julee","Marcia"],"index":53665,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9880248904,"difficulty":0.0119751096}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheri knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Vicki can now know that Cheri can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vicki","Cheri"],"index":42539,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993274212,"difficulty":0.0006725788}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"David can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Lois","Robert","David"],"index":45593,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991519451,"difficulty":0.0008480549}
+{"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 Virgil. Frederick's card is shown to Frederick. Philip's card is shown to John. Philip's card is shown to Philip. It is publicly announced that someone picked a red card. It is publicly announced that Philip does not know whether Frederick picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:4 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Virgil can now know whether Frederick picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Virgil","Frederick","John","Philip"],"index":36974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9465634227,"difficulty":0.0534365773}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tisha's forehead is not muddy. It is publicly announced that Thelma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Cynthia can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Thelma","Tisha","Cynthia"],"index":39247,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989004135,"difficulty":0.0010995865}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessie can now know that Myrna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jessie","Paul","Myrna","Timothy"],"index":11720,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988403916,"difficulty":0.0011596084}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Jon can now know that Mary can know that Carolyn is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Hugh","Carolyn","Mary","Jon"],"index":36294,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9864441752,"difficulty":0.0135558248}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rebecca is not thirsty. It is publicly announced that Russell is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] Agentd knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! 4 ] 0","hypothesis":"Russell can now know whether Gloria can know that Gloria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Billy","Gloria","Rebecca","Russell"],"index":5549,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7543139458,"difficulty":0.2456860542}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edward is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows that (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Edward can now know that Sara can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wendy","Sara","Barbara","Edward"],"index":63118,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999527812,"difficulty":0.000472188}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dallas does not know whether Dallas's forehead is muddy. It is publicly announced that Donald knows whether Dallas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether 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: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 4) ] 0","hypothesis":"Douglas can now know whether Dallas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Douglas","Kyle","Dallas"],"index":3553,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.970345974,"difficulty":0.029654026}
+{"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 Raymond is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether (1&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":"Scotty can now know whether Richard can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Scotty","Raymond","Richard"],"index":47651,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9425688386,"difficulty":0.0574311614}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joe does not know whether or not everyone is thirsty. It is publicly announced that Jose does not know 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] (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 2) ] 0","hypothesis":"Roy can now know that Alexandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexandra","Roy","Joe","Jose"],"index":5714,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.983248353,"difficulty":0.016751647}
+{"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 George. Donald's card is shown to Donald. Patricia's card is shown to Donald. George's card is shown to Patricia. Patricia's card is shown to Patricia. Jimmy's card is shown to Patricia. George's card is shown to Jimmy. Patricia's card is shown to Jimmy. Jimmy's card is shown to Jimmy. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether Donald picked a red card. It is publicly announced that Patricia knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc 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:3 Agentb:2,3 Agentc:1,3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jimmy can now know that George can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Donald","Patricia","Jimmy"],"index":12338,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990586638,"difficulty":0.0009413362}
+{"premise":"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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Richard can know whether Everett's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dan","Richard","Everett","Robert"],"index":37683,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988480806,"difficulty":0.0011519194}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Damien knows whether someone's forehead is muddy. It is publicly announced that Eva knows whether Damien's forehead is muddy. It is publicly announced that Maryjane does not know whether Maryjane's forehead is muddy.","smcdel_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 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":"Damien can now know that Maryjane can know whether Eva's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eva","Maryjane","Damien"],"index":5038,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992216825,"difficulty":0.0007783175}
+{"premise":"There are three persons. Everyone is visible 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 Alma's forehead is muddy. It is publicly announced that Kerry knows whether or not nobody's forehead is muddy. It is publicly announced that Alma knows whether Kerry's forehead is muddy.","smcdel_problem":"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":"Chong can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Chong","Kerry","Alma"],"index":41835,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994542003,"difficulty":0.0005457997}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Mason can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Mason","Frank"],"index":44955,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989191294,"difficulty":0.0010808706}
+{"premise":"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 Marjorie knows whether or not nobody's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! 2 ] 0","hypothesis":"Richard can now know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marjorie","Christopher","Richard"],"index":40066,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9881928563,"difficulty":0.0118071437}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rick's card is shown to Michael. Larry's card is shown to Larry. Rick's card is shown to Larry. Michael's card is shown to Rick. Larry's card is shown to Rick. Rick's card is shown to Rick. Larry'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:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rick can now know whether Larry can know whether Rick picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Larry","Rick","Randy"],"index":37257,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984313846,"difficulty":0.0015686154}
+{"premise":"There are two 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 Maureen's forehead is muddy. It is publicly announced that Maureen does not know whether Maureen's forehead is muddy. It is publicly announced that Philip knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Philip can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maureen","Philip"],"index":33616,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990051389,"difficulty":0.0009948611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley is not thirsty. It is publicly announced that Shirley does not know whether Louis is thirsty. It is publicly announced that Donald knows 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) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Andrew can now know whether Donald can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Louis","Donald","Andrew"],"index":51944,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994699359,"difficulty":0.0005300641}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Corine's card is shown to Corine. Donald's card is shown to Donald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] (Agentb knows whether (~(1|2)))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] 0","hypothesis":"Donald can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Corine","Donald"],"index":66840,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993732572,"difficulty":0.0006267428}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Olga's card is shown to Sandra. Gail's card is shown to Sandra. George's card is shown to George. Sandra's card is shown to Gail. Olga's card is shown to Gail. It is publicly announced that someone picked a red card. It is publicly announced that George picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:2 Agentc:1,3 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:2 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"George can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sandra","George","Olga","Gail"],"index":54801,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994242191,"difficulty":0.0005757809}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Scott's card is shown to Scott. Scott's card is shown to John. It is publicly announced that someone picked a red card. It is publicly announced that Scott knows whether 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 VALID? [ ! (1|2) ] [ ! (Agenta 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:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"John can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Scott","John"],"index":51896,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rene's card is shown to Anna. Rene's card is shown to Clint. Robert's card is shown to Clint. Anna's card is shown to Rene. It is publicly announced that someone picked a red card. It is publicly announced that Anna knows whether someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Clint can now know whether Rene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Anna","Clint","Rene","Robert"],"index":38540,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.6265354753,"difficulty":1.6265354753}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Rosa can now know that Cynthia can know that Loretta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rosa","Loretta","Cynthia","Arlene"],"index":9908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976249337,"difficulty":0.0023750663}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Robert can now know whether Gerry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ryan","Gerry","Pamela","Robert"],"index":65366,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990538955,"difficulty":0.0009461045}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony knows whether someone is thirsty. It is publicly announced that Helen does not know whether Danielle is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Danielle can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Helen","Anthony","Danielle"],"index":2522,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994149208,"difficulty":0.0005850792}
+{"premise":"There are three persons. Everyone is visible 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 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows whether 1)","n_announcements":1,"pbcheck":"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":"Gail can now know whether Darin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Darin","Joan","Gail"],"index":3234,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999401927,"difficulty":0.000598073}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows that (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":"Ed can now know whether James can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ray","Ed","Linda","James"],"index":58582,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994102716,"difficulty":0.0005897284}
+{"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 Corine does not know whether Katie is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (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":"Corine can now know that Katie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Katie","Corine"],"index":57811,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9956547022,"difficulty":1.9956547022}
+{"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 John. Amanda's card is shown to Douglas. John's card is shown to Amanda. Amanda's card is shown to Amanda. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Douglas","Amanda","Kum"],"index":42290,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989301562,"difficulty":0.0010698438}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Jose can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jose","Bobby","Michael","Julia"],"index":51098,"s-l":"forehead-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'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":"Barbara can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Stephanie","Nicholas"],"index":44471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992419481,"difficulty":0.0007580519}
+{"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. Elva's card is shown to Elva. Diane's card is shown to Diane. It is publicly announced that someone picked a red card. It is publicly announced that Diane does not know whether Jonathan picked a red card. It is publicly announced that Jonathan does not know whether Elva picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Jonathan can now know whether Jonathan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jonathan","Elva","Diane"],"index":21438,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8269267678,"difficulty":0.1730732322}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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":"Gayle can now know that Velma can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","Velma","Gayle"],"index":63038,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993342757,"difficulty":0.0006657243}
+{"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. Jane's card is shown to Calvin. Jane's card is shown to Amy. Calvin's card is shown to Amy. It is publicly announced that someone picked a red card. It is publicly announced that Jane 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 whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jane can now know whether Calvin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jane","Calvin","Amy"],"index":42850,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7167154551,"difficulty":0.2832845449}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosa's card is shown to Rosa. Valerie's card is shown to Coletta. Rosa's card is shown to Coletta. It is publicly announced that someone picked a red card. It is publicly announced that Valerie knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Valerie can now know that Rosa can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Valerie","Rosa","Coletta"],"index":32252,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.5146698356,"difficulty":0.4853301644}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Timothy does not know whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Kristina can now know whether Angela can know whether Kristina is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Kristina","Timothy"],"index":27044,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9987412095,"difficulty":0.0012587905}
+{"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 Troy. Richard's card is shown to Richard. Wayne's card is shown to Richard. Wayne's card is shown to Wayne. Richard's card is shown to Thomas. Wayne's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Troy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Troy can now know whether Thomas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Troy","Richard","Wayne","Thomas"],"index":30240,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9008330703,"difficulty":0.0991669297}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Carolyn can now know that Emily can know that Stephanie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emily","Carolyn","Stephanie","Erin"],"index":50656,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9968241453,"difficulty":0.0031758547}
+{"premise":"There are three persons. Everyone is visible 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 Lois's forehead is muddy. It is publicly announced that Marisa'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 (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! 3 ] [ ! (1&2&3) ] 0","hypothesis":"Marisa can now know that Stephanie can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephanie","Lois","Marisa"],"index":17651,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9703869224,"difficulty":0.0296130776}
+{"premise":"There are 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 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":"Gabriella can now know whether David can know whether David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","David","Gabriella","Paul"],"index":41233,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999399066,"difficulty":0.000600934}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Frankie can now know whether Brenda can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Frankie","Brenda"],"index":27038,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999153614,"difficulty":0.000846386}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawerence's card is shown to Delmar. Dawn's card is shown to Darrell. Lawerence's card is shown to Dawn. Dawn'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:2 Agentb:4 Agentc:2,4 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:4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Delmar can now know that Delmar picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Delmar","Lawerence","Darrell","Dawn"],"index":11135,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9939597845,"difficulty":0.0060402155}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Larry can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Jaime","James"],"index":67471,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991931319,"difficulty":0.0008068681}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Larry's card is shown to Larry. Gail's card is shown to Brenda. Brenda's card is shown to Gail. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Brenda can now know that Larry picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Larry","Brenda","Gail"],"index":16694,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9980576634,"difficulty":0.0019423366}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marlys's card is shown to Marlys. Lori's card is shown to Irene. Irene's card is shown to Lori. It is publicly announced that someone picked a red card. It is publicly announced that Sylvia does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 1)","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":"Sylvia can now know that Marlys picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marlys","Sylvia","Irene","Lori"],"index":36930,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9171848297,"difficulty":0.0828151703}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leslie does not know whether Leslie's forehead is muddy. It is publicly announced that Leslie does not know whether Leslie'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 (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Leslie can now know whether Rodney can know whether Rodney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rodney","Leslie"],"index":12276,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9878424406,"difficulty":1.9878424406}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy.","smcdel_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)","n_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":"Denise can now know whether Denise's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Reed","Martha","Denise"],"index":13317,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930463433,"difficulty":0.0069536567}
+{"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 Gloria. Abby's card is shown to Gloria. Abby's card is shown to Abby. 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 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":"Kevin can now know that Abby picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Gloria","Reuben","Abby"],"index":53912,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929324389,"difficulty":0.0070675611}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brenda does not know whether Julieta is thirsty. It is publicly announced that Harold 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)","n_announcements":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":"Keri can now know that Brenda is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brenda","Keri","Harold","Julieta"],"index":28338,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9450406432,"difficulty":0.0549593568}
+{"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. Dorothy's card is shown to Glen. Glen's card is shown to Glen. Dorothy's card is shown to Sallie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Sallie can now know that Dorothy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Glen","Sallie"],"index":64583,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993646741,"difficulty":0.0006353259}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Whitney 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))","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":"Shawn can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marylou","Shawn","Whitney"],"index":8755,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.977796495,"difficulty":0.022203505}
+{"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 Holly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 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) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Jennifer can now know that Amy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Holly","Jennifer","Amy","Maria"],"index":65340,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982699156,"difficulty":0.0017300844}
+{"premise":"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 Sandra's forehead is muddy. It is publicly announced that Brian knows whether or not everyone's forehead is muddy. It is publicly announced that Duane does not know whether Duane's forehead is muddy.","smcdel_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 (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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Duane can now know whether Sandra can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sandra","Duane","Brian"],"index":15906,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993243217,"difficulty":0.0006756783}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether Francisco's forehead is muddy.","smcdel_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 3)","n_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":"Brandy can now know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francisco","Brandy","Brenda"],"index":9079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976274371,"difficulty":0.0023725629}
+{"premise":"There are four persons. Everyone is visible 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 Antonia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] Agentb knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! ~(4) ] 0","hypothesis":"Robert can now know that Chantel can know that Ronald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Chantel","Robert","Ronald","Antonia"],"index":63254,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9963311553,"difficulty":0.0036688447}
+{"premise":"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 knows whether Irene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows 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":"Irene can now know that Ester can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ester","Irene","Natalie","Thomas"],"index":14147,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990237951,"difficulty":0.0009762049}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether someone's forehead is muddy. It is publicly announced that Donna knows whether Donna's forehead is muddy. It is publicly announced that Pauline 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|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Donna","Kenneth","Pauline"],"index":57516,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992610812,"difficulty":0.0007389188}
+{"premise":"There are two persons. Everyone is visible 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 Jesus knows whether Jesus'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 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":"Jesus can now know whether Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jesus","Michael"],"index":64032,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.99923563,"difficulty":0.00076437}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia does not know whether Gary is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] Agentc knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"David can now know that Gary can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Virginia","David","Gary"],"index":13649,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999362886,"difficulty":0.000637114}
+{"premise":"There are two persons. Everyone is visible 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 Troy'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 whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Troy can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tina","Troy"],"index":12091,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992258549,"difficulty":0.0007741451}
+{"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 or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Takisha can now know whether Pedro can know whether Beverly is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beverly","Pedro","Jason","Takisha"],"index":3836,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992673993,"difficulty":0.0007326007}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Jackie can now know that Leopoldo can know whether Jeanette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eugene","Jackie","Leopoldo","Jeanette"],"index":62372,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993112087,"difficulty":0.0006887913}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lucille does not know whether Timothy is thirsty. It is publicly announced that Shannon knows whether or not nobody is thirsty. It is publicly announced that Timothy does not know whether Shannon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 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) ] [ ! ~(Agentc knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Shannon can now know that Timothy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Timothy","Shannon","Lucille"],"index":63615,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9955621958,"difficulty":0.0044378042}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Donna can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donna","Angela","Andrew","Barbara"],"index":33016,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9914426208,"difficulty":0.0085573792}
+{"premise":"There are four persons. Everyone is visible 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 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":"Justin can now know that Blanca can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vina","Justin","Ava","Blanca"],"index":64673,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991565943,"difficulty":0.0008434057}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gerald is not thirsty.","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)","n_announcements":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":"Gerald can now know whether John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florence","Robert","John","Gerald"],"index":27776,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9949659705,"difficulty":0.0050340295}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Una 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 that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Una can now know that Jesus can know that Una is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jesus","Una"],"index":7254,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9345484972,"difficulty":0.0654515028}
+{"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 Phyllis. Phyllis's card is shown to James. James's card is shown to Ruben. Ruben's card is shown to Ruben. 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) ] Agentb knows whether (Agenta knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"James can now know whether Phyllis can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Phyllis","James","Ruben"],"index":9788,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9601935744,"difficulty":0.0398064256}
+{"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. Susan's card is shown to Derick. Mary's card is shown to Derick. 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 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 Agentb:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Susan can now know whether Mary can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Mary","Derick","Pamala"],"index":13744,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9992567897,"difficulty":0.0007432103}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Carylon's card is shown to Earl. Courtney's card is shown to Earl. Earl's card is shown to Carylon. Tammy's card is shown to Carylon. Earl's card is shown to Tammy. Carylon's card is shown to Tammy. Tammy's card is shown to Tammy. Earl's card is shown to Courtney. Courtney's card is shown to Courtney. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3 Agentc:1,2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3 Agentc:1,2,3 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carylon can now know that Courtney can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Earl","Carylon","Tammy","Courtney"],"index":58610,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993396401,"difficulty":0.0006603599}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Adell does not know whether Alex is thirsty. It is publicly announced that Antonio 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 that (Agentb knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Alex can now know that Antonio can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alex","Antonio","Robert","Adell"],"index":48291,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995043278,"difficulty":0.0004956722}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theodore's card is shown to Jessica. Jessica's card is shown to Wayne. Wayne's card is shown to Wayne. Wayne's card is shown to Theodore. Wayne's card is shown to Tammy. Theodore's card is shown to Tammy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,2 Agentc:2 Agentd:2,3 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:3 Agentb:1,2 Agentc:2 Agentd:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jessica can now know whether Tammy can know whether Tammy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Wayne","Theodore","Tammy"],"index":7203,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9797216654,"difficulty":0.0202783346}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ronald can now know that Melody can know that Melody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Ronald","Melody"],"index":46847,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977462888,"difficulty":0.0022537112}
+{"premise":"There are three persons. Everyone is visible 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 nobody's forehead is muddy. It is publicly announced that Bruce'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 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(3) ] 0","hypothesis":"Bruce can now know whether Karri's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jeffrey","Karri","Bruce"],"index":39927,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994562268,"difficulty":0.0005437732}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jada does not know whether Jada's forehead is muddy.","smcdel_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 that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jada can now know whether Morris can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andy","Jada","Morris"],"index":58199,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9562150836,"difficulty":0.0437849164}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Robert's forehead is muddy. It is publicly announced that Ronald knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ronald can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ronald","Robert"],"index":6283,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9802635312,"difficulty":0.0197364688}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Manuela does not know whether Luz is thirsty. It is publicly announced that Luz is not thirsty. It is publicly announced that Luz is not thirsty. It is publicly announced that Manuela knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(1) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows 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) ] [ ! ~(1) ] [ ! ~(1) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Manuela can now know whether Luz can know that Manuela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Luz","Manuela","Sheila"],"index":24532,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9812916517,"difficulty":0.0187083483}
+{"premise":"There are four persons. Everyone is visible 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 Minnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Kimberly can now know whether Minnie can know that Thomas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","John","Minnie","Thomas"],"index":29161,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994540811,"difficulty":0.0005459189}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"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":"Shanna can now know whether Donald can know whether Shanna's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roy","Donald","Shanna"],"index":42464,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993914366,"difficulty":0.0006085634}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"James can now know whether Judith can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Judith","James"],"index":5966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993788004,"difficulty":0.0006211996}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Max knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Max can now know that Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beverly","Max","Sarah","Clara"],"index":35143,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976738095,"difficulty":0.0023261905}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentd knows that (~(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":"William can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Bonnie","Jacklyn","William"],"index":21070,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9894970655,"difficulty":0.0105029345}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leon does not know whether Leon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jennifer can now know that Shannon can know whether Leon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leon","Shannon","Patricia","Jennifer"],"index":44186,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988431931,"difficulty":0.0011568069}
+{"premise":"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 Bernadette's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Charles can now know that Allene can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charles","Bernadette","Allene"],"index":36745,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993633628,"difficulty":0.0006366372}
+{"premise":"There are four persons. Everyone is visible 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 Carmen's forehead is muddy. It is publicly announced that Sean's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] [ ! ~(2) ] (Agenta knows that 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":"Ronald can now know that Carmen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Sean","Bobbie","Carmen"],"index":25349,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977155924,"difficulty":0.0022844076}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bessie does not know whether Larry is thirsty. It is publicly announced that Bessie does not know whether Leo is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] (Agentd knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Leo can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","Bessie","Paula","Leo"],"index":18004,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994214773,"difficulty":0.0005785227}
+{"premise":"There are four persons. Everyone is visible 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'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 (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":"Beth can now know whether Marcia can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Laura","Wayne","Beth","Marcia"],"index":40783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993157387,"difficulty":0.0006842613}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Karen. Teresa's card is shown to Susan. Karen's card is shown to Teresa. It is publicly announced that someone picked a red card. It is publicly announced that Karen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:1 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:3 Agentc:1 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Karen can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Susan","Teresa"],"index":24393,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994714856,"difficulty":0.0005285144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Theresa is thirsty. It is publicly announced that Donna 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)) ] (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 ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Christy can now know whether Rita is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Theresa","Donna","Christy","Rita"],"index":30744,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9891089201,"difficulty":0.0108910799}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kurt knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows that (Agenta knows 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":"Barry can now know that Luis can know that Kurt is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Luis","Kurt","Barry"],"index":20738,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979757667,"difficulty":0.0020242333}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry knows whether Barry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Barry can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Carolyn","Barry","Josie"],"index":63154,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987609386,"difficulty":0.0012390614}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adele's card is shown to Sharon. Jose's card is shown to Sharon. Adele's card is shown to Jose. Sharon's card is shown to Jose. Adele's card is shown to Ronald. Sharon's card is shown to Ronald. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Jose picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Sharon can now know that Adele can know whether Ronald picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Adele","Sharon","Jose","Ronald"],"index":56233,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9929032922,"difficulty":0.0070967078}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrew is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Lois can now know whether Morton is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lois","Andrew","Morton","William"],"index":14719,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9972557425,"difficulty":0.0027442575}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc 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) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Christina 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":["Shannon","Mary","Patricia","Christina"],"index":24999,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.58872962,"difficulty":0.41127038}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adam's card is shown to Adam. John's card is shown to John. John's card is shown to Francis. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc: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:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Francis can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Adam","John","Francis"],"index":47128,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990341663,"difficulty":0.0009658337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Stephen knows whether or not everyone is thirsty. It is publicly announced that William knows whether Anthony is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"William can now know that Stephen can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Anthony","Jamie","William"],"index":14342,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994756579,"difficulty":0.0005243421}
+{"premise":"There are three persons. Everyone is visible 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 Robbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 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":"Jean can now know that Jean's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Jean","Robbie"],"index":21674,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980390668,"difficulty":0.0019609332}
+{"premise":"There are two persons. Everyone is visible 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 Maria's forehead is not muddy. It is publicly announced that Rolando's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (~(1&2)) ] [ ! ~(2) ] [ ! 1 ] Agentb knows whether (Agenta knows that 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":"Maria can now know whether Rolando can know that Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rolando","Maria"],"index":56270,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993630052,"difficulty":0.0006369948}
+{"premise":"There are four persons. Everyone is visible 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 Susie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cathleen","Jimmy","Susie","Robert"],"index":5661,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990112782,"difficulty":0.0009887218}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agentc knows that 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":"Alberto can now know that Laronda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Laronda","Alberto"],"index":22297,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978208542,"difficulty":0.0021791458}
+{"premise":"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":"James can now know that Kimberly can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberly","James","Julie","Carol"],"index":33456,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9732993245,"difficulty":0.0267006755}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Cindy is thirsty. It is publicly announced that Katherine knows whether Katherine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agenta knows whether 1) ] (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) ] [ ! 4 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Marianne can now know whether Cindy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Katherine","William","Marianne","Cindy"],"index":63818,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.9703577757,"difficulty":1.9703577757}
+{"premise":"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 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":"Christopher can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mark","Christopher","John"],"index":49009,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988836646,"difficulty":0.0011163354}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geraldine does not know whether Geraldine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Danny can now know whether Geraldine can know whether Geraldine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Danny","Danielle","Geraldine"],"index":24125,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8782573342,"difficulty":1.8782573342}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nathan's card is shown to Elisabeth. Elisabeth's card is shown to Edmond. Elisabeth's card is shown to Angela. Elisabeth's card is shown to Nathan. Nathan's card is shown to Nathan. It is publicly announced that someone picked a red card. It is publicly announced that Elisabeth does not know whether Angela picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Elisabeth can now know that Edmond can know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elisabeth","Edmond","Angela","Nathan"],"index":32327,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9859899282,"difficulty":0.0140100718}
+{"premise":"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 Thelma's forehead is muddy. It is publicly announced that Gail does not know whether Gail's forehead is muddy. It is publicly announced that John knows whether Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agentb knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Gail can now know whether John can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thelma","John","Robert","Gail"],"index":10226,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994320273,"difficulty":0.0005679727}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vincent knows whether someone's forehead is muddy. It is publicly announced that Josef does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows 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 (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Vincent can now know that Josef can know whether Josef's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Josef","Vincent"],"index":42661,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5455007553,"difficulty":0.4544992447}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Ryan. Ryan's card is shown to 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:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Ryan can now know that Ryan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Ryan","John"],"index":15443,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9410187602,"difficulty":0.0589812398}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Chester can now know that Patricia can know that Chester's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Louise","Patricia","Chester"],"index":3989,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9944434762,"difficulty":0.0055565238}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea does not know whether Kevin is thirsty. It is publicly announced that Andrea knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta 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:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Kevin can now know whether Andrea can know whether Kevin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrea","Kevin"],"index":61180,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989383817,"difficulty":0.0010616183}
+{"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) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Richard can now know whether Robert can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Robert","Michael","Felicia"],"index":44088,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9956983328,"difficulty":0.0043016672}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leanne knows whether or not nobody's forehead is muddy. It is publicly announced that Leanne knows whether Leanne's forehead is muddy. It is publicly announced that Spencer's forehead is muddy. It is publicly announced that Gary knows whether Spencer's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! (Agentb knows whether 2) ] [ ! 1 ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Glen can now know whether Leanne can know whether Leanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Spencer","Leanne","Gary","Glen"],"index":49762,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999348104,"difficulty":0.000651896}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sarah's card is shown to Sarah. Erma's card is shown to Sarah. Luis's card is shown to Sarah. Sarah's card is shown to Erma. Norma's card is shown to Erma. Sarah's card is shown to Luis. Norma's card is shown to Norma. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:1 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Norma can now know whether Luis can know that Luis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sarah","Erma","Luis","Norma"],"index":26368,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9218853116,"difficulty":1.9218853116}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentc knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Blake can now know that Lucille can know whether Blake's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Aaron","Angela","Blake","Lucille"],"index":11812,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993284941,"difficulty":0.0006715059}
+{"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. It is publicly announced that Marco does not know whether Kimberly is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Kimberly can now know whether Jennifer can know whether Marco is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Kimberly","Marco","Mary"],"index":65511,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992526174,"difficulty":0.0007473826}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis knows whether 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 (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Lorena can now know whether Dennis can know whether Lorena's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Lorena"],"index":51400,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9941189289,"difficulty":0.0058810711}
+{"premise":"There are four persons. Everyone is visible 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 Gerald's forehead is muddy. It is publicly announced that James knows whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know that Teresa can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Gerald","Teresa","Harold"],"index":54567,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993645549,"difficulty":0.0006354451}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy. It is publicly announced that Francis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (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) ] 0","hypothesis":"Jennifer can now know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francis","Jennifer","Wilma"],"index":37158,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7682616115,"difficulty":0.2317383885}
+{"premise":"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 (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":"Anthony can now know whether Timothy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Cecil","Anthony","Timothy"],"index":46592,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992505908,"difficulty":0.0007494092}
+{"premise":"There are four persons. Everyone is visible 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'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 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Betty can now know that Carl's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Larry","Jessica","Carl"],"index":47205,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980064034,"difficulty":0.0019935966}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Susan's card is shown to Susan. Susan's card is shown to Marilyn. Marilyn's card is shown to Bridget. Bridget's card is shown to Lizzie. Lizzie's card is shown to Lizzie. 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|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2 Agentd:3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lizzie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Marilyn","Bridget","Lizzie"],"index":47267,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.998938024,"difficulty":0.001061976}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Shirley's card is shown to Marian. Tara's card is shown to Shirley. Tara's card is shown to Tara. It is publicly announced that someone picked a red card. It is publicly announced that Tara knows whether someone picked a red card. It is publicly announced that Shirley does not know whether Marian 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 whether (Agentc knows whether 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":"Shirley can now know whether Tara can know whether Marian picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marian","Shirley","Tara"],"index":48720,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9986692667,"difficulty":0.0013307333}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Patrick's card is shown to Patrick. Patrick's card is shown to Jerry. Patrick's card is shown to Shane. It is publicly announced that someone picked a red card. It is publicly announced that Patrick knows whether Patrick picked a red card. It is publicly announced that Patrick knows whether Patrick picked a red card. It is publicly announced that Patrick does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Shane can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Patrick","Jerry","Shane"],"index":14250,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
+{"premise":"There are four persons. Everyone is visible 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 Rodney knows whether or not nobody's forehead is muddy. It is publicly announced that Lee 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) ] [ ! (~(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":"Rodney can now know that Carolyn can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Rodney","Carolyn","Lee"],"index":50576,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993365407,"difficulty":0.0006634593}
+{"premise":"There are 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 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 Margret can know that Monica's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luis","Margret","Mabel","Monica"],"index":29548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9985578656,"difficulty":0.0014421344}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows 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":"Anthony can now know whether Vicente can know that Vicente's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Janet","Anthony","Vicente"],"index":57270,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5714560747,"difficulty":0.4285439253}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that Roosevelt's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(4) ] Agenta knows whether (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":"Yajaira can now know whether Chad can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Yajaira","Richard","Chad","Roosevelt"],"index":19163,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.841930151,"difficulty":0.158069849}
+{"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 Christa. Jeffrey's card is shown to Julia. Christa's card is shown to Michael. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeffrey can now know that Julia can know that Jeffrey picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeffrey","Christa","Julia","Michael"],"index":43006,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982523322,"difficulty":0.0017476678}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marc does not know whether Marc's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lloyd can now know that Lloyd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nicole","Marc","Lloyd","Don"],"index":9340,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9920592308,"difficulty":0.0079407692}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know that Nancy can know that Nancy is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lawrence","Herbert","William","Nancy"],"index":22325,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9944624305,"difficulty":0.0055375695}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna's forehead 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 (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Bennett can now know whether Grace can know that Bennett's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Grace","Donna","Bennett"],"index":21384,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9217781425,"difficulty":0.0782218575}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genevieve knows whether Carl's forehead is muddy.","smcdel_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 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":"Debra can now know whether Genevieve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carl","Genevieve","Debra"],"index":26976,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994267225,"difficulty":0.0005732775}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Norman's card is shown to Dale. Dale's card is shown to Warren. Norman's card is shown to Warren. Dale's card is shown to Norman. Norman's card is shown to Norman. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Warren can now know whether Norman can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dale","Warren","Norman"],"index":11087,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993890524,"difficulty":0.0006109476}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Dennis. Janet's card is shown to Janet. It is publicly announced that someone picked a red card. It is publicly announced that Charlotte does not know whether Carmen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb: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:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Charlotte can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dennis","Charlotte","Carmen","Janet"],"index":10415,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994609952,"difficulty":0.0005390048}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mattie's card is shown to Mattie. Micah's card is shown to Tracy. Mattie's card is shown to Tracy. Tracy's card is shown to Tracy. It is publicly announced that someone picked a red card. It is publicly announced that Micah does not know whether or not everyone picked a red card. It is publicly announced that Tracy picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! 3 ] 0","hypothesis":"Micah can now know whether Mattie can know that Mattie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Micah","Mattie","Tracy"],"index":57828,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9537810087,"difficulty":0.0462189913}
+{"premise":"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'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 (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Walter can now know that Edna can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","Edna"],"index":67059,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9180483222,"difficulty":0.0819516778}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Julius's card is shown to Gerald. Margaret's card is shown to Gerald. Gerald's card is shown to Julius. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mildred can now know that Margaret picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gerald","Mildred","Julius","Margaret"],"index":55708,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983469248,"difficulty":0.0016530752}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Esta does not know whether Ann is thirsty.","smcdel_problem":"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 (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Ann can now know whether Francis can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cathy","Francis","Esta","Ann"],"index":18850,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994387031,"difficulty":0.0005612969}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jeanne does not know whether Barry is thirsty. It is publicly announced that Barry does not know whether Carolyn is thirsty. It is publicly announced that Carolyn does not know whether Jeanne is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (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 4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Jeanne can now know that Nancy can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nancy","Jeanne","Carolyn","Barry"],"index":67443,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974024892,"difficulty":0.0025975108}
+{"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. Marie's card is shown to Robert. Robert'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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Marie can now know that Marie picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Robert","Marie"],"index":64716,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.95950526,"difficulty":0.04049474}
+{"premise":"There are four persons. Everyone is visible 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 not everyone's forehead is muddy. It is publicly announced that Phillip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! 3 ] (Agentd knows that 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":"Marlon can now know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shannon","Kimberly","Phillip","Marlon"],"index":36082,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9363723993,"difficulty":0.0636276007}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dale's card is shown to Dale. Kyle's card is shown to Kyle. Mary's card is shown to Mary. It is publicly announced that someone picked a red card. It is publicly announced that Mary does not know whether Dale 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Mary can now know that Dale can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dale","Kyle","Mary","Andrew"],"index":51046,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9745000005,"difficulty":0.0254999995}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth knows whether or not nobody's forehead is muddy. It is publicly announced that Ruth knows whether Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows 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) ] 0","hypothesis":"Ruth can now know that Joyce can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joyce","Ruth"],"index":25496,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.867560029,"difficulty":0.132439971}
+{"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 Leonard 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 (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Patricia can now know that Leonard can know whether Patricia is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leonard","Patricia","Mary"],"index":28509,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974919558,"difficulty":0.0025080442}
+{"premise":"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's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Therese's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW 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 ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Leslie can now know whether Tracy can know that Leslie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tracy","Leslie","Frederic","Therese"],"index":25843,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9234944582,"difficulty":0.0765055418}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tracy does not know whether Anna is thirsty. It is publicly announced that Tracy 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)","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":"Tracy can now know whether Tracy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Tracy","Anna"],"index":54975,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9965974689,"difficulty":0.0034025311}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy does not know whether Roy's forehead is muddy. It is publicly announced that Katie does not know whether Katie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Katie can now know whether Roy can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katie","Tanya","Roy"],"index":34003,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9741597176,"difficulty":0.0258402824}
+{"premise":"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 Bruce's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! ~(4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Beatrice can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Bruce","Beatrice","Charles"],"index":65435,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9787034392,"difficulty":0.0212965608}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Verna knows whether someone's forehead is muddy. It is publicly announced that Verna knows whether Elaine's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows 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":"Elaine can now know that Sharon can know that Odette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sharon","Odette","Elaine","Verna"],"index":20504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965867996,"difficulty":0.0034132004}
+{"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 Michael is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] Agentc knows that (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Michael can now know that Kathy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Kathy","Michael"],"index":25125,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993971586,"difficulty":0.0006028414}
+{"premise":"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 Maxwell's forehead is muddy. It is publicly announced that Andrew does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 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":"Maxwell can now know whether Andrew can know whether Maxwell's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Andrew","Maxwell"],"index":52304,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983726144,"difficulty":0.0016273856}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shannon does not know whether Steven is thirsty. It is publicly announced that Shannon does not know whether Eduardo is thirsty. It is publicly announced that Steven is thirsty. It is publicly announced that Eduardo does not know whether Shannon is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Shannon can now know whether Eduardo can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Eduardo","Shannon"],"index":9338,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9957980514,"difficulty":0.0042019486}
+{"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 John. Carol's card is shown to Eileen. Carol's card is shown to Shirley. Shirley'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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"John can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Eileen","Carol","Shirley"],"index":45590,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9933258295,"difficulty":0.0066741705}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nydia 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 3)","n_announcements":1,"pbcheck":"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":"Michael can now know that Nydia can know that Sonia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Nydia","Sonia"],"index":22867,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980074763,"difficulty":0.0019925237}
+{"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 Evan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 2)","n_announcements":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":"Robert can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","James","Evan","Mallory"],"index":37544,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983358979,"difficulty":0.0016641021}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Constance does not know whether Scott is thirsty. It is publicly announced that Michael knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Casey can now know that Constance can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Michael","Scott","Constance"],"index":47777,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.977938056,"difficulty":0.022061944}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brett's card is shown to Brenda. Marty's card is shown to Brenda. Brett's card is shown to David. Brenda's card is shown to Brett. David's card is shown to Brett. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know whether Brett can know whether Brett picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brenda","David","Brett","Marty"],"index":11381,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8841666579,"difficulty":0.1158333421}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Miriam knows whether or not nobody's forehead is muddy. It is publicly announced that Miriam knows whether 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)) ] 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 (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Doris can now know whether Christopher can know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Doris","Miriam"],"index":63156,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9403145313,"difficulty":0.0596854687}
+{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] Agenta knows that (Agentb knows that 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":"Nina can now know that Margaret can know that Margaret's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nina","Margaret","Martin"],"index":5147,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9938575625,"difficulty":0.0061424375}
+{"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. Joy's card is shown to Richard. Jeff's card is shown to Jeff. Jeff's card is shown to Joy. It is publicly announced that someone picked a red card. It is publicly announced that Jeff does not know whether Richard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Jeff can now know that Richard can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Jeff","Joy"],"index":19585,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990649819,"difficulty":0.0009350181}
+{"premise":"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 Wayne knows whether Wayne's forehead is muddy. It is publicly announced that Wayne knows whether Wayne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Kevin can now know whether Gene can know that Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gene","Kevin","Wayne"],"index":7262,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818284512,"difficulty":0.0181715488}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy.","smcdel_problem":"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 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":"Barbara can now know that Judith can know whether Judith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Judith","Christopher"],"index":27186,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9914643168,"difficulty":0.0085356832}
+{"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. Samuel's card is shown to Thelma. Thelma's card is shown to Edward. Edward's card is shown to Edward. Samuel's card is shown to Edward. Thelma's card is shown to Samuel. Samuel's card is shown to Samuel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:1,2,3 Agentc:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Edward can now know whether Samuel can know that Thelma picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thelma","Edward","Samuel"],"index":64391,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.93384552,"difficulty":0.06615448}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marla 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) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (1&2&3) ] 0","hypothesis":"Charles can now know that Keely's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Charles","Marla","Keely"],"index":53892,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9980449677,"difficulty":0.0019550323}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. Maryanne's card is shown to Curtis. Maryanne's card is shown to Maryanne. Curtis'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 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Curtis can now know that Curtis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Curtis","Maryanne","Jennifer"],"index":5813,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9825125933,"difficulty":0.0174874067}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Danna's card is shown to Mellissa. Genevieve's card is shown to Mellissa. Mellissa's card is shown to Tabitha. It is publicly announced that someone picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Genevieve can now know that Danna can know whether Genevieve picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danna","Genevieve","Mellissa","Tabitha"],"index":60760,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9162783623,"difficulty":0.0837216377}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathan knows whether Winnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agentd knows 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 2) ] 0","hypothesis":"Leslie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Winnie","Nathan","Leslie"],"index":63926,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994581342,"difficulty":0.0005418658}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Annette does not know whether or not everyone is thirsty. It is publicly announced that Annette knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows 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":"Annette can now know that Jerry can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jerry","Annette"],"index":14155,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998208642,"difficulty":0.001791358}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark is thirsty. It is publicly announced that Michael does not know whether Danny is thirsty. It is publicly announced that Carla knows whether or not nobody is thirsty. It is publicly announced that Carla is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] Agentc knows whether (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] [ ! ~(3) ] 0","hypothesis":"Carla can now know whether Mark can know that Danny is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danny","Michael","Carla","Mark"],"index":65097,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9880627394,"difficulty":0.0119372606}
+{"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. Edward's card is shown to Anthony. Anthony's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Anthony knows whether or not everyone picked a red card.","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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Edward can now know whether Anthony picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Anthony","Edward"],"index":40812,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9545019865,"difficulty":0.0454980135}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentb knows whether (Agentc knows that 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":"Amanda can now know whether Debra can know that Amanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Douglas","Amanda","Debra"],"index":50233,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993929863,"difficulty":0.0006070137}
+{"premise":"There are three persons. Everyone is visible 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 (1|2|3))","n_announcements":1,"pbcheck":"VARS 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":"Kurt can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kurt","John","Jenifer"],"index":34885,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993551373,"difficulty":0.0006448627}
+{"premise":"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 does not know whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Patrick can know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eddie","James","Patrick","John"],"index":18470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.974103272,"difficulty":0.025896728}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Harlan's card is shown to Harlan. Joseph's card is shown to Harlan. Harlan's card is shown to Joseph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Joseph can now know that Harlan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Harlan","Joseph","Iluminada"],"index":45706,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9944161177,"difficulty":0.0055838823}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marjorie'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":"Julio can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marjorie","Julio","Paul","Wesley"],"index":44919,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.968619287,"difficulty":0.031380713}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bud knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows that 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":"Annette can now know that Kenneth can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Patricia","Annette","Bud"],"index":32776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954282045,"difficulty":0.0045717955}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sterling's card is shown to Sterling. Sterling's card is shown to Susan. Sterling's card is shown to Kenneth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1 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:1 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know whether Kenneth can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sterling","Susan","Kenneth"],"index":26534,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9930226207,"difficulty":1.9930226207}
+{"premise":"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 Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] (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) ] [ ! 2 ] 0","hypothesis":"George can now know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Donna","Marie"],"index":17059,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994156361,"difficulty":0.0005843639}
+{"premise":"There are four persons. Everyone is visible 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 Fred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Mary can now know whether Fred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fred","Julia","Amanda","Mary"],"index":44926,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994338155,"difficulty":0.0005661845}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] 0","hypothesis":"David can now know that Alma can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["David","Alma"],"index":5381,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993688464,"difficulty":0.0006311536}
+{"premise":"There are four persons. Everyone is visible 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 Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Irvin can now know whether James can know whether Stacey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alexander","Irvin","James","Stacey"],"index":59084,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994031191,"difficulty":0.0005968809}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arlene knows whether Janice's forehead is muddy. It is publicly announced that Janice knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Donald can now know that Janice can know that Donald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donald","Janice","Arlene","Julia"],"index":54602,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9978522062,"difficulty":0.0021477938}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Martha's card is shown to Martha. Clara's card is shown to Clara. Martha's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that David does not know whether David picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc 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:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"David can now know whether Clara can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Martha","Clara","David"],"index":18255,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994118214,"difficulty":0.0005881786}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry knows whether Roseanna's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roseanna does not know whether Roseanna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Roseanna can now know whether Roseanna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kerry","Bobby","Roseanna"],"index":32074,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9853823185,"difficulty":1.9853823185}
+{"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. James's card is shown to James. David'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 James picked a red card. It is publicly announced that John knows whether John picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:1,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know that James can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["David","James","John"],"index":1748,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.99856323,"difficulty":0.00143677}
+{"premise":"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 Ella's forehead is not muddy. It is publicly announced that Francis knows whether Ella's forehead is muddy. It is publicly announced that Ella knows whether Francis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Amy can now know whether Ella can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Francis","Amy","Ella"],"index":24964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9936743975,"difficulty":0.0063256025}
+{"premise":"There are two persons. Everyone is visible 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":"Michael can now know whether Emily can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Emily","Michael"],"index":24251,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993712306,"difficulty":0.0006287694}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether 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 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Opal can now know that Norman can know that Opal is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norman","Opal","James"],"index":31611,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9959430099,"difficulty":0.0040569901}
+{"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 Phillip. 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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 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 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"Paul can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Paul","Phillip"],"index":40398,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994561076,"difficulty":0.0005438924}
+{"premise":"There are four persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know that Howard can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Curt","Robert","Cynthia","Howard"],"index":67554,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993078709,"difficulty":0.0006921291}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Elisa's card is shown to Mary. Dorla's card is shown to Mary. Mary's card is shown to Elisa. Mary's card is shown to Dorla. It is publicly announced that someone picked a red card. It is publicly announced that Elisa does not know whether Elisa picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows 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":"Dorla can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Elisa","Dorla"],"index":22966,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9938440323,"difficulty":0.0061559677}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether (~(1|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":"Denise can now know that Nicole can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nicholas","Denise","Nicole"],"index":22056,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994499087,"difficulty":0.0005500913}
+{"premise":"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 Larry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Susan can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Larry","William","Susan","James"],"index":30238,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993537068,"difficulty":0.0006462932}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela is thirsty. It is publicly announced that Angela knows whether Angela is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 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) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Edith can now know that Jennifer can know that Jennifer is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jennifer","Edith","Angela"],"index":45052,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.936919868,"difficulty":0.063080132}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharleen does not know whether Sharleen's forehead is muddy. It is publicly announced that Lashonda does not know whether Lashonda's forehead is muddy.","smcdel_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 (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":"Sharleen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lashonda","Elizabeth","Sharleen"],"index":5482,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753379822,"difficulty":0.0246620178}
+{"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. Elijah's card is shown to Jason. Jason's card is shown to Elijah. It is publicly announced that someone picked a red card. It is publicly announced that Elijah does not know whether Elijah picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Elijah can now know whether Jason can know whether Elijah picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jason","Elijah"],"index":53866,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981350899,"difficulty":0.0018649101}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dawn's card is shown to Dawn. Lupe's card is shown to Aaron. Aaron's card is shown to Lupe. Lupe's card is shown to Lupe. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:4 Agentc:3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 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":"Aaron can now know that Jeremy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jeremy","Dawn","Aaron","Lupe"],"index":59670,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9983474016,"difficulty":0.0016525984}
+{"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. Jose's card is shown to Francisco. Holly's card is shown to Francisco. Jose's card is shown to Jose. Holly's card is shown to Holly. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether Holly picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (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":"Francisco can now know that Jose can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Francisco","Jose","Holly"],"index":47669,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990687966,"difficulty":0.0009312034}
+{"premise":"There are three persons. Everyone is visible 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 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 John knows whether Jacqueline's forehead is muddy. It is publicly announced that Billy 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) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 2) ] Agenta knows whether (Agentc knows whether 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":"Jacqueline can now know whether John can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jacqueline","Billy","John"],"index":31634,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993995428,"difficulty":0.0006004572}
+{"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 Mariano. Mariano's card is shown to Stacey. Mariano's card is shown to Nicole. Mariano's card is shown to Jason. Jason's card is shown to Jason. It is publicly announced that someone picked a red card. It is publicly announced that Mariano does not know whether Nicole picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agenta knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Mariano can now know that Jason can know whether Mariano picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mariano","Stacey","Nicole","Jason"],"index":2128,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8318855166,"difficulty":0.1681144834}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Tracey can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","James","Natasha"],"index":7926,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970393181,"difficulty":0.0029606819}
+{"premise":"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 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)","n_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":"Christine can now know whether Jo can know whether Kevin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Christine","Jo"],"index":57674,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988502264,"difficulty":0.0011497736}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Deborah does not know whether Deborah's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Paul can now know whether Deborah can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Deborah","Paul","Jean"],"index":23260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992815852,"difficulty":0.0007184148}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gloria does not know whether Elizabeth is thirsty. It is publicly announced that Cindy 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 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Peggy can now know that Peggy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peggy","Gloria","Elizabeth","Cindy"],"index":60999,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9070519805,"difficulty":0.0929480195}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linsey knows whether or not nobody's forehead is muddy. It is publicly announced that Jennifer'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":"Ronald can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ronald","Roger","Linsey","Jennifer"],"index":12568,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989326596,"difficulty":0.0010673404}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Margie 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":"Margie can now know whether Cecil can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margie","Catherine","Cecil"],"index":45653,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9990504384,"difficulty":0.0009495616}
+{"premise":"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 Kristin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (~(1|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":"Richard can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Kristin"],"index":20212,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987517595,"difficulty":0.0012482405}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether Paul's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_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 whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 2) ] [ ! (1&2&3) ] 0","hypothesis":"Wade can now know whether Bryan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wade","Paul","Bryan"],"index":16912,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994427562,"difficulty":0.0005572438}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Herbert","Dena","Susan","Joann"],"index":16850,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989247918,"difficulty":0.0010752082}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know that Gilbert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Gilbert","Charles","Jorge"],"index":46960,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989709854,"difficulty":0.0010290146}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Stephen does not know whether Julia is thirsty. It is publicly announced that Terry knows whether someone is thirsty. It is publicly announced that Stephen does not know whether or not everyone is thirsty. It is publicly announced that Nicole does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (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) ] [ ! ~(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":"Julia can now know whether Stephen can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Stephen","Julia","Nicole"],"index":36023,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993702769,"difficulty":0.0006297231}
+{"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 (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Joshua can now know whether Robert can know whether David is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","David","Joshua"],"index":4357,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991686344,"difficulty":0.0008313656}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Daniel's card is shown to Daniel. Crystal's card is shown to Daniel. Crystal's card is shown to Crystal. It is publicly announced that someone picked a red card. It is publicly announced that Crystal picked a red card. It is publicly announced that Crystal 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 whether 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":"Daniel can now know whether Crystal picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Daniel","Crystal"],"index":40745,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9747237563,"difficulty":0.0252762437}
+{"premise":"There are three persons. Everyone is visible 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 Billie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"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":"Billie can now know that James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Billie","William"],"index":19616,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977909327,"difficulty":0.0022090673}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Shirley does not know whether or not everyone is thirsty. It is publicly announced that Bernard is thirsty. It is publicly announced that Bernard is thirsty.","smcdel_problem":"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 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] [ ! 3 ] 0","hypothesis":"Patricia can now know that Melinda can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Melinda","Bernard","Shirley"],"index":49649,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9964333773,"difficulty":0.0035666227}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeff knows whether or not everyone's forehead is muddy. It is publicly announced that Jeff does not know whether Jeff's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patsy can now know whether Jose's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Patsy","Jeff","Patricia","Jose"],"index":50467,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993023872,"difficulty":0.0006976128}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy. It is publicly announced that Dorothy knows whether Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Valerie can now know whether Dorothy can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Valerie","Dorothy"],"index":17005,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7813405395,"difficulty":0.2186594605}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Toni's card is shown to Toni. Toni's card is shown to Dean. Dean's card is shown to Anthony. Anthony's card is shown to Anthony. Anthony's card is shown to Nicholas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:1 Agentc:2,3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Toni can now know that Dean can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Toni","Dean","Anthony","Nicholas"],"index":11164,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9916702509,"difficulty":0.0083297491}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Julie knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (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&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Julie","David","Mary"],"index":6594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9944506884,"difficulty":0.0055493116}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wesley does not know whether Wesley's forehead is muddy. It is publicly announced that Wesley does not know whether Wesley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that 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":"Wesley can now know that Norma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Norma","Wesley"],"index":45272,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9899677038,"difficulty":1.9899677038}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Edith does not know whether or not everyone is thirsty. It is publicly announced that Harry knows whether Harry is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Maryam can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Edith","Harry","Carolyn","Maryam"],"index":33557,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990078807,"difficulty":0.0009921193}
+{"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 Trevor is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentc knows that (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) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Rose can now know that Donald can know that Donald is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Peter","Trevor","Rose","Donald"],"index":23212,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9946892262,"difficulty":0.0053107738}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Mary's card is shown to Amy. Amy's card is shown to Patricia. Patricia's card is shown to Patricia. Sandra's card is shown to Sandra. Mary's card is shown to Sandra. Amy'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:1,2 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3,4 Agentd:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandra can now know whether Amy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amy","Patricia","Sandra","Mary"],"index":43390,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993964434,"difficulty":0.0006035566}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cornelia knows whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Michael's forehead is muddy. It is publicly announced that Cornelia knows whether Cornelia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Cornelia can now know whether Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Cornelia","Michael"],"index":61463,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994444251,"difficulty":0.0005555749}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Regina's card is shown to Regina. Regina's card is shown to Michael. Michael's card is shown to Yolanda. Yolanda's card is shown to Yolanda. Yolanda's card is shown to Calvin. 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) ] Agentb knows whether (Agentd knows whether 1)","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":"Michael can now know whether Calvin can know whether Regina picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Regina","Michael","Yolanda","Calvin"],"index":9995,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989920259,"difficulty":0.0010079741}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Madeline does not know whether Jamar is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows whether 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":"Jamar can now know that Madeline can know whether Ashley is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jamar","Madeline","Ashley","William"],"index":1619,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998283267,"difficulty":0.001716733}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ashleigh does not know whether Lorena is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows 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":"Lorena can now know that Ashleigh can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ashleigh","Lorena","Dorothy"],"index":32826,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993959665,"difficulty":0.0006040335}
+{"premise":"There are three persons. Everyone is visible 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 everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Gail can now know whether James's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["James","Gail","Cameron"],"index":11901,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994505048,"difficulty":0.0005494952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kimberly does not know whether Ryan is thirsty. It is publicly announced that James does not know whether Dustin is thirsty. It is publicly announced that Kimberly does not know whether James is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] Agentc knows whether (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) ] [ ! ~(Agentd knows whether 3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Ryan can now know whether James can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Dustin","Ryan","Kimberly"],"index":33458,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9714639783,"difficulty":1.9714639783}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan does not know whether Bryan'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) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jesse can now know that Mariano's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bryan","Mariano","Jesse","Norma"],"index":57640,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947992563,"difficulty":0.0052007437}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dennis knows whether Dennis is thirsty. It is publicly announced that Walter does not know whether Dennis is thirsty. It is publicly announced that William does not know whether Sandra is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sandra can now know that Dennis can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dennis","Sandra","Walter","William"],"index":41627,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993913174,"difficulty":0.0006086826}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jimmy does not know whether Jesus is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! (1|2|3) ] Agentb knows 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 2) ] [ ! (1|2|3) ] 0","hypothesis":"Jesus can now know whether Jimmy can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jimmy","Jesus","Efrain"],"index":34852,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994412065,"difficulty":0.0005587935}
+{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] Agentc knows whether (Agentb knows 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":"Paul can now know whether Clarence can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Clarence","Paul"],"index":62568,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993398786,"difficulty":0.0006601214}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ted's card is shown to Ted. Deborah's card is shown to Deborah. Deborah's card is shown to Claudio. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Deborah can now know whether Ted can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ted","Deborah","Claudio"],"index":9244,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994145632,"difficulty":0.0005854368}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lorene's card is shown to Lorene. Kathleen's card is shown to Kathleen. 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 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Lorene can now know that Lorene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lorene","Kathleen"],"index":27073,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9502896667,"difficulty":0.0497103333}
+{"premise":"There are two 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 Paul is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 1) ] (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)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Paul can now know that Paul is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paul","John"],"index":24011,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6881565452,"difficulty":0.3118434548}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Arlene's card is shown to Thomas. Thomas's card is shown to Linda. Arlene's card is shown to Linda. Linda's card is shown to Arlene. Arlene's card is shown to Arlene. It is publicly announced that someone picked a red card. It is publicly announced that Linda knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Arlene can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Thomas","Linda","Arlene"],"index":14898,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994126558,"difficulty":0.0005873442}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Desiree's card is shown to Desiree. Carol's card is shown to Desiree. Wayne's card is shown to David. David's card is shown to Wayne. Carol's card is shown to Carol. It is publicly announced that someone picked a red card. It is publicly announced that Desiree does not know whether Wayne picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:2 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"David can now know whether Carol can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Desiree","David","Wayne","Carol"],"index":17465,"s-l":"explicit-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 David does not know whether David's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Richard can now know whether David can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rosa","Richard","David"],"index":3478,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9744918346,"difficulty":0.0255081654}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Joseph's card is shown to Joseph. Lewis's card is shown to Joseph. Joseph's card is shown to Lewis. Lewis's card is shown to Lewis. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Lewis can now know whether Joseph can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Joseph","Lewis"],"index":12534,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9821003079,"difficulty":0.0178996921}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Howard's card is shown to Howard. Howard's card is shown to Deangelo. It is publicly announced that someone picked a red card. It is publicly announced that Ivy does not know whether or not everyone picked a red card. It is publicly announced that Ivy does not know whether or not everyone picked a red card. It is publicly announced that Ivy knows whether Howard picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Ivy can now know that Deangelo picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Howard","Ivy","Deangelo"],"index":30284,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9296978712,"difficulty":0.0703021288}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Bettie does not know whether or not everyone is thirsty. It is publicly announced that Eric does not know whether George is thirsty. It is publicly announced that George does not know whether or not everyone is thirsty. It is publicly announced that George does not know whether Eric is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows 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":"Bettie can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["George","Bettie","Eric"],"index":64828,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994699359,"difficulty":0.0005300641}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Glen can now know whether James can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Charles","Glen"],"index":7651,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994458556,"difficulty":0.0005541444}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alexander does not know whether Carol is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Carol can now know that Rebecca can know whether Carol is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antonio","Carol","Rebecca","Alexander"],"index":27099,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7547283769,"difficulty":0.2452716231}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roderick knows whether someone's forehead is muddy. It is publicly announced that Brian knows whether someone's forehead is muddy. It is publicly announced that Diane knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Kimberly can now know that Kimberly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Diane","Kimberly","Roderick","Brian"],"index":13380,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980313182,"difficulty":0.0019686818}
+{"premise":"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 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 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) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Ronnie can now know whether Lloyd can know that Lloyd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["April","Ronnie","Lloyd"],"index":41449,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939180613,"difficulty":0.0060819387}
+{"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. Gerald's card is shown to Gerald. Robert's card is shown to Robert. It is publicly announced that someone picked a red card. It is publicly announced that Ruth does not know whether Richard picked a red card. It is publicly announced that Ruth does not know whether Ruth picked a red card. It is publicly announced that Richard does not know whether Ruth 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) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta 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:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 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","Gerald","Ruth","Robert"],"index":1625,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9828315973,"difficulty":0.0171684027}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rolland does not know whether Rolland's forehead is muddy. It is publicly announced that not everyone'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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Rolland can now know whether Rolland's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rolland","Mary"],"index":27744,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6821377277,"difficulty":1.6821377277}
+{"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 Edward 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 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":"Edward can now know whether Edward is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paul","Edward","Karen"],"index":52431,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9960220456,"difficulty":0.0039779544}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether Milton's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Whitley can now know that Milton's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Milton","Catherine","Whitley","Donald"],"index":2925,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993729949,"difficulty":0.006270051}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Branda does not know whether John is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that John does not know whether Branda is thirsty. It is publicly announced that Branda knows whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Carlton can now know that John can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Branda","John","Carlton"],"index":53463,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994816184,"difficulty":0.0005183816}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). David's card is shown to David. Shawn's card is shown to David. David's card is shown to Shawn. David's card is shown to Guy. It is publicly announced that someone picked a red card. It is publicly announced that Guy knows whether David picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"David can now know that David picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Shawn","Guy","Gracia"],"index":2144,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9640903473,"difficulty":0.0359096527}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS 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 (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":"Milton can now know that Anthony can know that Milton's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vern","Sarah","Milton","Anthony"],"index":35973,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965079427,"difficulty":0.0034920573}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mohammed knows whether Vicki's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mohammed can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vicki","Mohammed","George"],"index":4969,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990193844,"difficulty":0.0009806156}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Amber does not know whether Marjorie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows that 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":"Olivia can now know whether Marjorie can know that Amber is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Olivia","Marjorie","Amber"],"index":3361,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9913139939,"difficulty":0.0086860061}
+{"premise":"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 does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ismael can now know whether Ken's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","James","Ismael","Ken"],"index":63057,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993185997,"difficulty":0.0006814003}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Eduardo does not know whether or not everyone is thirsty. It is publicly announced that Eduardo does not know whether Donald is thirsty. It is publicly announced that Donald does not know whether Paul is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] (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)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 1) ] [ ! (1&2&3) ] 0","hypothesis":"Paul can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Paul","Eduardo","Donald"],"index":45830,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994817376,"difficulty":0.0005182624}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wallace's card is shown to Franklin. Wallace's card is shown to Wallace. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Franklin can now know that Wallace picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Franklin","Wallace","Jerry"],"index":65878,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9894683957,"difficulty":0.0105316043}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Kathleen can now know that Denise can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cristy","Edward","Denise","Kathleen"],"index":58804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999120295,"difficulty":0.000879705}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows 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":"Henry can now know whether George can know whether Michele's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Henry","George","Michele"],"index":56871,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993848801,"difficulty":0.0006151199}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Virginia is 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) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] [ ! (1|2|3|4) ] 0","hypothesis":"Mack can now know that Virginia can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walter","Virginia","Beverly","Mack"],"index":25103,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994975328,"difficulty":0.0005024672}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alex does not know whether Fred is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Laura is thirsty. It is publicly announced that Alex knows whether Laura is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] (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 4) ] [ ! (~(1&2&3&4)) ] [ ! 2 ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Laura can now know that Nancy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nancy","Laura","Alex","Fred"],"index":13572,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9971452355,"difficulty":0.0028547645}
+{"premise":"There are four persons. Everyone is visible 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 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":"Peter can now know that Melvin can know whether Melvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Melvin","Juan","Miguel"],"index":64497,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999215126,"difficulty":0.000784874}
+{"premise":"There are four persons. Everyone is visible 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. 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) ] [ ! ~(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:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(2) ] 0","hypothesis":"Shannon can now know that Lillian can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shannon","Laura","Lillian","Gregory"],"index":37963,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989935756,"difficulty":0.0010064244}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Destiny does not know whether Destiny's forehead is muddy. It is publicly announced that Mark knows whether or not nobody's forehead is muddy. It is publicly announced that Mark knows whether Mark's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Destiny can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Destiny","Mark"],"index":8552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993376136,"difficulty":0.0006623864}
+{"premise":"There are three 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 Todd knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Todd can now know whether Frances can know whether Priscilla's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Todd","Frances","Priscilla"],"index":17108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993568063,"difficulty":0.0006431937}
+{"premise":"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 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)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"William can now know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Dennis","Martha"],"index":53932,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956265688,"difficulty":0.0043734312}
+{"premise":"There are four persons. Everyone is visible 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 Christopher's forehead is muddy. It is publicly announced that Casey knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Christopher can now know that Casey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Casey","Christopher","Yvette","Sonya"],"index":40186,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989683628,"difficulty":0.0010316372}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Verna's card is shown to Jayne. Jayne's card is shown to Dave. Jayne's card is shown to Mary. Jayne's card is shown to Verna. Verna's card is shown to Verna. It is publicly announced that someone picked a red card. It is publicly announced that Jayne does not know whether Mary picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentb knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Dave can now know whether Verna can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jayne","Dave","Mary","Verna"],"index":12719,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8339009285,"difficulty":0.1660990715}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lorenzo does not know whether Mary is thirsty. It is publicly announced that Lorenzo does not know whether Jimmie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether 4) ] 0","hypothesis":"Mary can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Lorenzo","Keith","Jimmie"],"index":23396,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989087582,"difficulty":0.0010912418}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tracy's card is shown to Tracy. Evan's card is shown to Evan. It is publicly announced that someone picked a red card. It is publicly announced that Lloyd knows 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) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lloyd can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tracy","Lloyd","Evan"],"index":50364,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9986404777,"difficulty":0.0013595223}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica does not know whether or not everyone is thirsty. It is publicly announced that Judith does not know whether William is thirsty. It is publicly announced that Jessica does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows 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)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Jessica can now know whether William can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jessica","William","Judith"],"index":22546,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994466901,"difficulty":0.0005533099}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tony knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (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":"Tony can now know whether Zandra can know whether Zandra is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Zandra","Tony","Deana"],"index":9680,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9892553091,"difficulty":0.0107446909}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jan's card is shown to Jan. Jan's card is shown to Jill. Jill's card is shown to Jill. Jan's card is shown to Nicholas. Jill's card is shown to Nicholas. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jan can now know that Nicholas picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jan","Jill","Nicholas"],"index":4091,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982548356,"difficulty":0.0017451644}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Agnes's card is shown to Mary. Agnes's card is shown to Agnes. Mary's card is shown to Floyd. It is publicly announced that someone picked a red card. It is publicly announced that Agnes does not know whether Floyd picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Floyd can now know that Mary can know that Floyd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Agnes","Floyd"],"index":43626,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977413416,"difficulty":0.0022586584}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel's forehead is muddy. It is publicly announced that Rachel knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agentb knows whether (Agenta knows 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":"Henry can now know whether Rachel can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rachel","Henry"],"index":44464,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9652942419,"difficulty":0.0347057581}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marty knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 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) ] 0","hypothesis":"Jennifer can now know that Anthony can know that Anthony's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anthony","Pauline","Jennifer","Marty"],"index":38714,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9946405292,"difficulty":0.0053594708}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward knows whether 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 (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":"Edith can now know that Edward can know that Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Melissa","Edward","Edith","Margaret"],"index":47249,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974198341,"difficulty":0.0025801659}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ann's card is shown to Chelsea. James's card is shown to Ann. Chelsea's card is shown to James. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:1 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ann can now know whether Edward can know whether Edward picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Chelsea","Edward","Ann","James"],"index":18598,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9172495008,"difficulty":1.9172495008}
+{"premise":"There are two persons. Everyone is visible 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 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":"Linda can now know that Morgan's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Morgan"],"index":15679,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9883382916,"difficulty":0.0116617084}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Susan knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Susan can now know whether Melissa can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Gary","Melissa","Amy"],"index":54707,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9017400146,"difficulty":0.0982599854}
+{"premise":"There are three persons. Everyone is visible 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 1,2,3 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":"Vanessa can now know that Gary can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Vanessa","Kenneth"],"index":60804,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992789626,"difficulty":0.0007210374}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Troy 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 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":"Troy can now know whether Gerald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Joseph","Gerald","Troy"],"index":44578,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993104935,"difficulty":0.0006895065}
+{"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 Kimberly. Claudia's card is shown to Kimberly. Claudia's card is shown to Claudia. Thomas's card is shown to Claudia. Kimberly's card is shown to Angelique. Claudia's card is shown to Angelique. Kimberly's card is shown to Thomas. Thomas's card is shown to Thomas. It is publicly announced that someone picked a red card. It is publicly announced that Kimberly knows whether Kimberly picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,4 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know whether Claudia can know whether Angelique picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Claudia","Angelique","Thomas"],"index":21268,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9981941581,"difficulty":0.0018058419}
+{"premise":"There are three persons. Everyone is visible 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 not muddy. It is publicly announced that Alisa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentc knows 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) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Edward","Alisa","Kenneth"],"index":57309,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992794394,"difficulty":0.0007205606}
+{"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 Constance. Constance's card is shown to Todd. Beth's card is shown to Yee. Todd's card is shown to Beth. Beth's card is shown to Beth. 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:4 Agentd:2,4 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:2 Agentb:1 Agentc:4 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Beth can now know that Yee can know that Todd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Constance","Todd","Yee","Beth"],"index":29440,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9978910089,"difficulty":0.0021089911}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ka's card is shown to Ka. Richard's card is shown to Ka. Russell's card is shown to Richard. Ka's card is shown to Russell. Richard's card is shown to Russell. Russell's card is shown to Russell. It is publicly announced that someone picked a red card. It is publicly announced that Ka does not know whether Terrell picked a red card. It is publicly announced that Richard knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:1,2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Ka can now know whether Richard can know whether Ka picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ka","Richard","Terrell","Russell"],"index":62158,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985381365,"difficulty":0.0014618635}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agenta knows that 1)","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":"Bret can now know that John can know that John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Michael","Bret","Robert"],"index":55109,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9986358285,"difficulty":0.0013641715}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Raymond does not know whether Jason is thirsty. It is publicly announced that Jason does not know whether or not everyone is thirsty. It is publicly announced that Jason does not know whether Mark is thirsty. It is publicly announced that Jason 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) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agenta knows that (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta: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":"Raymond can now know that Mark can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Raymond","Jason","Mark"],"index":4590,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982642531,"difficulty":0.0017357469}
+{"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 Jean is thirsty. It is publicly announced that Cheryl does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (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":"Cheryl can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cheryl","Lydia","Pam","Jean"],"index":55771,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995218515,"difficulty":0.0004781485}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Diana knows whether someone is thirsty. It is publicly announced that Michael does not know whether Diana is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Rita can now know whether Diana is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Diana","Michael","Rita"],"index":14095,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8955846429,"difficulty":0.1044153571}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jordan's card is shown to Pamela. Pamela's card is shown to Clyde. Catherine's card is shown to Clyde. Pamela's card is shown to Catherine. It is publicly announced that someone picked a red card. It is publicly announced that Jordan knows whether Pamela picked a red card. It is publicly announced that Clyde does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Pamela can now know whether Clyde can know whether Catherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pamela","Jordan","Clyde","Catherine"],"index":64742,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988933206,"difficulty":0.0011066794}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wendy does not know whether Doyle 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 that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Carl can now know that Doyle can know that Carl is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carl","Doyle","Wendy"],"index":57984,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974669218,"difficulty":0.0025330782}
+{"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 Jon 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)","n_announcements":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":"Emily can now know whether James is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Emily","Jon","Sabrina"],"index":56963,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7755498886,"difficulty":0.2244501114}
+{"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 Denise is thirsty. It is publicly announced that Stephanie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! 1 ] 0","hypothesis":"Donald can now know whether Donald is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephanie","Edward","Donald","Denise"],"index":21078,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9948205948,"difficulty":0.0051794052}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Donna is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 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) ] [ ! 4 ] 0","hypothesis":"Donna can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gail","Sidney","Kelsey","Donna"],"index":26661,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995222092,"difficulty":0.0004777908}
+{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"George can now know whether Kendra can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kendra","George"],"index":14330,"s-l":"forehead_mirror-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). Diane's card is shown to Edward. Edward's card is shown to Roy. Roy's card is shown to Roy. Juanita's card is shown to Roy. Roy's card is shown to Juanita. It is publicly announced that someone picked a red card. It is publicly announced that Roy does not know whether Edward picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] Agenta knows that (Agentb knows whether (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":"Edward can now know that Diane can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Diane","Roy","Juanita"],"index":4352,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993857145,"difficulty":0.0006142855}
+{"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 Robert is thirsty. It is publicly announced that Robert does not know whether Gregory is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] Agentd knows whether (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Gregory can now know whether Mildred can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Joseph","Mildred","Gregory"],"index":51909,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994169474,"difficulty":0.0005830526}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Salvatore does not know whether Esther is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that Salvatore knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows 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 3) ] [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Esther can now know that Carlos is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carlos","Salvatore","Esther","Shyla"],"index":57716,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984042048,"difficulty":0.0015957952}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley does not know whether Bradley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS 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":"Steve can now know whether Debra can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Delbert","Bradley","Steve","Debra"],"index":6077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9660412073,"difficulty":0.0339587927}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether or not everyone's forehead is muddy. It is publicly announced that Howard knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows 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":"Gerald can now know whether Howard can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Howard","Gerald"],"index":16067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994524121,"difficulty":0.0005475879}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that 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 (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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that Lindsey can know that James is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Mary","Joseph","Lindsey"],"index":58241,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8431451321,"difficulty":0.1568548679}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether 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) ] [ ! (Agentb knows whether 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 3) ] 0","hypothesis":"Denise can now know whether Michael can know that Michael's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Denise","Jacqueline"],"index":55341,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992076755,"difficulty":0.0007923245}
+{"premise":"There are four persons. Everyone is visible to others. 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 someone's forehead is muddy. It is publicly announced that Allen 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 (Agenta knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Allen can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Allen","Sandra","Christina","Robert"],"index":2035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9940142035,"difficulty":0.0059857965}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Teresa's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Teresa can now know that Christopher can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Teresa","Christopher"],"index":48830,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994391799,"difficulty":0.0005608201}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jan's card is shown to Jan. William's card is shown to Jan. James's card is shown to James. Ferdinand's card is shown to James. James's card is shown to Ferdinand. Ferdinand's card is shown to Ferdinand. Jan's card is shown to William. James's card is shown to William. It is publicly announced that someone picked a red card. It is publicly announced that Ferdinand does not know whether William picked a red card. It is publicly announced that James picked a black card. It is publicly announced that Ferdinand picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3 Agentc:2,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(2) ] [ ! 3 ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2,3 Agentc:2,3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 4) ] [ ! ~(2) ] [ ! 3 ] 0","hypothesis":"William can now know that Ferdinand can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jan","James","Ferdinand","William"],"index":4986,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8542081118,"difficulty":0.1457918882}
+{"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 Vivian. Brian's card is shown to Brian. Julie's card is shown to Julie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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":"Vivian can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Vivian","Brian","Julie"],"index":59184,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993711114,"difficulty":0.0006288886}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jayne does not know whether Diane is thirsty. It is publicly announced that Diane knows whether or not everyone is thirsty. It is publicly announced that Tommy knows whether or not everyone is thirsty. It is publicly announced that Tommy does not know whether Jayne is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Tommy can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Tommy","Jayne","Diane"],"index":49100,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990814924,"difficulty":0.0009185076}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Virginia's card is shown to Virginia. Kenya's card is shown to Lisa. Lisa's card is shown to Kenya. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 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":"Virginia can now know whether Kenya can know that Kenya picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Virginia","Lisa","Kenya"],"index":29598,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7391000986,"difficulty":0.2608999014}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Steven does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether 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":"Russell can now know whether Jame can know whether Brooke is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jame","Brooke","Russell","Steven"],"index":23073,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991596937,"difficulty":0.0008403063}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Herbert can now know that Terry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elvira","Herbert","Terry","Tommy"],"index":35154,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993102551,"difficulty":0.0006897449}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Teresa knows whether or not nobody is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows whether (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":"Teresa can now know whether Patricia can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patricia","Teresa","Diane"],"index":7719,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992948771,"difficulty":0.0007051229}
+{"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 Robert. Linda's card is shown to Francesca. Robert's card is shown to Linda. Linda's card is shown to Linda. Linda's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:1,3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Francesca can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Francesca","Linda","Patricia"],"index":18753,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9969013929,"difficulty":0.0030986071}
+{"premise":"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 June's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agenta knows whether (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":"Jose can now know whether Michelle can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Michelle","Evelyn","June"],"index":46594,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993316531,"difficulty":0.0006683469}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Nicholas does not know whether Robin is thirsty. It is publicly announced that Robin does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Julie","Robin","Nicholas","Michael"],"index":6779,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990752935,"difficulty":0.0009247065}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that Louise's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agenta knows whether (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":"Louise can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Louise","David"],"index":47236,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994847775,"difficulty":0.0005152225}
+{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy.","smcdel_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|2|3)))","n_announcements":1,"pbcheck":"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":"Anamaria can now know that Dorothy can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Dorothy","Anamaria"],"index":41783,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991962314,"difficulty":0.0008037686}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tanya does not know whether Stewart is thirsty. It is publicly announced that Carolyn does not know whether Stewart is thirsty. It is publicly announced that Carolyn is not thirsty. It is publicly announced that Tanya is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] (Agentc knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(1) ] [ ! ~(3) ] 0","hypothesis":"Tanya can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carolyn","Stewart","Tanya"],"index":37512,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8134972453,"difficulty":0.1865027547}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Maria does not know whether Jane is thirsty. It is publicly announced that Jessica 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)","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":"Jane can now know that Maria can know that Jane is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jane","Jessica","Maria"],"index":11078,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9705703855,"difficulty":0.0294296145}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to James. Willie's card is shown to Willie. Willie's card is shown to Curtis. It is publicly announced that someone picked a red card. It is publicly announced that Curtis 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)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Willie can know that Curtis picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Willie","Curtis"],"index":4675,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9184131026,"difficulty":0.0815868974}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark does not know whether Henry 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 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":"Mark can now know that Henry can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mark","Henry"],"index":64540,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994280934,"difficulty":0.0005719066}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie does not know whether Jessie's forehead is muddy. It is publicly announced that Joannie knows whether or not everyone's forehead is muddy. It is publicly announced that Joannie 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 whether 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":"Joannie can now know whether Joannie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jessie","Joannie"],"index":60733,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6893233657,"difficulty":1.6893233657}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marie's card is shown to Aracely. Jose's card is shown to Jose. Marie's card is shown to Jose. Marie's card is shown to Marie. Jose's card is shown to Branden. Marie's card is shown to Branden. It is publicly announced that someone picked a red card. It is publicly announced that Aracely 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: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:3 Agentb:2,3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Marie can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Aracely","Jose","Marie","Branden"],"index":6022,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999008894,"difficulty":0.000991106}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anthony is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc: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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Linda can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Linda","Anne","Anthony"],"index":41932,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990411401,"difficulty":0.0009588599}
+{"premise":"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 or not nobody's forehead is muddy. It is publicly announced that Iluminada's forehead is muddy. It is publicly announced that Betty does not know whether or not everyone's forehead is muddy. It is publicly announced that Betty's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Iluminada can now know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Michael","Iluminada","Joe"],"index":40744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7684305906,"difficulty":0.2315694094}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows that 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":"Virginia can now know that Verda can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Virginia","John","Verda"],"index":64468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996147275,"difficulty":0.003852725}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows that 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":"Karen can now know that Timothy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Brian","Timothy","Mary"],"index":43805,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9966879487,"difficulty":0.0033120513}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Crystal. Lindsey's card is shown to Crystal. Lindsey's card is shown to Lindsey. 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 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Crystal can now know that Jennifer can know that Jennifer picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Crystal","Lindsey","Jennifer"],"index":51906,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9877943993,"difficulty":0.0122056007}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether Fernando'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 (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) ] 0","hypothesis":"Fernando can now know whether Carmen can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Fernando","Carmen"],"index":45043,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9235044122,"difficulty":0.0764955878}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bette 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 (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":"Bette can now know whether Charles can know that Bette's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Larry","Zina","Bette","Charles"],"index":1462,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999409318,"difficulty":0.000590682}
+{"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 Keisha is thirsty. It is publicly announced that Mary does not know whether Angel 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) ] (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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Angel can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Keisha","Angel"],"index":19771,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994223118,"difficulty":0.0005776882}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Brad does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows 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":"Brad can now know whether Geraldine can know that Geraldine is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Geraldine","Patricia","Brad","Elizabeth"],"index":1899,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8944827914,"difficulty":0.1055172086}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee'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) ] Agenta knows whether (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) ] [ ! 2 ] [ ! (1&2&3) ] 0","hypothesis":"Bruce can now know whether Renee can know whether Brandy's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bruce","Renee","Brandy"],"index":60890,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994443059,"difficulty":0.0005556941}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John does not know whether Margaret is thirsty. It is publicly announced that John knows whether John is thirsty. It is publicly announced that Margaret does not know whether John is thirsty. It is publicly announced that Linda does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Linda can now know whether Margaret can know whether Margaret is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Margaret","John","Linda"],"index":5004,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9984762073,"difficulty":0.0015237927}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vickie's card is shown to Vickie. Vickie's card is shown to Thomas. Thomas'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 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:1 Agentb:1 Agentc:2 VALID? [ ! (1|2|3) ] 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":["Vickie","Thomas","William"],"index":56581,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9964244962,"difficulty":0.0035755038}
+{"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. Candice's card is shown to Shirley. Julie's card is shown to Julie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shirley can now know whether Julie can know whether Candice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Julie","Sylvia","Candice"],"index":48302,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985639453,"difficulty":0.0014360547}
+{"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 Stella. Marvin's card is shown to Stella. Stella's card is shown to Juan. Elizabeth's card is shown to Juan. Juan's card is shown to Marvin. Elizabeth's card is shown to Marvin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:1,3 Agentc:2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know that Stella can know whether Marvin picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stella","Juan","Elizabeth","Marvin"],"index":34098,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9967201352,"difficulty":1.9967201352}
+{"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 Tammy. Beverly's card is shown to Jose. William's card is shown to William. Jose's card is shown to Beverly. William's card is shown to Beverly. It is publicly announced that someone picked a red card. It is publicly announced that William does not know whether Jose picked a red card. It is publicly announced that Tammy knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:4 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Beverly can now know whether Jose can know whether Tammy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tammy","Jose","William","Beverly"],"index":6469,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9988177419,"difficulty":0.0011822581}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shannon does not know whether Shannon's forehead is muddy. It is publicly announced that Peter's forehead is muddy. It is publicly announced that Gene 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)) ] (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) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gene can now know whether Gene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Gene","Julie","Shannon"],"index":60694,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.665229857,"difficulty":0.334770143}
+{"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 Robert 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 whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Robert can now know whether Julie can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Julie"],"index":15208,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8640735745,"difficulty":0.1359264255}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 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":"Jackson can now know whether Jeanne can know that Jeanne's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Celesta","Mike","Jackson","Jeanne"],"index":16489,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992291927,"difficulty":0.0007708073}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashlee's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"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":"Autumn can now know whether Autumn's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Autumn","Ashlee","Chris"],"index":21635,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994164705,"difficulty":0.0005835295}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Larry does not know whether Lavelle is thirsty. It is publicly announced that John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] Agentc knows whether (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! 3 ] 0","hypothesis":"John can now know whether Victor can know that Larry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lavelle","Larry","John","Victor"],"index":45259,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9896402955,"difficulty":0.0103597045}
+{"premise":"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 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":"Adam can now know whether Christopher can know that Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christopher","Frances","Adam"],"index":51298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939661622,"difficulty":0.0060338378}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lazaro is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows 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":"Maurice can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juan","Lazaro","Maurice","Josephine"],"index":39668,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995127916,"difficulty":0.0004872084}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentc knows that 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":"Kim can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kim","Josephine","Michael"],"index":9921,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950358272,"difficulty":0.0049641728}
+{"premise":"There are three persons. Everyone is visible 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) ] [ ! (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":"Allen can now know that Allen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Allen","Jennifer","Vivian"],"index":60929,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998259604,"difficulty":0.001740396}
+{"premise":"There are three persons. Everyone is visible 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 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 (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":"Ellis can now know whether Teresa can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ellis","David","Teresa"],"index":10523,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994620681,"difficulty":0.0005379319}
+{"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 Janet is thirsty. It is publicly announced that Mathew does not know whether Janet is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"Janet can now know whether Mathew can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Mathew","Janet"],"index":66346,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9951262474,"difficulty":0.0048737526}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Suzanne does not know whether Lana is thirsty. It is publicly announced that Lana does not know whether Veronica is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 2) ] Agentb knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Veronica can now know that Lana can know that Lana is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Suzanne","Veronica","Lana"],"index":67227,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.990783453,"difficulty":0.009216547}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joshua is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Joshua can now know that Ronnie can know whether Ronnie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Ronnie","Joshua"],"index":9142,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.8692584038,"difficulty":0.1307415962}
+{"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 Nan is thirsty. It is publicly announced that Kathleen does not know whether Nan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 1) ] (Agentd knows 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) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Kathleen can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nan","Tonya","Laura","Kathleen"],"index":33525,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994027615,"difficulty":0.0005972385}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Tammy's card is shown to Tammy. Nicholas's card is shown to Tammy. Tammy's card is shown to Ricky. Erica's card is shown to Ricky. Nicholas's card is shown to Ricky. Erica's card is shown to Erica. Nicholas's card is shown to Erica. Tammy's card is shown to Nicholas. Nicholas's card is shown to Nicholas. It is publicly announced that someone picked a red card. It is publicly announced that Ricky knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,3,4 Agentc:3,4 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agenta knows that 3)","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":"Tammy can now know that Erica picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tammy","Ricky","Erica","Nicholas"],"index":20974,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9971812963,"difficulty":0.0028187037}
+{"premise":"There are four persons. Everyone is visible 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 muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows that (Agenta knows 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":"Frank can now know that Ryan can know that Victor's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Angelina","Victor","Frank"],"index":34979,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966285825,"difficulty":0.0033714175}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that not everyone is thirsty. It is publicly announced that Mary does not know whether Janet is thirsty. It is publicly announced that James does not know whether Dominique is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] Agenta knows that (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"James can now know that Mary can know whether Dominique is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Mary","Janet","Dominique"],"index":28801,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9973958731,"difficulty":0.0026041269}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that 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":"Lisa can now know that Lisa is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Donald","Lisa","Gregory","Jon"],"index":24229,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.8089673519,"difficulty":0.1910326481}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne's forehead is not muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(1) ] 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) ] [ ! ~(2) ] [ ! ~(1) ] 0","hypothesis":"Shane can now know that William can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Suzanne","Shane"],"index":23540,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998791635,"difficulty":0.001208365}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ron is thirsty. It is publicly announced that Cassandra does not know whether or not everyone is thirsty. It is publicly announced that Ron does not know whether Marjorie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] (Agentb knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Frank can now know whether Cassandra is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marjorie","Frank","Ron","Cassandra"],"index":27047,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.7953416109,"difficulty":1.7953416109}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Thomas is thirsty. It is publicly announced that Christine is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! 1 ] (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) ] [ ! 4 ] [ ! 1 ] 0","hypothesis":"Don can now know that Don is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Katrina","Don","Thomas"],"index":54615,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9388644099,"difficulty":0.0611355901}
+{"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. Edward's card is shown to Donald. Leona's card is shown to Edward. It is publicly announced that someone picked a red card. It is publicly announced that Edward picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Leona can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Leona","Donald","Edward"],"index":62752,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990484118,"difficulty":0.0009515882}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Florence does not know whether Florence's forehead is muddy.","smcdel_problem":"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 that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Florence can now know that William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Florence","William","Terry"],"index":8254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948319197,"difficulty":0.0051680803}
+{"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 Ronald is thirsty. It is publicly announced that Jayson does not know whether Ronald is thirsty. It is publicly announced that Ronald does not know whether David is thirsty. It is publicly announced that David is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentb knows whether 3) ] [ ! 3 ] 0","hypothesis":"David can now know that everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jayson","Ronald","David"],"index":16976,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979159236,"difficulty":0.0020840764}
+{"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 Frank is thirsty. It is publicly announced that Larry does not know whether Lorena is thirsty.","smcdel_problem":"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) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Frank can now know that Lorena is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Deborah","Lorena","Frank","Larry"],"index":41476,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9975546002,"difficulty":0.0024453998}
+{"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 Mark. Toni's card is shown to Mark. Scott's card is shown to Scott. James's card is shown to Toni. Mark's card is shown to Toni. Scott's card is shown to Toni. 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:3,4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(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:3,4 Agentb:3 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Mark can now know whether James can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Mark","Scott","Toni"],"index":51110,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993003607,"difficulty":0.0006996393}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ashley knows whether Ashley is thirsty. It is publicly announced that William does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Ashley can now know that William can know whether William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Ashley"],"index":34349,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9933000803,"difficulty":0.0066999197}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Loise does not know whether Michael is thirsty. It is publicly announced that Nathaniel is thirsty. It is publicly announced that Michael is thirsty. It is publicly announced that Nathaniel 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 that (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! 1 ] [ ! 2 ] [ ! 1 ] 0","hypothesis":"Nathaniel can now know that Michael can know that Nathaniel is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nathaniel","Michael","Loise"],"index":52912,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.7077889442,"difficulty":0.2922110558}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Morgan does not know whether Morgan's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Morgan 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 whether (Agenta knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Morgan can now know whether Mary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Robert","Morgan","Stephanie"],"index":8075,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8325880766,"difficulty":0.1674119234}
+{"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 William. Charles's card is shown to Ruth. Ruth's card is shown to Ruth. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know that Charles can know that Charles picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Charles","Ruth"],"index":27830,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9974179268,"difficulty":0.0025820732}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fay knows whether Fay's forehead is muddy. It is publicly announced that Michelle knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Michelle can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Fay","Michelle","Jack"],"index":17809,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9987248778,"difficulty":0.0012751222}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dan's card is shown to Bertha. Ivonne's card is shown to Dan. Ivonne's card is shown to Ronald. Dan's card is shown to Ronald. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ivonne can now know whether Dan can know that Dan picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ivonne","Bertha","Dan","Ronald"],"index":66462,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9340920448,"difficulty":0.0659079552}
+{"premise":"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 does not know whether Steven's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Frances knows whether Frances's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb 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) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Michael can now know whether Frances can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Frances","Steven"],"index":25453,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9974722266,"difficulty":0.0025277734}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Myrl 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) ] [ ! ~(Agentc knows whether 2) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Wayne can now know whether Myrl is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patricia","Wayne","Myrl"],"index":17050,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9590601921,"difficulty":0.0409398079}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Phoebe knows whether Phoebe's forehead is muddy. It is publicly announced that Phoebe knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Corina can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Phoebe","Francisco","Corina","David"],"index":47972,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990518689,"difficulty":0.0009481311}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juan does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Juan can now know whether Renita can know that Mary is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Juan","Renita","Mary"],"index":43022,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9939082861,"difficulty":0.0060917139}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce knows whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Bruce can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Roberta","Bruce"],"index":58030,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988074303,"difficulty":0.0011925697}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel knows whether or not everyone's forehead is muddy. It is publicly announced that Anna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc 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:1,2,3,4 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":"Anna can now know that Manuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","Iva","Manuel","Lucille"],"index":33548,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9730782509,"difficulty":0.0269217491}
+{"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 Dorothy. Kelsey's card is shown to Kelsey. 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 whether (Agenta 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":"Kelsey can now know whether Dorothy can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dorothy","Kelsey","Rebecca"],"index":54953,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991932511,"difficulty":0.0008067489}
+{"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 Gwendolyn. Shawn's card is shown to Tammy. Gwendolyn's card is shown to Tammy. It is publicly announced that someone picked a red card. It is publicly announced that Shawn knows whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Shawn can now know whether Gwendolyn can know whether Tammy picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Shawn","Gwendolyn","Tammy"],"index":35221,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9987817407,"difficulty":1.9987817407}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Jeffrey can now know that William can know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffrey","George","William","Victoria"],"index":45746,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8837310076,"difficulty":0.1162689924}
+{"premise":"There are two persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Don 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 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":"Don can now know that Patrick's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Don","Patrick"],"index":51188,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979174733,"difficulty":0.0020825267}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joanne knows whether someone's forehead is muddy. It is publicly announced that Joanne's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Mary can now know whether Frank can know whether Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joanne","Frank","Mary"],"index":67380,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992098808,"difficulty":0.0007901192}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tim does not know whether Traci 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) ] Agenta knows whether (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) ] [ ! ~(Agentc knows whether 1) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Traci can now know whether Annie can know whether Traci is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Traci","Annie","Tim","Marian"],"index":35668,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988803267,"difficulty":0.0011196733}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_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":"Gina can now know whether Ariel can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Rose","Gina","Ariel"],"index":57752,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994683862,"difficulty":0.0005316138}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether 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":"Janet can now know whether Carl can know whether Carl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Romaine","Carl","Janet"],"index":4447,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945928454,"difficulty":0.0054071546}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Linda knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":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":"Jean can now know whether Anissa can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Anissa","Jean","Don"],"index":43144,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993251562,"difficulty":0.0006748438}
+{"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 Paula is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] (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 3) ] 0","hypothesis":"Paula can now know that Marna is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Marna","Paula","Bernardo"],"index":8105,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998208642,"difficulty":0.001791358}
+{"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":"Jeffrey can now know that Ramon can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pearl","Ramon","Jeffrey","Kim"],"index":12512,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9988498688,"difficulty":0.0011501312}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Frances's card is shown to Joshua. Frances'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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Frances can now know whether Joshua can know that Paul picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joshua","Frances","Paul"],"index":37194,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9543628693,"difficulty":0.0456371307}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy. It is publicly announced that Julius knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows 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":"Mary can now know whether Julius can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Julius","Harold","William","Mary"],"index":55970,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994633794,"difficulty":0.0005366206}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Neil's card is shown to Neil. Todd's card is shown to Neil. Harry's card is shown to Todd. Harry's card is shown to Harry. Andrew's card is shown to Andrew. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 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:1,2 Agentb:3 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Neil can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Neil","Todd","Harry","Andrew"],"index":40205,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989475608,"difficulty":0.0010524392}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows 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":"Sherman can now know that Lucille can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sherman","Lucille"],"index":56415,"s-l":"forehead_mirror-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's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Willie knows whether Dan'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) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Willie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Eunice","Dan","Betty"],"index":3216,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966650605,"difficulty":0.0033349395}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg knows whether or not nobody's forehead is muddy. It is publicly announced that Denise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Danielle can now know that Danielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danielle","Denise","Greg"],"index":900,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977987409,"difficulty":0.0022012591}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Wonda does not know whether Angela is thirsty. It is publicly announced that Angela 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) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"Angela can now know whether Kimberly can know that Angela is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Angela","Kimberly","Wonda"],"index":5041,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9905429482,"difficulty":0.0094570518}
+{"premise":"There are two persons. Everyone is visible 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 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta 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) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Michael can now know that Clara's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Clara"],"index":61307,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977220893,"difficulty":0.0022779107}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rebecca knows whether 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 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) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Rebecca can now know whether Jasmine can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jasmine","Rebecca","Valentin","Paul"],"index":21956,"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 Charles knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether 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":"Janice can now know whether Charles is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Troy","Charles","Janice","Marilyn"],"index":29769,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9914317131,"difficulty":0.0085682869}
+{"premise":"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 someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jay can now know that Harold can know whether Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Roy","Jay","Donna","Harold"],"index":31754,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992895126,"difficulty":0.0007104874}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Warren does not know whether Warren's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentd knows whether (Agentb knows whether 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":"Sandy can now know whether Jina can know whether Jina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Warren","Jina","Janice","Sandy"],"index":5424,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8240503669,"difficulty":0.1759496331}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessica knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jessica can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christina","Stephanie","Michael","Jessica"],"index":47506,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994083643,"difficulty":0.0005916357}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dean's card is shown to Dean. Angel's card is shown to Dean. Jane's card is shown to Jane. Dean's card is shown to Angel. Jane's card is shown to Angel. It is publicly announced that someone picked a red card. It is publicly announced that Angel does not know whether Angel picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Dean can now know that Jane can know whether Angel picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dean","Jane","Angel"],"index":63164,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.8178350925,"difficulty":1.8178350925}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Crystal's card is shown to Robert. Robert's card is shown to Crystal. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Robert can now know whether Raymond can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Raymond","Crystal"],"index":6411,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993591905,"difficulty":0.0006408095}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Eleanor knows whether Camilla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Esther can now know that Eleanor can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eleanor","Esther","Erin","Camilla"],"index":67481,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9945018291,"difficulty":0.0054981709}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that John is not thirsty. It is publicly announced that Nick does not know whether Richard is thirsty. It is publicly announced that Richard does not know whether Nick is 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) ] Agentd knows that (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) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Richard can now know that Nick can know that Nick is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Nick","Herman","Richard"],"index":2998,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9592787623,"difficulty":0.0407212377}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doyle knows whether Shane's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Shane can now know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Rose","Doyle","Shane"],"index":14298,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993909597,"difficulty":0.0006090403}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy 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 (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Timothy can now know that William can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["William","Andrew","Timothy"],"index":51345,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990235567,"difficulty":0.0009764433}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret knows whether someone's forehead is muddy. It is publicly announced that Bret's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! 1 ] Agenta knows whether (Agentb knows 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":"Bret can now know whether Mark can know that Mark's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bret","Mark"],"index":20998,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999422431,"difficulty":0.000577569}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Gladys does not know whether Richard is thirsty. It is publicly announced that Gladys 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Gladys can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Howard","Richard","Gladys"],"index":43621,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993883371,"difficulty":0.0006116629}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Vernell's card is shown to Vernell. Ryan's card is shown to Vernell. Alice's card is shown to Vernell. Vernell's card is shown to Don. Ryan's card is shown to Don. Alice's card is shown to Ryan. Vernell's card is shown to Alice. Ryan's card is shown to Alice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 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:1,3,4 Agentb:1,3 Agentc:4 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Vernell can now know that Don can know that Alice picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vernell","Don","Ryan","Alice"],"index":32814,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9968984127,"difficulty":0.0031015873}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Curtis's card is shown to Curtis. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Curtis can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Curtis","Betty"],"index":34453,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994679093,"difficulty":0.0005320907}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Muriel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Jesus 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":["Laura","Valda","Muriel","Jesus"],"index":65224,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9958101511,"difficulty":0.0041898489}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy. It is publicly announced that Ethel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Willie can now know that Ethel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","Arthur","Willie"],"index":39812,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6739034653,"difficulty":0.3260965347}
+{"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 Donna. Donna's card is shown to Maryann. Michael's card is shown to Maryann. Donna's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Dorothy picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Maryann can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Donna","Maryann","Michael","Dorothy"],"index":34278,"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. It is publicly announced that Lisa does not know whether Lisa's forehead is muddy. It is publicly announced that Danielle 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))) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Saundra can now know that Saundra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Saundra","Lisa","William","Danielle"],"index":47086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958635569,"difficulty":0.0041364431}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Nell knows whether Sarah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Sarah can now know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dale","Sarah","Steven","Nell"],"index":31329,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9936109185,"difficulty":0.0063890815}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lori's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"John can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","William","Lori","Krystal"],"index":63934,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999507308,"difficulty":0.000492692}
+{"premise":"There are three persons. Everyone is visible 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. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas 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) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jeffrey can now know that Norman can know that Jeffrey's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Norman","Thomas"],"index":34836,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9915322661,"difficulty":0.0084677339}
+{"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 William. William's card is shown to Anthony. William's card is shown to Mary. Anthony's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Mary can know that Anthony picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Anthony","Mary"],"index":48704,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9599137902,"difficulty":0.0400862098}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy. It is publicly announced that Evelyn knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Evelyn can now know whether Stephen can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Stephen","Evelyn","Clair"],"index":16807,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7370009422,"difficulty":0.2629990578}
+{"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 Hazel is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta 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 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Sharon can now know that Brenda can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Brenda","Hazel","Sharon"],"index":47134,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9970865846,"difficulty":0.0029134154}
+{"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 Patricia is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 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) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Sam can now know that Patricia is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sam","Sherry","Patricia"],"index":59720,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9969082475,"difficulty":0.0030917525}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bobby 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 whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Bobby can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Christopher","Erica","Douglas","Bobby"],"index":24150,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992635846,"difficulty":0.0007364154}
+{"premise":"There are two 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 Joyce's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether 1)","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":"Matthew can now know whether Joyce can know whether Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Matthew","Joyce"],"index":56308,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990573525,"difficulty":0.0009426475}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry 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 (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Barry can now know whether Linda can know that Barry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barry","Linda","Mildred"],"index":56073,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943014383,"difficulty":0.0056985617}
+{"premise":"There are four persons. Everyone is visible 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 Karin knows whether Wilfred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Karlene can now know that Wilfred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karlene","Wilfred","Karin","Willie"],"index":4314,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9980377555,"difficulty":0.0019622445}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 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":"Marion can now know whether Paul can know whether Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Paul","Nellie","Marion","Bryan"],"index":19805,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992440939,"difficulty":0.0007559061}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William knows whether William is thirsty. It is publicly announced that Claudette does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows whether (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know whether Claudette can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Claudette","Robert"],"index":29450,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994607568,"difficulty":0.0005392432}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Robert's card is shown to Robert. Virginia's card is shown to Robert. Nicole's card is shown to Virginia. Robert's card is shown to Nicole. Nicole's card is shown to Nicole. Mary's card is shown to Nicole. Nicole's card is shown to Mary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:1,3,4 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know whether Virginia can know that Mary picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Virginia","Nicole","Mary"],"index":62202,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8070052862,"difficulty":0.1929947138}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mildred's card is shown to Felipe. Felipe's card is shown to Mildred. Mildred's card is shown to Mildred. Mildred'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:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Felipe can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Felipe","Mildred","Paul"],"index":47431,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99935323,"difficulty":0.00064677}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hazel's card is shown to Hazel. Kenneth's card is shown to Hazel. Kenneth's card is shown to Kenneth. Hazel's card is shown to Cindy. Kenneth's card is shown to Cindy. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Hazel can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Hazel","Kenneth","Cindy"],"index":43811,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990108013,"difficulty":0.0009891987}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luis knows whether Luis's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Darin can now know that Luis can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Darin","Luis"],"index":37375,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990371466,"difficulty":0.0009628534}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Renita's card is shown to Renita. Mary's card is shown to Renita. Mary's card is shown to Mary. Michael's card is shown to Mary. Jane's card is shown to Michael. Mary's card is shown to Jane. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:4 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether Renita can know whether Jane picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Renita","Mary","Michael","Jane"],"index":44634,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987158775,"difficulty":0.0012841225}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Leslie's card is shown to Leslie. Lawrence's card is shown to Leslie. Lawrence's card is shown to Lawrence. Leslie's card is shown to Bonnie. Bonnie's card is shown to Bonnie. Lawrence's card is shown to Kathy. Kathy's card is shown to Kathy. 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 Lawrence picked a red card. It is publicly announced that Lawrence 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))) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 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":"Lawrence can now know that Leslie can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Leslie","Lawrence","Bonnie","Kathy"],"index":14046,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994470477,"difficulty":0.0005529523}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vanessa knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! (1&2) ] (Agentb knows 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":"Alma can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vanessa","Alma"],"index":225,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994850159,"difficulty":0.0005149841}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Manuel can now know that Charles can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Manuel","Charles"],"index":39489,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9891321063,"difficulty":0.0108678937}
+{"premise":"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. It is publicly announced that Richard knows whether Natalie's forehead is muddy. It is publicly announced that Natalie 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 that (Agentb 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)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Christopher can now know that Richard can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Christopher","Richard","John","Natalie"],"index":40765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977629185,"difficulty":0.0022370815}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roy's forehead is muddy. It is publicly announced that Amy's forehead is not muddy. It is publicly announced that Roy knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Amy can now know that Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Roy","Martha","Amy"],"index":62092,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8620136976,"difficulty":0.1379863024}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Caroline's card is shown to William. Heather's card is shown to Rick. Rick's card is shown to Caroline. Rick's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:4 Agentc:2 Agentd: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:3 Agentb:4 Agentc:2 Agentd:2,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Caroline can now know that Heather picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","Rick","Caroline","Heather"],"index":12559,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9947001934,"difficulty":0.0052998066}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lea's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Lea can now know that William can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lea","William"],"index":42851,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986460805,"difficulty":0.0013539195}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Amy's card is shown to Amy. Randall's card is shown to Amy. Joan's card is shown to Amy. Amy's card is shown to Randall. Joan's card is shown to Randall. Elizabeth's card is shown to Randall. Amy's card is shown to Elizabeth. Randall's card is shown to Elizabeth. Joan's card is shown to Elizabeth. It is publicly announced that someone picked a red card. It is publicly announced that Randall does not know whether Randall picked a red card. It is publicly announced that Elizabeth picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,3,4 Agentc:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"Amy can now know whether Amy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amy","Randall","Joan","Elizabeth"],"index":7893,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9194731116,"difficulty":0.0805268884}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Keith's card is shown to Erin. Keith's card is shown to Keith. It is publicly announced that someone picked a red card. It is publicly announced that Erin does not know whether or not everyone 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 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Erin can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Erin","Keith"],"index":45040,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994592071,"difficulty":0.0005407929}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Roger does not know whether or not everyone is thirsty. It is publicly announced that Roger knows whether someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Roger can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amy","Roger"],"index":41529,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994978905,"difficulty":0.0005021095}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is muddy.","smcdel_problem":"VARS 1,2 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":"Christopher can now know whether Steven can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Christopher"],"index":53375,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993377328,"difficulty":0.0006622672}
+{"premise":"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 Ruth's forehead is muddy.","smcdel_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 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":"Arthur can now know that Arthur's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Arthur","Ruth","James"],"index":31176,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963750243,"difficulty":0.0036249757}
+{"premise":"There are 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 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":"Tiffany can now know that Peter can know that Alberto's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tiffany","Alberto","Peter"],"index":59333,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977378845,"difficulty":0.0022621155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ray does not know whether Ray's forehead is muddy. It is publicly announced that Ray does not know whether Ray's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Mamie can now know whether Natalie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Natalie","Ray","Mamie","William"],"index":27128,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992637038,"difficulty":0.0007362962}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Connie's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Debra can now know whether Gary can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Gary","Connie","Debra"],"index":48930,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958623648,"difficulty":0.0041376352}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Victoria 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) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Victoria can now know that Ryan can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ryan","Robert","Victoria"],"index":14445,"s-l":"internal-1","deberta_pred":0,"deberta_confidence":0.8370764852,"difficulty":1.8370764852}
+{"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 Lisa. Ayana's card is shown to Lisa. Isaias's card is shown to Ayana. Ayana's card is shown to Isaias. Isaias's card is shown to Isaias. 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:2,3 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 Agentc:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Isaias can now know whether Lisa can know that Lisa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Ayana","Isaias"],"index":41271,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.7676653862,"difficulty":0.2323346138}
+{"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. It is publicly announced that Richard does not know whether Jessica is thirsty. It is publicly announced that David does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Richard can know that Jessica is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Jessica","David"],"index":10972,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9471380115,"difficulty":0.0528619885}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"George can now know that Richard can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["George","Richard"],"index":56183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998960495,"difficulty":0.001039505}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Juanita is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Juanita can now know that Billy can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Juanita","Billy"],"index":21394,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9984974861,"difficulty":0.0015025139}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows that 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":"Beatrice can now know whether Edwin can know that Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Beatrice","Tina","Edwin","Jean"],"index":58940,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9709118009,"difficulty":0.0290881991}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laurie can now know that David can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tamara","David","Laurie","John"],"index":13454,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989228845,"difficulty":0.0010771155}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dominic knows whether someone's forehead is muddy. It is publicly announced that Frances 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 that (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Carolyn can now know that Frances can know whether Frances's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dominic","Carolyn","Frances"],"index":18133,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5649847984,"difficulty":0.4350152016}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Brandon can now know that Jenna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pauline","Brandon","Robert","Jenna"],"index":48913,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997516036,"difficulty":0.002483964}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angelina knows whether Angelina 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 (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":"Angelina can now know whether James can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Dianna","Angelina"],"index":48091,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.928689599,"difficulty":0.071310401}
+{"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 Lee. Ella's card is shown to Ella. Nicole's card is shown to Ella. Lee's card is shown to Nicole. Ella's card is shown to Nicole. Nicole's card is shown to Nicole. Ella's card is shown to Don. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:2,3 Agentc:1,2,3 Agentd:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lee can now know that Ella can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Ella","Nicole","Don"],"index":24497,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990599751,"difficulty":0.0009400249}
+{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Geraldine knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Lavern can now know that Geraldine can know that Lavern's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lisa","Lavern","Ike","Geraldine"],"index":11279,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8784355521,"difficulty":0.1215644479}
+{"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 Tamika is thirsty. It is publicly announced that Tamika does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Derick can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tamika","Derick","John"],"index":55975,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994250536,"difficulty":0.0005749464}
+{"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. John's card is shown to William. William's card is shown to James. John's card is shown to James. James's card is shown to Gina. It is publicly announced that someone picked a red card. It is publicly announced that John does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:1,2 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"James can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["William","John","James","Gina"],"index":58497,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.999045074,"difficulty":0.000954926}
+{"premise":"There are 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 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Amy can now know that David can know that David's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Gregory","David","Amy"],"index":31826,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984266758,"difficulty":0.0015733242}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nadine's card is shown to Joseph. Jennifer's card is shown to Michael. Jennifer's card is shown to Jennifer. Michael's card is shown to Nadine. Jennifer's card is shown to Nadine. 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 Nadine does not know whether Nadine picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:3 Agentc:3 Agentd:2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Nadine can now know whether Joseph can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Joseph","Michael","Jennifer","Nadine"],"index":23450,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994282126,"difficulty":0.0005717874}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nancy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agenta knows that 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":"Nancy can now know that Alexander can know that Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alexander","Brian","Nancy"],"index":57731,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99597013,"difficulty":0.00402987}
+{"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. Rosie's card is shown to James. James's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether someone picked a red card. It is publicly announced that James does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether 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":"Rosie can now know whether James can know whether Rosie picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Rosie","Heather"],"index":51681,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9970101118,"difficulty":0.0029898882}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows whether 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":"Jane can now know whether Nelson can know whether Nelson's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jane","Nelson","Thomas"],"index":22706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5195842385,"difficulty":0.4804157615}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacey knows whether or not everyone's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Paul can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Becky","Paul","Stacey"],"index":63845,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990472198,"difficulty":0.0009527802}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lawanda does not know whether Chris is thirsty. It is publicly announced that Chris 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 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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Lawanda can now know that Chris can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lawanda","Chris"],"index":59397,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995081425,"difficulty":0.0004918575}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] Agenta knows whether (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1&2) ] 0","hypothesis":"Betsy can now know whether William can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Betsy","William"],"index":31985,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994218349,"difficulty":0.0005781651}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Deborah can now know whether Adeline can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Adeline","George","Deborah","Lisa"],"index":11263,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9991447926,"difficulty":0.0008552074}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tamika is not thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(2) ] (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":"Tamika can now know whether Tamika is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Nancy","Tamika"],"index":26022,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9979507327,"difficulty":0.0020492673}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur does not know whether Arthur's forehead is muddy. It is publicly announced that Roseanne 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 whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Dennis can now know whether Roseanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dennis","Arthur","Roseanne"],"index":54980,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976952672,"difficulty":0.0023047328}
+{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Lee can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lee","Ronnie","Christoper","Jerry"],"index":29399,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.99894315,"difficulty":0.00105685}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Helen's card is shown to Helen. Stacie's card is shown to Stacie. It is publicly announced that someone picked a red card. It is publicly announced that Stacie picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1&2) ] 0","hypothesis":"Helen can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Helen","Stacie"],"index":65730,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9977090359,"difficulty":0.0022909641}
+{"premise":"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 Timothy's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 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) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Leah can know whether Leah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Jessica","Timothy","Leah"],"index":39655,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9933011532,"difficulty":1.9933011532}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 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":"Natalie can now know that Mary can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Natalie","Richard","Virginia","Mary"],"index":35234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956620336,"difficulty":0.0043379664}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Charles can now know that Rose can know that Charles's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Grace","Charles","Richard"],"index":57725,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984676242,"difficulty":0.0015323758}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sari can now know that Robert can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sari","David","Robert","Patricia"],"index":59036,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991782308,"difficulty":0.0008217692}
+{"premise":"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 David'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 (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":"Susie can now know whether David can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Susie","David"],"index":29573,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993946552,"difficulty":0.0006053448}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Robert does not know whether Emily is thirsty. It is publicly announced that Robert knows whether someone is thirsty. It is publicly announced that George does not know whether Emily is thirsty. It is publicly announced that Emily 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 whether (1|2|3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] (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) ] [ ! ~(Agenta knows whether 2) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Emily can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robert","Emily","George"],"index":48788,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994599223,"difficulty":0.0005400777}
+{"premise":"There are four persons. Everyone is visible 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 Margaret 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 that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Margaret can now know that Lesley can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margaret","Enrique","Lesley","Carl"],"index":21030,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992341995,"difficulty":0.0007658005}
+{"premise":"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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Dawn can now know that David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dawn","Dierdre","Jennifer","David"],"index":27880,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9845087528,"difficulty":0.0154912472}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agentb knows 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":"Marilee can now know whether Kristine can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kristine","Marilee"],"index":66155,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993952513,"difficulty":0.0006047487}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lydia does not know whether Patricia is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Patricia can now know that Marni is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lydia","Patricia","Maria","Marni"],"index":11033,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982860684,"difficulty":0.0017139316}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Grace's card is shown to Grace. Audrey's card is shown to Audrey. 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 whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Audrey can now know whether Grace can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Grace","Audrey"],"index":10953,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994420409,"difficulty":0.0005579591}
+{"premise":"There are four persons. Everyone is visible 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 Stacey's forehead is muddy. It is publicly announced that Eleanor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Rebecca can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stacey","Mara","Eleanor","Rebecca"],"index":13909,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999340117,"difficulty":0.000659883}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Laura's card is shown to Jesus. Laura's card is shown to Laura. Glen's card is shown to Glen. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 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:3 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Laura can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesus","Lisa","Laura","Glen"],"index":43644,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989963174,"difficulty":0.0010036826}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Calvin knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Un can now know that Calvin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Un","Cathy","Calvin"],"index":40025,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980242252,"difficulty":0.0019757748}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline knows whether Delores's forehead is muddy. It is publicly announced that Pauline's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentb knows 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 3) ] [ ! 2 ] 0","hypothesis":"Pauline can now know that Delores can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Deborah","Pauline","Delores"],"index":8511,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984824061,"difficulty":0.0015175939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows 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":"David can now know whether Frank can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Frank","Jessica","David"],"index":62960,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9958803654,"difficulty":0.0041196346}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stella's card is shown to Stella. Bradley's card is shown to Stella. Stella's card is shown to Bradley. It is publicly announced that someone picked a red card. It is publicly announced that Stella picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Bradley can now know whether Stella can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Stella","Bradley"],"index":55170,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9839192033,"difficulty":0.0160807967}
+{"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 James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Gregory can now know that Martha can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Gregory","Martha"],"index":67221,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989838004,"difficulty":0.0010161996}
+{"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 Zachery. Erin's card is shown to Zachery. Michael's card is shown to Erin. Naomi's card is shown to Erin. Naomi's card is shown to Naomi. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Erin can now know that Erin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Zachery","Erin","Naomi"],"index":4364,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9935411215,"difficulty":0.0064588785}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Hubert's card is shown to Paul. Paul's card is shown to Hubert. It is publicly announced that someone picked a red card. It is publicly announced that Paul picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Paul can now know whether Paul picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Paul","Eric","Jean","Hubert"],"index":11747,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9829698801,"difficulty":0.0170301199}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jay knows whether Jay's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Carol can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Catherine","Jay","Carol","Michelle"],"index":44987,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989424348,"difficulty":0.0010575652}
+{"premise":"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 Carolyn knows whether Willie's forehead is muddy. It is publicly announced that Carolyn knows whether or not everyone'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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] (Agentc knows that (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) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Willie can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carolyn","Barry","Willie"],"index":27721,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979997277,"difficulty":0.0020002723}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luke knows whether or not nobody's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Luke can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Luke"],"index":26240,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972561002,"difficulty":0.0027438998}
+{"premise":"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 someone's forehead is muddy. It is publicly announced that Norman knows whether Ann'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) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Norman can now know that Jennifer can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Kathy","Ann","Norman"],"index":39083,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990085959,"difficulty":0.0009914041}
+{"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 that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Trevor can now know whether Nicholas can know that Nicholas is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicholas","Christine","Trevor"],"index":21103,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9172155857,"difficulty":0.0827844143}
+{"premise":"There are four persons. Everyone is visible 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 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":"Victoria can now know whether Stephen can know whether Anastacia's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Victoria","Quentin","Anastacia"],"index":66018,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999317646,"difficulty":0.000682354}
+{"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 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 (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) ] [ ! 3 ] 0","hypothesis":"William can now know whether Nicola can know that William is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eileen","Nicola","Shawn","William"],"index":19218,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9704090357,"difficulty":0.0295909643}
+{"premise":"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 Cynthia knows whether Kenneth's forehead is muddy. It is publicly announced that Phyllis knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Kenneth can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","Margaret","Kenneth","Phyllis"],"index":63462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996250689,"difficulty":0.003749311}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lawrence's card is shown to Lawrence. Lawrence's card is shown to Patsy. Patsy's card is shown to Patsy. It is publicly announced that someone picked a red card. It is publicly announced that Patsy knows whether Patsy picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] 0","hypothesis":"Lawrence can now know that Patsy can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lawrence","Patsy"],"index":11241,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994391799,"difficulty":0.0005608201}
+{"premise":"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 Elizabeth's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Muoi knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (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) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Elizabeth can now know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Muoi"],"index":17515,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9755656719,"difficulty":0.0244343281}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jessica does not know whether Beatrice is thirsty.","smcdel_problem":"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 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":"Carmen can now know that Jessica is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Beatrice","Carmen","Jessica","Hector"],"index":7884,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997035265,"difficulty":0.002964735}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Opal's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Opal can now know that Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vincent","Mary","Opal","John"],"index":18803,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909015894,"difficulty":0.0090984106}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Anne does not know whether Anthony is thirsty. It is publicly announced that Anthony is not thirsty. It is publicly announced that Adele does not know whether Anne is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] (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) ] [ ! ~(3) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Anthony can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anne","Adele","Anthony"],"index":14997,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994649291,"difficulty":0.0005350709}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lela","Hilda","Daniel","Kendra"],"index":47125,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988858104,"difficulty":0.0011141896}
+{"premise":"There are two persons. Everyone is visible 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 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 2) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Carolyn can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carolyn","William"],"index":50573,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990179539,"difficulty":0.0009820461}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Camille's card is shown to Camille. Camille's card is shown to Jimmy. Jimmy's card is shown to Jimmy. Ralph's card is shown to Jimmy. Camille's card is shown to Ralph. Jimmy's card is shown to Ralph. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jimmy can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Camille","Jimmy","Ralph"],"index":2189,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9927615523,"difficulty":1.9927615523}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Richard can now know whether Brandie can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patti","Jeffrey","Richard","Brandie"],"index":52261,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993706346,"difficulty":0.0006293654}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Randal does not know whether or not everyone is thirsty. It is publicly announced that Marquis does not know whether Lynda is thirsty. It is publicly announced that Marquis does not know whether Lynda is thirsty. It is publicly announced that Lynda knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether (1|2|3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Lynda can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Marquis","Randal","Lynda"],"index":15822,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994793534,"difficulty":0.0005206466}
+{"premise":"There are two persons. Everyone is visible 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 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":"John can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Teodoro","John"],"index":6126,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988930821,"difficulty":0.0011069179}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Adam does not know whether Adam's forehead is muddy. It is publicly announced that Adam's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 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 4) ] [ ! 4 ] 0","hypothesis":"Angela can now know that Sherri can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherri","Angela","Amber","Adam"],"index":12343,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984273911,"difficulty":0.0015726089}
+{"premise":"There are three 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 Maureen's forehead is muddy. It is publicly announced that Alan 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":"Alan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Tracy","Maureen","Alan"],"index":26727,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995076656,"difficulty":0.0004923344}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Aaron can now know that Hyacinth can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Aaron","Hyacinth"],"index":48227,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9586543441,"difficulty":0.0413456559}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celina does not know whether Celina's forehead is muddy. It is publicly announced that Elaine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Celina can now know that Elaine can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elaine","Celina"],"index":28275,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986798167,"difficulty":0.0013201833}
+{"premise":"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 Kathleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(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) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(3) ] 0","hypothesis":"Tonya can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tonya","Jeremy","Kathleen","Dennis"],"index":41321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994811416,"difficulty":0.0005188584}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Derrick does not know whether William is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"William can now know that Derrick can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Derrick","William","Mariann"],"index":64907,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.99694103,"difficulty":0.00305897}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda'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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (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) ] 0","hypothesis":"Linda can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Donna","Linda"],"index":26643,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725339413,"difficulty":0.0274660587}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to Douglas. Kristy's card is shown to Douglas. Douglas's card is shown to Carl. Erma's card is shown to Kristy. It is publicly announced that someone picked a red card. It is publicly announced that Douglas does not know whether Carl picked a red card. It is publicly announced that Carl does not know whether Carl picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1 Agentc:2 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Carl can now know whether Erma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Douglas","Erma","Carl","Kristy"],"index":7479,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.9892452955,"difficulty":1.9892452955}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 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) ] [ ! ~(2) ] 0","hypothesis":"Maria can now know whether Scott can know whether Maria's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Matthew","Maria"],"index":780,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994220734,"difficulty":0.0005779266}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Holly's card is shown to Holly. Holly's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that Holly picked a red card. It is publicly announced that Holly 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 whether (1|2))","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":"Carl can now know that Holly can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Holly","Carl"],"index":12879,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994783998,"difficulty":0.0005216002}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Roslyn's card is shown to Charlene. Charlene's card is shown to Roslyn. Lorelei's card is shown to Roslyn. Charlene's card is shown to Lorelei. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Charlene can now know whether Lorelei can know whether Lorelei picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Charlene","Roslyn","Lorelei"],"index":47501,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9910178185,"difficulty":0.0089821815}
+{"premise":"There are three persons. Everyone is visible 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 everyone's forehead is muddy.","smcdel_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 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":"Dallas can now know whether Dallas's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Kathleen","Carol","Dallas"],"index":17403,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994142056,"difficulty":0.0005857944}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Marcie's card is shown to Marcie. Angela's card is shown to Angela. James's card is shown to Angela. Angela'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 James does not know whether James 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 whether 2)","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":"Marcie can now know whether Angela picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Marcie","Angela","James"],"index":23750,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9515150189,"difficulty":1.9515150189}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma knows whether Mathilde's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Virginia can now know whether Wilma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephanie","Mathilde","Virginia","Wilma"],"index":67600,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994407296,"difficulty":0.0005592704}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Lois can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Josie","Shirley","Michael","Lois"],"index":37503,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988535643,"difficulty":0.0011464357}
+{"premise":"There are three persons. Everyone is visible 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 Tonya's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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))","n_announcements":1,"pbcheck":"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":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michael","Tonya","Carmen"],"index":18707,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9990310669,"difficulty":0.0009689331}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether 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 Nicole's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agenta knows that (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)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nicole can now know that Annette can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nicole","Annette","Paul","Walter"],"index":64202,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942094088,"difficulty":0.0057905912}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Rose can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rose","Lori","Richard"],"index":16993,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990082383,"difficulty":0.0009917617}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lyn's card is shown to Stephanie. Barbara's card is shown to Barbara. Barbara's card is shown to Lyn. It is publicly announced that someone picked a red card. It is publicly announced that Lyn 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)) ] 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 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Barbara can now know whether Stephanie can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephanie","Barbara","Lyn"],"index":22888,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9991771579,"difficulty":0.0008228421}
+{"premise":"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 knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 3)","n_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":"Margaret can now know that Stephanie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Margaret","Stephanie"],"index":28809,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979222417,"difficulty":0.0020777583}
+{"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 (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":"Ernest can now know whether Joseph can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Robert","Joseph","Ernest"],"index":23987,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994587302,"difficulty":0.0005412698}
+{"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 Raymond is thirsty. It is publicly announced that Juan does not know whether William is thirsty. It is publicly announced that Juan knows whether or not nobody is thirsty. It is publicly announced that Raymond does not know whether Darlene is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] [ ! ~(Agentb knows whether 4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Darlene can now know that Raymond is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Juan","Darlene","William"],"index":39230,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997304678,"difficulty":0.002695322}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows that (Agenta knows 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":"Irene can now know that Louis can know whether Irene's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Zana","Willard","Irene"],"index":56867,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999345839,"difficulty":0.000654161}
+{"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 Norman. Norman's card is shown to Amanda. Amanda's card is shown to Joe. Norman's card is shown to George. Amanda's card is shown to George. Joe'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:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:2 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"George can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Norman","Amanda","Joe","George"],"index":57685,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993169308,"difficulty":0.0006830692}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that 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) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Tyler can now know that Jerry can know whether someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tyler","Andy","Jerry"],"index":38996,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993746877,"difficulty":0.0006253123}
+{"premise":"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 or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (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":"Agnes can now know that Jamie can know that Agnes's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Agnes","Jamie"],"index":51200,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.60395962,"difficulty":1.60395962}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Manuel does not know whether Manuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Helen can now know that Manuel can know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Manuel","Helen","Sharon"],"index":42032,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9937449098,"difficulty":0.0062550902}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Josefina does not know whether Fern is thirsty.","smcdel_problem":"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 (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Josefina can now know that Fern can know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Josefina","Linda","Fern","Lena"],"index":21410,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9968371391,"difficulty":0.0031628609}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Corey knows whether Albert's forehead is muddy. It is publicly announced that Corey'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":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Corey can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Albert","Corey"],"index":46221,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9249738455,"difficulty":0.0750261545}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim does not know whether Jim's forehead is muddy. It is publicly announced that Joleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows that (Agentc knows that (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":"Joleen can now know that Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jim","Joleen","Robert"],"index":38751,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994712472,"difficulty":0.0005287528}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kathleen's card is shown to Kathleen. Barbara's card is shown to Kathleen. Alan's card is shown to Kathleen. Barbara's card is shown to Barbara. Alan's card is shown to Alan. It is publicly announced that someone picked a red card. It is publicly announced that Barbara does not know whether Alan 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 that (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":"Barbara can now know that Alan can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kathleen","Barbara","Alan"],"index":60405,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994012117,"difficulty":0.0005987883}
+{"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. Michael's card is shown to Bobby. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Stephen can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stephen","Michael","Raymundo","Bobby"],"index":33979,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.999432981,"difficulty":0.000567019}
+{"premise":"There are three persons. Everyone is visible 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 (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":"Christopher can now know whether Grace can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Grace","Marvin","Christopher"],"index":10368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993201494,"difficulty":0.0006798506}
+{"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 Scott is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] Agenta knows whether (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! 1 ] 0","hypothesis":"Scott can now know whether Irene can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Scott","Joseph","Elenora","Irene"],"index":19137,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9968351722,"difficulty":0.0031648278}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris knows whether someone's forehead is muddy. It is publicly announced that Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] (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)) ] [ ! 1 ] 0","hypothesis":"Luther can now know that Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Doris","Gregory","Luther"],"index":66956,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6279829144,"difficulty":0.3720170856}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dorthy's card is shown to Margaret. Margaret's card is shown to Dorthy. 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 that (1|2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] 0","hypothesis":"Margaret can now know whether Dorthy can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Margaret","Dorthy"],"index":41108,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994170666,"difficulty":0.0005829334}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Willie does not know whether or not everyone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Willie can now know whether Michael can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Willie"],"index":60119,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994584918,"difficulty":0.0005415082}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Betty's card is shown to Kara. Dan's card is shown to Betty. Dan's card is shown to Dan. It is publicly announced that someone picked a red card. It is publicly announced that Dan does not know whether Betty 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 2) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Dan can now know that Dan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kara","Betty","Dan"],"index":11599,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.982637465,"difficulty":0.017362535}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bruce does not know whether Bruce's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 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) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Daniel can now know whether Bruce can know that Wm's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Bruce","Wm"],"index":52039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.966147542,"difficulty":0.033852458}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that William is thirsty. It is publicly announced that 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 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] (Agentb knows whether (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Brad can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["William","Brad"],"index":61336,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994300008,"difficulty":0.0005699992}
+{"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 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":"Alison can now know that Rex can know that Alison's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rex","Alison","Alberto","Lenard"],"index":22823,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977799058,"difficulty":0.0022200942}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tracie knows whether Tracie is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Tracie can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Garrett","Tracie","Juan","Corey"],"index":56861,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9625319242,"difficulty":0.0374680758}
+{"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 Jesus. Jesus's card is shown to Jesus. Jennifer's card is shown to Jesus. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 VALID? [ ! (1|2|3|4) ] (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jack can now know whether Jesus picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jack","Judith","Jesus","Jennifer"],"index":57714,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7983602881,"difficulty":0.2016397119}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elsa knows whether Antoinette's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Antoinette can now know whether Elsa can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Elsa","Antoinette"],"index":41735,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.912442565,"difficulty":0.087557435}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Donna's card is shown to Jonathon. Jesica's card is shown to Jonathon. Jonathon's card is shown to Benjamin. Donna's card is shown to Benjamin. Donna's card is shown to Donna. Jonathon's card is shown to Jesica. Donna's card is shown to Jesica. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:1,3 Agentc:3 Agentd:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jonathon can now know whether Jesica can know whether Jonathon picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathon","Benjamin","Donna","Jesica"],"index":22507,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9983061552,"difficulty":0.0016938448}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sean's card is shown to Sean. Randee's card is shown to Sean. Sean's card is shown to Juan. Juan's card is shown to Juan. Thomas's card is shown to Thomas. Sean's card is shown to Randee. Juan's card is shown to Randee. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:1,2 Agentc:3 Agentd:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Thomas can now know that Randee can know whether Sean picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sean","Juan","Thomas","Randee"],"index":30687,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.901070714,"difficulty":0.098929286}
+{"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 Brenda is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows whether 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":"Tammy can now know whether Brenda can know whether Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Tammy","Brenda","Michael"],"index":63031,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9991829991,"difficulty":0.0008170009}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sam's card is shown to Sam. Robert's card is shown to Sam. Heather's card is shown to Sam. Ruth's card is shown to Robert. Ruth's card is shown to Heather. Heather's card is shown to Heather. It is publicly announced that someone picked a red card. It is publicly announced that Robert picked a black card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1 Agentc:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Robert can now know that Ruth can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ruth","Sam","Robert","Heather"],"index":52637,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993846416,"difficulty":0.0006153584}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Dennis's card is shown to Lillie. Dennis's card is shown to Grace. Dennis's card is shown to Kristin. Kristin's card is shown to Kristin. It is publicly announced that someone picked a red card. It is publicly announced that Grace does not know whether Kristin picked a red card. It is publicly announced that Lillie does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Grace can now know whether Dennis picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lillie","Grace","Dennis","Kristin"],"index":1233,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.7263424397,"difficulty":0.2736575603}
+{"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 Angela. Carl's card is shown to James. James's card is shown to Carl. It is publicly announced that someone picked a red card. It is publicly announced that Angela knows whether someone picked a red card. It is publicly announced that James does not know whether Angela picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"James can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","James","Carl"],"index":49614,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9989515543,"difficulty":0.0010484457}
+{"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 Ruth. Twila's card is shown to Ruth. Jose's card is shown to Jose. Ruth's card is shown to Twila. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Twila can now know that Ruth can know whether Jose picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Jose","Twila"],"index":63432,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6110038757,"difficulty":0.3889961243}
+{"premise":"There are four persons. Everyone is visible 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 (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":"Stella can now know whether Blair can know that Chris's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stella","Lisa","Chris","Blair"],"index":57887,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994207621,"difficulty":0.0005792379}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alvin does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows that (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":"Diana can now know that Alvin can know whether Alvin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Diana","Alvin"],"index":59159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6452065706,"difficulty":0.3547934294}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marian knows whether Gordon's forehead is muddy. It is publicly announced that Gordon's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! 2 ] 0","hypothesis":"Marian can now know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Marian","Gordon"],"index":12255,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994674325,"difficulty":0.0005325675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Kathy does not know whether Grace is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Grace can now know whether Kathy can know whether Grace is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathy","James","Grace","Deidre"],"index":9372,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9988929629,"difficulty":0.0011070371}
+{"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 Alma. Andrea's card is shown to Alma. Matthew's card is shown to Matthew. Andrea's card is shown to Andrea. It is publicly announced that someone picked a red card. It is publicly announced that Andrea does not know whether Alma picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Andrea can now know whether Matthew can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alma","Matthew","Andrea"],"index":53193,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9644562602,"difficulty":0.0355437398}
+{"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. Nancy's card is shown to Janice. Johnnie's card is shown to Janice. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Janice can now know whether Nancy can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nancy","Janice","Johnnie"],"index":61395,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9811413884,"difficulty":0.0188586116}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Claud's card is shown to Claud. Claud'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 or not everyone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card. It is publicly announced that Claud knows whether or not nobody picked a red card. It is publicly announced that Claud 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)) ] (Agenta knows that (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":"Claud can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Claud","Joseph"],"index":16805,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994539618,"difficulty":0.0005460382}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Elizabeth does not know whether Malcom is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] (Agentc knows that 4)","n_announcements":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":"Jane can now know that Lindsay is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elizabeth","Malcom","Jane","Lindsay"],"index":38268,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9982697964,"difficulty":0.0017302036}
+{"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. Jose's card is shown to Justin. Pamela's card is shown to Carla. Jose's card is shown to Pamela. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carla can now know whether Justin can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Justin","Carla","Pamela","Jose"],"index":8907,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.856279552,"difficulty":0.143720448}
+{"premise":"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. It is publicly announced that Donna knows whether Gloria's forehead is muddy. It is publicly announced that Evelyn knows whether Evelyn's forehead is muddy.","smcdel_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 whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Donna can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Evelyn","Gloria","Donna"],"index":42435,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8981098533,"difficulty":1.8981098533}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alta knows whether or not nobody's forehead is muddy. It is publicly announced that Manuel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(2) ] 0","hypothesis":"Alta can now know that Manuel's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["John","Manuel","Alta"],"index":54505,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9925550818,"difficulty":0.0074449182}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kevin's card is shown to Helen. Helen's card is shown to Darrell. Darrell's card is shown to Darrell. Kevin's card is shown to Darrell. Helen's card is shown to Kevin. Darrell's card is shown to Kevin. Kevin's card is shown to Kevin. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Helen can now know whether Kevin can know whether Darrell picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Darrell","Kevin"],"index":3385,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9985161424,"difficulty":0.0014838576}
+{"premise":"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 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 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":"Leticia can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leticia","Angelica","Matthew"],"index":64328,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994879961,"difficulty":0.0005120039}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Felecia knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":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":"Felecia can now know that Kristy is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Felecia","Robert","Ronnie","Kristy"],"index":35719,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9909124374,"difficulty":0.0090875626}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Edwin's card is shown to Edwin. Edwin's card is shown to Jacob. Edwin's card is shown to Adam. Jacob's card is shown to Adam. It is publicly announced that someone picked a red card. It is publicly announced that Edwin knows whether Edwin 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) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:1 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jacob can now know whether Adam picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Edwin","Jacob","Adam"],"index":49068,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9873349667,"difficulty":0.0126650333}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alfredo does not know whether Ronald is thirsty. It is publicly announced that Alfredo does not know whether Pauline is thirsty. It is publicly announced that Ronald does not know whether Natasha is thirsty. It is publicly announced that Natasha is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] (Agentb knows whether (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether 4) ] [ ! 4 ] 0","hypothesis":"Ronald can now know whether or not everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alfredo","Ronald","Pauline","Natasha"],"index":789,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9825912118,"difficulty":0.0174087882}
+{"premise":"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 not muddy. It is publicly announced that Louis knows whether Janice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 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 (Agentd knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Maria can now know whether Richard can know that Janice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Louis","Janice","Maria","Richard"],"index":8108,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.979985714,"difficulty":0.020014286}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chris does not know whether Chris's forehead is muddy. It is publicly announced that Chris knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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 (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Chris can now know whether Martha can know that Chris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Milford","Martha","Chris"],"index":64541,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7640830278,"difficulty":0.2359169722}
+{"premise":"There are three persons. Everyone is visible 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 Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 3 ] 0","hypothesis":"Lisa can now know that Monica can know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Monica","Hester","Lisa"],"index":33342,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993900061,"difficulty":0.0006099939}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ramon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agenta knows 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":"Ramon can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ramon","Mary","Henry","George"],"index":65137,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989970326,"difficulty":0.0010029674}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Nicholas can now know whether Janice can know that Joseph's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nicholas","Janice","Barbara","Joseph"],"index":7187,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994339347,"difficulty":0.0005660653}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Rosalind's card is shown to Allan. Meredith's card is shown to Allan. Allan's card is shown to Lorraine. Rosalind's card is shown to Meredith. Meredith's card is shown to Meredith. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:2 Agentc:1,4 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:1,4 Agentb:2 Agentc:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lorraine can now know whether Allan can know whether Meredith picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rosalind","Allan","Lorraine","Meredith"],"index":60491,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9987718463,"difficulty":0.0012281537}
+{"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. Christopher's card is shown to Joseph. Mary's card is shown to Mary. Christopher's card is shown to Mary. Joseph's card is shown to Christopher. Mary's card is shown to Christopher. It is publicly announced that someone picked a red card. It is publicly announced that Joseph knows whether someone picked a red card. It is publicly announced that Christopher picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Joseph does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether Joseph picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Joseph","Mary","Christopher"],"index":12011,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.810415864,"difficulty":0.189584136}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Leanne can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Donald","Georgia","Leanne"],"index":4080,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988340735,"difficulty":0.0011659265}
+{"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 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":"Mitchell can now know that Robert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Thomas","Mitchell","Robert"],"index":41137,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953106046,"difficulty":0.0046893954}
+{"premise":"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 Barbara'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) ] [ ! (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 ] 0","hypothesis":"Barbara can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Barbara","John"],"index":37051,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987888932,"difficulty":0.0012111068}
+{"premise":"There are three persons. Everyone is visible 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 someone's forehead is muddy. It is publicly announced that Jerry knows whether Jerry's forehead is muddy. It is publicly announced that Peter knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] (Agentb knows that 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":"Robert can now know that Robert's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jerry","Robert","Peter"],"index":51547,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9967709184,"difficulty":0.0032290816}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Katherine's card is shown to Katherine. Deanne's card is shown to Katherine. Katherine's card is shown to Deanne. Deanne's card is shown to Deanne. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Deanne can now know whether Katherine can know that Katherine picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Katherine","Deanne"],"index":23924,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8876356483,"difficulty":0.1123643517}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carly knows whether Dale's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"Antione can now know that Carly can know that Carly's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Antione","Carly","Dale","Joseph"],"index":12727,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9980022311,"difficulty":0.0019977689}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emily knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (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":"Elizabeth can now know whether Emily can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Emily","Elizabeth","Denise"],"index":48054,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994377494,"difficulty":0.0005622506}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 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) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"George can now know that Stanley can know that Kathleen's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Irving","Stanley","George","Kathleen"],"index":20882,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982300401,"difficulty":0.0017699599}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether Richard is thirsty. It is publicly announced that someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Robert can now know whether Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Robert","Richard"],"index":30065,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9971810579,"difficulty":0.0028189421}
+{"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 Leonard. David's card is shown to Alfred. David's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Leonard does not know whether or not everyone picked a red card. It is publicly announced that Alfred 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"David can now know that Leonard picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leonard","Alfred","David"],"index":30210,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.946696341,"difficulty":1.946696341}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Lisa does not know whether or not everyone is thirsty. It is publicly announced that Lisa knows whether or not nobody is thirsty. It is publicly announced that Michael 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) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Lisa can now know whether Gary can know that Michael is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lisa","Gary","Michael"],"index":31956,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9927950501,"difficulty":0.0072049499}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether David's forehead is muddy. It is publicly announced that Donna knows whether David's forehead is muddy. It is publicly announced that David knows whether Derek's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (Agenta knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows whether 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":"Derek can now know that Josie can know whether Josie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Derek","David","Josie"],"index":18548,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994008541,"difficulty":0.0005991459}
+{"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. Randy's card is shown to Susan. Randy's card is shown to Randy. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether Susan picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 1) ] Agenta knows that (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":"Susan can now know that Randy can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Susan","Randy"],"index":28447,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9556232691,"difficulty":0.0443767309}
+{"premise":"There are two 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 Carlos does not know whether Lisa 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)","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":"Carlos can now know whether Lisa can know that Lisa is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lisa","Carlos"],"index":15047,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.635769248,"difficulty":1.635769248}
+{"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. It is publicly announced that Fallon 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) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Fallon can now know whether Elmer is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Fallon","Elmer","Karen","Emmanuel"],"index":55596,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9983677268,"difficulty":0.0016322732}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmen knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dane knows whether or not nobody's forehead is muddy. It is publicly announced that Dane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] (Agentb knows 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) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! ~(1) ] 0","hypothesis":"Gregory can now know that Dane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dane","Gregory","Carmen"],"index":61494,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9423854351,"difficulty":0.0576145649}
+{"premise":"There are three persons. Everyone is visible 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 3)","n_announcements":1,"pbcheck":"VARS 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":"Karen can now know whether Curtis's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Karen","Elba","Curtis"],"index":32638,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994245768,"difficulty":0.0005754232}
+{"premise":"There are four persons. Everyone is visible to others. 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 Ian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Basil can now know whether Teresa can know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Teresa","Susan","Basil","Ian"],"index":9962,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994051456,"difficulty":0.0005948544}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy. It is publicly announced that Joan does not know whether Joan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether 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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Joan can now know whether Casey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Larry","Casey","Joan"],"index":50268,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993603826,"difficulty":0.0006396174}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dixie knows whether Dixie is thirsty.","smcdel_problem":"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)","n_announcements":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":"Susan can now know whether Dixie is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Dixie","Lucille","Susan","Dorothy"],"index":27577,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9373431206,"difficulty":1.9373431206}
+{"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. Gilbert's card is shown to Gilbert. Gilbert's card is shown to Emily. It is publicly announced that someone picked a red card. It is publicly announced that Gilbert does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Gilbert can now know that Emily picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kenneth","Gilbert","Emily"],"index":28681,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9066586494,"difficulty":0.0933413506}
+{"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 Alonzo. Susan's card is shown to Susan. Tina'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:2 Agentb:2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Susan can now know that Alonzo can know that Alonzo picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Alonzo","Susan","Tina"],"index":7253,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9977232814,"difficulty":0.0022767186}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrice 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) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"George can now know whether Patrice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","George","Patrice"],"index":47196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9295451641,"difficulty":0.0704548359}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Tyrone does not know whether Kim is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] Agenta knows that (Agentb knows that 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":"Tyrone can now know that Kim can know that Kim is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tyrone","Kim","Carlos"],"index":59221,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9882740974,"difficulty":0.0117259026}
+{"premise":"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 does not know whether Debra's forehead is muddy. It is publicly announced that Debra knows whether Carlos's forehead is muddy. It is publicly announced that Carlos knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Debra can now know whether Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Debra","Carlos"],"index":20563,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6934528947,"difficulty":0.3065471053}
+{"premise":"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 muddy.","smcdel_problem":"VARS 1,2,3,4 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 (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":"Vernon can now know that Henry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vernon","Ryan","Ronald","Henry"],"index":1579,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989458919,"difficulty":0.0010541081}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Adan's card is shown to Adan. Lisa's card is shown to Adan. Amira's card is shown to Lisa. James's card is shown to James. James's card is shown to Amira. 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 Lisa does not know whether James picked a red card. It is publicly announced that James does not know whether Lisa picked a red card. It is publicly announced that James does not know whether Lisa picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2 Agentb:4 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Amira can now know whether Adan picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Adan","Lisa","James","Amira"],"index":20135,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.956515789,"difficulty":0.043484211}
+{"premise":"There are two persons. Everyone is visible 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 Denise 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 (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agenta knows whether (1&2)) ] 0","hypothesis":"Denise can now know that Wanda can know whether Wanda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Denise","Wanda"],"index":4798,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992675185,"difficulty":0.0007324815}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Buddy knows whether Buddy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 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 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":"Scott can now know that Buddy can know that Scott's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Buddy","Elizabeth","Scott"],"index":27167,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9981003404,"difficulty":0.0018996596}
+{"premise":"There are four persons. Everyone is visible 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 (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":"James can now know that Kathleen can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Thomas","Kathleen","James"],"index":13641,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9928289056,"difficulty":0.0071710944}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows that (Agenta knows 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":"Brooke can now know that Shari can know that Reginald's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Shari","Reginald","Mattie","Brooke"],"index":20857,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9976522326,"difficulty":0.0023477674}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosa does not know whether Rosa's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2)) ] 0","hypothesis":"Brittany can now know whether Rosa can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Brittany","Rosa"],"index":4465,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992726445,"difficulty":0.0007273555}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agenta knows that 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":"Valencia can now know whether Jessica can know that Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jessica","Valencia","Mark","Lena"],"index":63789,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6547693014,"difficulty":0.3452306986}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lula knows whether Jason's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (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":"Lula can now know whether Cristina can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sheri","Cristina","Jason","Lula"],"index":62113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989762306,"difficulty":0.0010237694}
+{"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 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":"Myra can now know that Flor can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Myra","Flor","Brian"],"index":14149,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9916639328,"difficulty":0.0083360672}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Rodney knows whether Rodney is thirsty. It is publicly announced that Boyd does not know whether Rodney is thirsty. It is publicly announced that Gordon does not know whether Patricia is thirsty. It is publicly announced that not everyone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentd knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Boyd can now know that Gordon can know whether Boyd is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rodney","Patricia","Boyd","Gordon"],"index":32209,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.7248321176,"difficulty":1.7248321176}
+{"premise":"There are four persons. Everyone is visible 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 Danielle 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) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Raymond can now know whether Danielle can know whether Danielle's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","Joshua","Raymond","Danielle"],"index":50419,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994501472,"difficulty":0.0005498528}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Georgia knows whether or not everyone's forehead is muddy. It is publicly announced that Georgia does not know whether Georgia's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_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":"Georgia can now know that Georgia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Georgia","Lori","Patricia"],"index":14402,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9605391026,"difficulty":0.0394608974}
+{"premise":"There are four persons. Everyone is visible 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 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 3) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"John can now know that Thomas can know that Danny's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danny","Mary","John","Thomas"],"index":57739,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9972254038,"difficulty":0.0027745962}
+{"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 William is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] 0","hypothesis":"William can now know whether Laura can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lois","Laura","William","Richard"],"index":14588,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994389415,"difficulty":0.0005610585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie does not know whether Carrie's forehead is muddy. It is publicly announced that Martha knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Martha can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Ignacio","Carrie","Martha"],"index":198,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.962931633,"difficulty":0.037068367}
+{"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 Frances. Marilyn's card is shown to Frances. Rebecca's card is shown to William. Frances's card is shown to Marilyn. William's card is shown to Marilyn. Rebecca's card is shown to Rebecca. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3 Agentb:4 Agentc:1,2 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Marilyn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frances","William","Marilyn","Rebecca"],"index":3374,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9982339144,"difficulty":0.0017660856}
+{"premise":"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 Christopher 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":"Christopher can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Karmen","Christopher"],"index":34916,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994276166,"difficulty":0.0005723834}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy. It is publicly announced that Francisco knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows 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":"Rose can now know that Ted's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Francisco","Ted","Rose"],"index":6523,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9971394539,"difficulty":0.0028605461}
+{"premise":"There are four persons. Everyone is visible 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":"Linda can now know that Patricia can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Patricia","Ronald","Anthony"],"index":38070,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999273479,"difficulty":0.000726521}
+{"premise":"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 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 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Melissa can now know whether Linda can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Linda","Melissa"],"index":33270,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994643331,"difficulty":0.0005356669}
+{"premise":"There are three persons. Everyone is visible 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 Jerome's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agenta knows that 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":"Jerome can now know that Martin can know that Jerome's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Jerome","Jennifer"],"index":46789,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966470599,"difficulty":0.0033529401}
+{"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 (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":"Ivan can now know whether Jonas can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonas","Kimberly","Ivan","Chi"],"index":30399,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992589355,"difficulty":0.0007410645}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Douglas's card is shown to David. Candy's card is shown to Douglas. Douglas's card is shown to Jennifer. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Douglas can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Candy","David","Douglas","Jennifer"],"index":24104,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993329644,"difficulty":0.0006670356}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 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":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Priscilla","Charles","Ruth","Kenneth"],"index":47917,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7280811071,"difficulty":0.2719188929}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annemarie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows whether (Agentc knows 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":"David can now know whether William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Annemarie","William"],"index":17831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6241753697,"difficulty":0.3758246303}
+{"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. Roland's card is shown to Louis. Roland's card is shown to Roland. Peter's card is shown to Roland. Roland's card is shown to Peter. It is publicly announced that someone picked a red card. It is publicly announced that Peter does not know whether Louis picked a red card. It is publicly announced that Louis does not know whether Peter picked a red card. It is publicly announced that Peter knows whether or not everyone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2,3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Roland can now know that Louis can know whether Roland picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Louis","Roland","Peter"],"index":60799,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9055093527,"difficulty":0.0944906473}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 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 ] 0","hypothesis":"Katherine can now know that Stacey can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Brandon","Katherine","Stacey"],"index":21692,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988634586,"difficulty":0.0011365414}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Heather knows whether Heather's forehead is muddy. It is publicly announced that Kathy knows whether Kathy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agenta knows whether 1) ] [ ! (Agentb knows whether 2) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Carlos can now know whether or not nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Heather","Kathy","Carlos","Elizabeth"],"index":54999,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993672967,"difficulty":0.0006327033}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1&2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Mark can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thomas","Mark"],"index":45975,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9595278502,"difficulty":0.0404721498}
+{"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 Marc is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] Agentd knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 1) ] 0","hypothesis":"Robert can now know that Neva can know whether Marc is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marc","Neva","Bill","Robert"],"index":65316,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.997212708,"difficulty":0.002787292}
+{"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 Laura. Laura's card is shown to Lillian. David's card is shown to Lillian. Lillian's card is shown to Lillian. It is publicly announced that someone picked a red card. It is publicly announced that David knows whether Lillian picked a red card. It is publicly announced that Laura does not know whether Lillian picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Laura can now know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","David","Lillian"],"index":3464,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9862018228,"difficulty":0.0137981772}
+{"premise":"There are 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 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":"Andrew can now know whether Migdalia can know whether John's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andrew","John","Migdalia"],"index":23298,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993975163,"difficulty":0.0006024837}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether Frieda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Evelyn can now know that Frieda can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Evelyn","Frieda"],"index":50902,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989653826,"difficulty":0.0010346174}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (1|2) ] 0","hypothesis":"William can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["William","Lynette"],"index":46521,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9911651015,"difficulty":0.0088348985}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Rick can now know that Mamie can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Rick","Felipe","Lea","Mamie"],"index":61192,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992889166,"difficulty":0.0007110834}
+{"premise":"There are four persons. Everyone is visible 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 Floyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentd knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Floyd can now know that Gregory can know that Ann's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Douglas","Gregory","Ann","Floyd"],"index":58134,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982625842,"difficulty":0.0017374158}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy. It is publicly announced that Rose knows whether Edward's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] Agentd knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know that Rose can know that Jesus's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rose","Edward","Jesus","Margaret"],"index":46722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942352176,"difficulty":0.0057647824}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Stella's card is shown to Stella. Stella's card is shown to Kevin. It is publicly announced that someone picked a red card. It is publicly announced that Kevin knows whether someone picked a red card. It is publicly announced that Kevin does not know whether Kevin 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 Kevin picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kevin can now know that Stella can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stella","Kevin"],"index":65596,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987057447,"difficulty":0.0012942553}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kirsten 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 that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Nancy can now know that Kirsten can know whether Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nancy","Kirsten"],"index":67518,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9267517328,"difficulty":0.0732482672}
+{"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. Michael's card is shown to Lisa. Lisa's card is shown to Michael. Michael's card is shown to Michael. It is publicly announced that someone picked a red card. It is publicly announced that everyone picked a red card.","smcdel_problem":"VARS 1,2 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":"Lisa can now know that Michael can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Lisa","Michael"],"index":33563,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9802470207,"difficulty":0.0197529793}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Cheryl's card is shown to Cheryl. Cheryl's card is shown to James. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that James knows whether Cheryl picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Cheryl can now know whether James can know that someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Cheryl","James"],"index":35992,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.99943012,"difficulty":0.00056988}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Antony does not know whether or not everyone is thirsty. It is publicly announced that Darren does not know whether Tiffany is thirsty.","smcdel_problem":"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 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 2) ] 0","hypothesis":"Antony can now know that Tiffany is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Darren","Tiffany","Antony","Nicki"],"index":8879,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9701768756,"difficulty":0.0298231244}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy. It is publicly announced that Roy 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 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Carlos can now know that Roy can know that Carlos's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roy","Carlos","James"],"index":42316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9260514975,"difficulty":0.0739485025}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl does not know whether Cheryl's forehead is muddy. It is publicly announced that Randall does not know whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (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) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Cheryl can now know that Lauren can know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cheryl","Lauren","Randall"],"index":51300,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937397242,"difficulty":0.0062602758}
+{"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 Thelma. Timothy's card is shown to Timothy. It is publicly announced that someone picked a red card. It is publicly announced that Timothy does not know whether Thelma 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":"Thelma can now know whether Thelma picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Thelma","Timothy"],"index":51541,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9703501463,"difficulty":0.0296498537}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Conrad's card is shown to Ronald. Eric's card is shown to Eric. Jean's card is shown to Jean. Jean's card is shown to Conrad. 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 whether (Agentd knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:2 Agentc:3 Agentd:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know whether Conrad can know whether Conrad picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronald","Eric","Jean","Conrad"],"index":44904,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9879806638,"difficulty":0.0120193362}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Joyce is not thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentb knows that (Agenta knows that 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":"Joyce can now know that Aubrey can know that Joyce is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Aubrey","Joyce","Kim"],"index":4918,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9921397567,"difficulty":0.0078602433}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether Dana'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 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":"Tony can now know that Dana's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Tony","Dana"],"index":51991,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9959646463,"difficulty":0.0040353537}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Felix knows whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentd knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Felix can now know that Michael can know that Linda's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Dennis","Linda","Felix"],"index":14838,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9979300499,"difficulty":0.0020699501}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Debbie can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Leonard","Patrick","Joseph","Debbie"],"index":65234,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989752769,"difficulty":0.0010247231}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet knows whether Janet's forehead is muddy.","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)","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":"Janet can now know that Allen can know that Janet's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Janet","Allen"],"index":50600,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966551065,"difficulty":0.0033448935}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether Barbara's forehead is muddy. It is publicly announced that Barbara knows whether Lawrence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 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: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":"Steven can now know that Lawrence can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Lawrence","Barbara","Greg"],"index":46359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990493655,"difficulty":0.0009506345}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Beatriz's card is shown to Patricia. Patricia's card is shown to Beatriz. Beatriz's card is shown to Beatriz. It is publicly announced that someone picked a red card. It is publicly announced that Patricia knows whether or not everyone picked a red card. It is publicly announced that Beatriz picked a black card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] (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&2)) ] [ ! ~(2) ] 0","hypothesis":"Beatriz can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Patricia","Beatriz"],"index":36658,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994636178,"difficulty":0.0005363822}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephany's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"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":"Timothy can now know that Stephany can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nadine","Stephany","Timothy"],"index":37562,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989687204,"difficulty":0.0010312796}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe knows whether someone's forehead is muddy. It is publicly announced that Guadalupe knows whether Alberta's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Alberta can now know that Lyman can know that Gary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gary","Alberta","Lyman","Guadalupe"],"index":48436,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9974478483,"difficulty":0.0025521517}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lewis's card is shown to Jeremy. Lewis's card is shown to Lewis. It is publicly announced that someone picked a red card. It is publicly announced that Lewis does not know whether or not everyone picked a red card. It is publicly announced that Jeremy knows whether Lewis picked a red card. It is publicly announced that Lewis does not know whether Jeremy picked a red card. It is publicly announced that Lewis knows whether or not nobody picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 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:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Lewis can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Lewis"],"index":45173,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994619489,"difficulty":0.0005380511}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Brad's card is shown to Linda. Linda's card is shown to Amanda. Linda's card is shown to Kevin. Linda's card is shown to Brad. Brad's card is shown to Brad. It is publicly announced that someone picked a red card. It is publicly announced that Linda does not know whether Kevin picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] Agentd knows whether (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:4 Agentb:1 Agentc:1 Agentd:1,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 3) ] 0","hypothesis":"Brad can now know whether Kevin can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Amanda","Kevin","Brad"],"index":36298,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994088411,"difficulty":0.0005911589}
+{"premise":"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 (1&2&3))","n_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":"Beth can now know whether David can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Beth","John"],"index":52767,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977972507,"difficulty":0.0022027493}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Marie knows whether Marie is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether (~(1|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":"Robert can now know whether Marie can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ruth","Robert","Marie"],"index":42116,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999461472,"difficulty":0.000538528}
+{"premise":"There are two persons. Everyone is visible 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 Margaret's forehead is muddy. It is publicly announced that Tammy knows whether Margaret's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Margaret can now know whether Tammy can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tammy","Margaret"],"index":54368,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993991852,"difficulty":0.0006008148}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Jesse knows whether Jesse is thirsty. It is publicly announced that Jesse does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Jesse can now know whether Cheree is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Cheree","Jesse"],"index":64762,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9437639117,"difficulty":0.0562360883}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarice knows whether Bobby'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)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Clarice can now know whether Bobby's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bobby","Clarice"],"index":4565,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992514253,"difficulty":0.0007485747}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows 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":"Barry can now know whether Luann can know that someone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barry","Reba","Luann"],"index":53918,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992524981,"difficulty":0.0007475019}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dan does not know whether Florence is thirsty. It is publicly announced that Edgar does not know whether Dan is thirsty. It is publicly announced that Florence does not know whether or not everyone is thirsty. It is publicly announced that Terry does not know whether Dan is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Dan can now know whether Terry can know whether Terry is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dan","Edgar","Terry","Florence"],"index":40041,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9977145195,"difficulty":0.0022854805}
+{"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 or not everyone is thirsty. It is publicly announced that Tracie knows whether someone is thirsty. It is publicly announced that Robin does not know whether Tracie is thirsty. It is publicly announced that Robin 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) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agentc knows whether 2) ] 0","hypothesis":"Andrea can now know whether Tracie can know whether Andrea is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracie","Andrea","Robin","Mercedes"],"index":22403,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9989282489,"difficulty":0.0010717511}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Billy's forehead is muddy. It is publicly announced that Gloria knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Gail can now know whether Zula can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gloria","Billy","Gail","Zula"],"index":58985,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992505908,"difficulty":0.0007494092}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy.","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 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 2) ] 0","hypothesis":"Kevin can now know that Cynthia can know that Kevin's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Cynthia","Kevin"],"index":63654,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9957362413,"difficulty":0.0042637587}
+{"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 Vincent. Gail's card is shown to Carl. John's card is shown to Gail. Vincent's card is shown to John. Carl's card is shown to John. Gail'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 Vincent does not know whether John picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:3 Agentc:4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"Gail can now know that Vincent can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vincent","Carl","Gail","John"],"index":51907,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990534186,"difficulty":0.0009465814}
+{"premise":"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 Megan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentd knows 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 4) ] 0","hypothesis":"Megan can now know that Megan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexis","Diane","Gale","Megan"],"index":2935,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9798380136,"difficulty":0.0201619864}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Gerard's card is shown to Gerard. Gerard's card is shown to Shaneka. Shaneka's card is shown to Shaneka. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":0,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:1,2 VALID? [ ! (1|2) ] 0","hypothesis":"Gerard can now know that Shaneka can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Gerard","Shaneka"],"index":35207,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988794923,"difficulty":0.0011205077}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shona knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"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":"Matthew can now know that Shona's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elvira","Matthew","Shona"],"index":55881,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998044014,"difficulty":0.001955986}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that David's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] Agenta knows whether (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"David can now know whether Melissa can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Matthew","William","Melissa"],"index":11706,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.97945261,"difficulty":0.02054739}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy. It is publicly announced that William 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 that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"William can now know that Oscar's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Oscar","Tamara","Charlotte","William"],"index":48832,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9863311052,"difficulty":0.0136688948}
+{"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 Marjorie. Marjorie's card is shown to Carol. Christina's card is shown to Carol. James's card is shown to James. Christina's card is shown to James. Marjorie's card is shown to Christina. James's card is shown to Christina. Christina's card is shown to Christina. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] (Agentc knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1,4 Agentc:3,4 Agentd:1,3,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"James can now know that Carol picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marjorie","Carol","James","Christina"],"index":33779,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9975905418,"difficulty":0.0024094582}
+{"premise":"There are four persons. Everyone is visible 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 Agnes's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Agnes can now know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Agnes","Meghan","Annabelle","Timothy"],"index":16368,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.998989284,"difficulty":0.001010716}
+{"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.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that Robert is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":1,"names":["George","Robert"],"index":60616,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6214833856,"difficulty":0.3785166144}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mary does not know whether or not everyone is thirsty.","smcdel_problem":"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 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":"Shelia can now know that Todd can know that Todd is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Todd","Shelia","Leonardo"],"index":53637,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6641151905,"difficulty":0.3358848095}
+{"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 Jessica. Jessica's card is shown to Leslie. Eliza's card is shown to Leslie. Eliza's card is shown to Eliza. It is publicly announced that someone picked a red card. It is publicly announced that Eliza does not know whether Jessica 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 (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:1,3 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] 0","hypothesis":"Eliza can now know whether Leslie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jessica","Leslie","Eliza"],"index":16746,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.966997683,"difficulty":0.033002317}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Irene's card is shown to Wanda. Wanda's card is shown to Dorothy. It is publicly announced that someone picked a red card. It is publicly announced that Irene picked a black card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Irene can now know whether Irene picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Irene","Wanda","Dorothy"],"index":28429,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9794036746,"difficulty":0.0205963254}
+{"premise":"There are four persons. Everyone is visible 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 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) ] [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Joyce can now know that Maria can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juli","Kimberley","Joyce","Maria"],"index":49293,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993414283,"difficulty":0.0006585717}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rodger knows whether Trenton's forehead is muddy.","smcdel_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)))","n_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":"Michael can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Trenton","Rodger","Michael"],"index":9646,"s-l":"forehead-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's forehead is muddy. It is publicly announced that Benjamin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 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":"Alfred can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terry","Benjamin","Robert","Alfred"],"index":4775,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987990856,"difficulty":0.0012009144}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 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) ] [ ! 4 ] 0","hypothesis":"Kimberley can now know that Aaron can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kimberley","Justin","Aaron","Karen"],"index":42008,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989725351,"difficulty":0.0010274649}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lloyd's card is shown to Lloyd. Kirk's card is shown to Lloyd. David's card is shown to David. Kirk's card is shown to Kirk. It is publicly announced that someone picked a red card. It is publicly announced that Kirk does not know whether Lloyd 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) ] Agenta knows whether (Agentc knows whether 1)","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":"Lloyd can now know whether Kirk can know whether Lloyd picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lloyd","David","Kirk"],"index":5028,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9967924953,"difficulty":0.0032075047}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Kim's card is shown to Shad. Hazel's card is shown to Shad. Kim's card is shown to Susan. Hazel's card is shown to Susan. Susan's card is shown to Hazel. Hazel's card is shown to Hazel. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3,4 Agentb:3,4 Agentc:2,4 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 1)","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":"Kim can now know whether Susan can know whether Shad picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shad","Susan","Kim","Hazel"],"index":11447,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9984813333,"difficulty":0.0015186667}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carlota knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether 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":"Ralph can now know whether Ralph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Carlota","Ralph"],"index":56722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9932649136,"difficulty":0.0067350864}
+{"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 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) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"David can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kellie","George","Suzanne","David"],"index":49166,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994584918,"difficulty":0.0005415082}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darline knows whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Darline can now know that Jose can know that Jose's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Nicole","Darline"],"index":64283,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9320924878,"difficulty":0.0679075122}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Theresa's card is shown to Theresa. Rita's card is shown to Theresa. Vincent's card is shown to Theresa. Vincent'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:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] Agentb knows that (Agenta knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Rita can now know that Theresa can know that Theresa picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Theresa","Rita","Vincent"],"index":30500,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9954946041,"difficulty":0.0045053959}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Erma's card is shown to Evelyn. Evelyn's card is shown to Carl. Carl's card is shown to Erma. 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) ] Agentc knows that (Agenta knows whether 1)","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":"Carl can now know that Gladys can know whether Gladys picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Gladys","Evelyn","Carl","Erma"],"index":29793,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9962887764,"difficulty":0.0037112236}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Andrea's card is shown to Andrea. Patricia's card is shown to Ivy. Patricia's card is shown to Vicky. Ivy's card is shown to Vicky. It is publicly announced that someone picked a red card. It is publicly announced that Andrea knows whether or not everyone picked a red card. It is publicly announced that Patricia knows whether Andrea picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] (Agentc knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ivy can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Patricia","Andrea","Ivy","Vicky"],"index":45038,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9987963438,"difficulty":0.0012036562}
+{"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 Leah. Leah's card is shown to David. It is publicly announced that someone picked a red card. It is publicly announced that Leah knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows whether (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":"Leah can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Leah","David"],"index":51235,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993909597,"difficulty":0.0006090403}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roxie knows whether someone's forehead is muddy. It is publicly announced that Roxie's forehead is muddy.","smcdel_problem":"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 whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] 0","hypothesis":"Roxie can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Roxie","John","Randy"],"index":41601,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994927645,"difficulty":0.0005072355}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Andrea does not know whether Ryan is thirsty. It is publicly announced that Ryan 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 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) ] [ ! 2 ] 0","hypothesis":"Ryan can now know that someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrea","Ryan","Frances"],"index":7791,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9995259047,"difficulty":0.0004740953}
+{"premise":"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 everyone'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:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Catherine can now know that Charles can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Charles"],"index":47626,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994776845,"difficulty":0.0005223155}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Frank does not know whether John is thirsty. It is publicly announced that everyone is thirsty. It is publicly announced that Jeri is thirsty. It is publicly announced that Jeri is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] (Agentd knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 2) ] [ ! (1&2&3&4) ] [ ! 1 ] [ ! 1 ] 0","hypothesis":"Frank can now know that John is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jeri","John","Ruby","Frank"],"index":35326,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9941514134,"difficulty":0.0058485866}
+{"premise":"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) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Clarence can now know whether Cynthia can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Clarence","Cynthia","Ruth"],"index":21542,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.95106107,"difficulty":0.04893893}
+{"premise":"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 Todd knows whether George's forehead is muddy. It is publicly announced that George knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"George can now know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Todd","George"],"index":13198,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983709455,"difficulty":0.0016290545}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Nichole's card is shown to Nichole. Paula's card is shown to Nichole. Nichole's card is shown to Paula. Paula's card is shown to Paula. Jovita's card is shown to Paula. Paula's card is shown to Jovita. 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) ] (Agentc knows whether 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":"Paula can now know whether Jovita picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kevin","Nichole","Paula","Jovita"],"index":66509,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.6119216084,"difficulty":1.6119216084}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ann does not know whether Chang is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] Agentc knows that (Agenta knows whether (~(1|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":"Ann can now know that Chang can know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Chang","Stanley","Ann"],"index":3359,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993738532,"difficulty":0.0006261468}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Mckinley's card is shown to Stephen. Lynn's card is shown to Stephen. Lewis's card is shown to Lewis. Mckinley's card is shown to Lynn. Stephen's card is shown to Lynn. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3 Agentc:1,2 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mckinley can now know that Lynn picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mckinley","Stephen","Lewis","Lynn"],"index":41155,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976524711,"difficulty":0.0023475289}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1|2|3|4) ] (Agentb knows 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":"Larry can now know whether Willie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willie","Larry","Emily","Portia"],"index":47895,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994117022,"difficulty":0.0005882978}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Harley knows whether or not nobody is thirsty. It is publicly announced that Bessie knows whether Harley 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)","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":"Bessie can now know that Harley can know that Bessie is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bessie","Harley"],"index":6668,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9954263568,"difficulty":0.0045736432}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Mark knows whether someone is thirsty. It is publicly announced that Gloria knows whether or not nobody is thirsty. It is publicly announced that Gloria 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 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 (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Gloria can now know that Mark can know whether Gloria is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gloria","Mark"],"index":66339,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.904297471,"difficulty":0.095702529}
+{"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 John is thirsty. It is publicly announced that Linda does not know whether John is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd 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:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 3) ] [ ! ~(Agentd knows whether 3) ] 0","hypothesis":"Douglas can now know whether John can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Pam","Douglas","John","Linda"],"index":4172,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9914214015,"difficulty":0.0085785985}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys knows whether Gladys's forehead is muddy.","smcdel_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)","n_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":"Gladys can now know whether Herman can know that Herman's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herman","Jennifer","Gladys"],"index":38384,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9889166355,"difficulty":1.9889166355}
+{"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 Joseph. Joanne's card is shown to Joseph. Joseph's card is shown to Christopher. Christopher's card is shown to Christopher. Joanne's card is shown to Christopher. Christopher's card is shown to Joanne. Joanne'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:1,2,3 Agentc:2,3 VALID? [ ! (1|2|3) ] (Agentb knows whether (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,2,3 Agentc:2,3 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":1,"names":["Joseph","Christopher","Joanne"],"index":20428,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.993252337,"difficulty":1.993252337}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy. It is publicly announced that Russell does not know whether Russell's forehead is muddy. It is publicly announced that Dixie does not know whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth knows whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Dixie can now know whether Russell's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Russell","Elizabeth","David","Dixie"],"index":28544,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989278913,"difficulty":0.0010721087}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether Hershel's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that (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":"Hershel can now know that Lewis can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lewis","Hershel","Danielle"],"index":49748,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.993614018,"difficulty":0.006385982}
+{"premise":"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 does not know whether or not everyone's forehead is muddy. It is publicly announced that Juan knows whether Ronald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta: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":"Ronald can now know that Juan can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Juan","Darlene","Millicent","Ronald"],"index":33273,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990296364,"difficulty":0.0009703636}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ricky does not know whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know whether Ricky can know that nobody is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ricky","Joseph","John"],"index":21280,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993316531,"difficulty":0.0006683469}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nolan knows whether Rochelle's forehead is muddy. It is publicly announced that Rochelle 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 whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Rochelle can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rochelle","Nolan"],"index":46155,"s-l":"forehead-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 is thirsty. It is publicly announced that Madelyn knows whether someone is thirsty. It is publicly announced that Marylou knows whether Marylou 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)","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":"Madelyn can now know that Marylou can know that Marylou is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marylou","Madelyn"],"index":16443,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.95558393,"difficulty":0.04441607}
+{"premise":"There are four persons. Everyone is visible 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) ] [ ! 1 ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know that Leonardo's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jessica","Nancy","John","Leonardo"],"index":28050,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9966358542,"difficulty":0.0033641458}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 2 ] 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) ] [ ! 2 ] 0","hypothesis":"Katie can now know that Barbara can know whether Katie's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Katie","Barbara","Darren"],"index":12536,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994670749,"difficulty":0.0005329251}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Heather's card is shown to Nicholas. James's card is shown to James. It is publicly announced that someone picked a red card. It is publicly announced that Heather does not know whether Nicholas picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Heather can now know that Heather picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Heather","Nicholas","James"],"index":33594,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9825012088,"difficulty":0.0174987912}
+{"premise":"There are four persons. Everyone is visible 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 Barry's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] Agentb knows 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) ] [ ! (Agentd knows whether 1) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Dewayne can now know whether Leola can know whether Barry's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barry","Dewayne","Leola","Christopher"],"index":23336,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994140863,"difficulty":0.0005859137}
+{"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 (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":"Anthony can now know whether Mitchell can know whether someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mitchell","William","Ben","Anthony"],"index":57843,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9993053675,"difficulty":0.0006946325}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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 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":"David can now know whether Susan can know whether Wilma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Susan","Tamiko","Wilma"],"index":10319,"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 Kelly knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Kelly can now know whether Norman can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norman","Nancy","Florine","Kelly"],"index":38420,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999260366,"difficulty":0.000739634}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Coleen does not know whether Coleen's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Diane does not know whether Diane's forehead is muddy. It is publicly announced that Amanda knows whether Coleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agenta knows whether (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Coleen can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Coleen","Diane","Amanda"],"index":452,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8667322993,"difficulty":0.1332677007}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows whether (Agenta knows 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":"Elaine can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Elaine","Kenneth"],"index":11260,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994268417,"difficulty":0.0005731583}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Patricia can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["James","Patricia","Robert","Carl"],"index":31190,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7141662836,"difficulty":0.2858337164}
+{"premise":"There are three persons. Everyone is visible 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's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Alma can now know whether Velma's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wayne","Alma","Velma"],"index":43068,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994775653,"difficulty":0.0005224347}
+{"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. John's card is shown to Roger. Kelly's card is shown to John. Roger's card is shown to John. Kelly'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 Agentb:3 Agentc:1,2 Agentd:1,4 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 Agentb:3 Agentc:1,2 Agentd:1,4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Kelly can know that everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Roger","John","Mary"],"index":34255,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9988161325,"difficulty":0.0011838675}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Misty's forehead is muddy. It is publicly announced that Gregory knows whether Misty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Bertha can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bertha","Misty","Pete","Gregory"],"index":64075,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994949102,"difficulty":0.0005050898}
+{"premise":"There are four persons. Everyone is visible 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 Alyssa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 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) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Nadine can now know that Alyssa can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alyssa","Steven","Charles","Nadine"],"index":13213,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989293218,"difficulty":0.0010706782}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joe knows whether Joe's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 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) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Ronald can now know that Thomas can know that Joe's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joe","Thomas","Ronald","John"],"index":48774,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9977827668,"difficulty":0.0022172332}
+{"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 Joshua is not thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(2) ] Agentc knows that (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":"Evelyn can now know that Joshua can know that everyone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Joshua","Evelyn","Edward"],"index":39188,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9974350333,"difficulty":0.0025649667}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teri knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows 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":"Marcy can now know that Giovanni can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Teri","Marcy","Giovanni"],"index":63936,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989668131,"difficulty":0.0010331869}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler does not know whether Tyler's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marion can now know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ronald","Tyler","Patrick","Marion"],"index":32830,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992398024,"difficulty":0.0007601976}
+{"premise":"There are four persons. Everyone is visible 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 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) ] 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 4) ] 0","hypothesis":"Joseph can now know whether Raymond can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ernest","Jerry","Joseph","Raymond"],"index":20295,"s-l":"forehead_mirror-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) ] (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":"Jermaine can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Barbara","Jermaine","Robin","Anne"],"index":58165,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984120131,"difficulty":0.0015879869}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! (1&2) ] 0","hypothesis":"Robert can now know that Candy can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Candy"],"index":52113,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9727023244,"difficulty":0.0272976756}
+{"premise":"There are three persons. Everyone is visible 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 Nicole knows whether someone's forehead is muddy. It is publicly announced that Nicole knows whether or not nobody's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"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 that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] [ ! (1|2|3) ] 0","hypothesis":"Peggy can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Nicole","Peggy","Jennifer"],"index":55296,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.98814255,"difficulty":0.01185745}
+{"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. Linda's card is shown to Linda. It is publicly announced that someone picked a red card. It is publicly announced that Steven knows whether someone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta: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":"Steven can now know whether Linda can know whether someone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Steven","Linda"],"index":22160,"s-l":"explicit-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 Britney does not know whether or not everyone's forehead is muddy. It is publicly announced that Sanford'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 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Sanford can now know that Britney's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Britney","Sanford"],"index":7964,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.705057621,"difficulty":1.705057621}
+{"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 Michael. Frank's card is shown to Michael. Elizabeth's card is shown to Bridget. Bridget's card is shown to Frank. Frank's card is shown to Frank. It is publicly announced that someone picked a red card. It is publicly announced that Frank picked a black card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentb knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,4 Agentb:2 Agentc:3,4 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Elizabeth can now know that Bridget can know that Frank picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Elizabeth","Bridget","Frank"],"index":23901,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.98470819,"difficulty":0.01529181}
+{"premise":"There are 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 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":"Raymond can now know that Carmelo can know whether Tanisha's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Carmelo","Tanisha"],"index":18514,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993562102,"difficulty":0.0006437898}
+{"premise":"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 knows whether someone's forehead is muddy. It is publicly announced that Erin 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 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":"Erin can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erin","Jaime"],"index":4551,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9875178933,"difficulty":0.0124821067}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] (Agentd knows whether (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Steven can now know whether or not nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rose","Jorge","Thomasina","Steven"],"index":66691,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9992579818,"difficulty":0.0007420182}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1&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":"Lyle can now know that Nona can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nona","Lyle","Richard","Rodney"],"index":19578,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9862282276,"difficulty":0.0137717724}
+{"premise":"There are two persons. Everyone is visible 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 Anne'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 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":"Rita can now know that Anne can know that Rita's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anne","Rita"],"index":48707,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9984790683,"difficulty":0.0015209317}
+{"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 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) ] [ ! ~(Agentd knows whether 2) ] 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) ] [ ! ~(Agentd knows whether 2) ] 0","hypothesis":"Arthur can now know that Anthony can know whether Arthur is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charlie","Anthony","Charles","Arthur"],"index":14931,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.6694982052,"difficulty":0.3305017948}
+{"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 Maria. It is publicly announced that someone picked a red card. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Christine can now know whether Michael can know whether Michael picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christine","Michael","Maria"],"index":63735,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9980864525,"difficulty":0.0019135475}
+{"premise":"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 3)","n_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":"Geneva can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Geneva","James","Robert"],"index":3390,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9222339988,"difficulty":0.0777660012}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Wade's card is shown to Wade. Donna's card is shown to Wade. Donna's card is shown to Donna. Wade's card is shown to Bonnie. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wade can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Wade","Donna","Bonnie"],"index":41026,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994043112,"difficulty":0.0005956888}
+{"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 Daisy. David's card is shown to David. Robert's card is shown to David. David'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:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:3,4 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Daisy can now know that Robert picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daisy","Arthur","David","Robert"],"index":487,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9976020455,"difficulty":0.0023979545}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Lydia's card is shown to Jonathan. Jonathan's card is shown to Ann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta: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:3 Agentb:1 VALID? [ ! (1|2|3) ] 0","hypothesis":"Ann can now know whether Jonathan can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jonathan","Ann","Lydia"],"index":26553,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993758798,"difficulty":0.0006241202}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy. It is publicly announced that Pamela 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) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"John can now know that Pamela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Allan","John"],"index":40811,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9884323478,"difficulty":0.0115676522}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard does not know whether Lynn is thirsty. It is publicly announced that Lynn is not thirsty. It is publicly announced that Lynn does not know whether Richard is thirsty. It is publicly announced that Richard knows 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 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Richard can now know whether Allen can know whether Richard is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Lynn","Allen"],"index":60129,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9988002777,"difficulty":1.9988002777}
+{"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 Larry. Larry's card is shown to Larry. Jamie's card is shown to Larry. Clarence's card is shown to Jamie. Helen's card is shown to Jamie. Helen's card is shown to Helen. It is publicly announced that someone picked a red card. It is publicly announced that Helen picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3 Agentb:1,4 Agentc:4 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Clarence can now know that Jamie can know that Clarence picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Clarence","Larry","Jamie","Helen"],"index":57423,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9872034192,"difficulty":0.0127965808}
+{"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 Mary is thirsty. It is publicly announced that Mary does not know whether Hung is thirsty.","smcdel_problem":"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) ] (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 3) ] [ ! ~(Agentc knows whether 4) ] 0","hypothesis":"Mary can now know whether Hung is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Denise","Mary","Hung"],"index":3653,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9978468418,"difficulty":0.0021531582}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Sheryl's card is shown to Sheryl. Lee's card is shown to Sheryl. Richard's card is shown to Richard. Lee's card is shown to Richard. It is publicly announced that someone picked a red card. It is publicly announced that Sheryl knows whether or not nobody picked a red card. It is publicly announced that not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,4 Agentb:3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Frank can now know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Sheryl","Frank","Richard","Lee"],"index":18261,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993352294,"difficulty":0.0006647706}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Janice's card is shown to Janice. Linda's card is shown to Janice. Patricia's card is shown to Janice. Patricia's card is shown to Jennifer. Janice's card is shown to Linda. Janice's card is shown to Patricia. It is publicly announced that someone picked a red card. It is publicly announced that Jennifer does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 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)) ] Agenta knows that (Agentb knows whether 4)","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":"Janice can now know that Jennifer can know whether Patricia picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Janice","Jennifer","Linda","Patricia"],"index":36052,"s-l":"explicit-1","deberta_pred":0,"deberta_confidence":0.8984212875,"difficulty":1.8984212875}
+{"premise":"There are two persons. Everyone is visible 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 Rodney's forehead is muddy. It is publicly announced that Rodney knows whether Ryan'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 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) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Ryan can now know whether Rodney can know whether or not everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rodney","Ryan"],"index":38521,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9992897511,"difficulty":0.0007102489}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Michele's card is shown to Sandra. Arthur's card is shown to Sandra. Michele's card is shown to Michele. Sandra's card is shown to Arthur. It is publicly announced that someone picked a red card. It is publicly announced that Michele does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:2 Agentc:1 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Michele can now know whether Arthur picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Michele","Arthur"],"index":40774,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9052972198,"difficulty":0.0947027802}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laverne knows whether Billy's forehead is muddy. It is publicly announced that Laverne 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)","n_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":"Billy can now know whether Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Dale","Billy","Laverne"],"index":4381,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992241859,"difficulty":0.0007758141}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta 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:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Karen can now know that Michael can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Michael","Adam"],"index":28368,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988976717,"difficulty":0.0011023283}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentd knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Genevieve can now know whether Lori can know whether Genevieve's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Steven","Paul","Lori","Genevieve"],"index":38674,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994485974,"difficulty":0.0005514026}
+{"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 Judith. Barbara's card is shown to Judith. Fay's card is shown to Judith. Fay's card is shown to Barbara. Barbara's card is shown to Fay. It is publicly announced that someone picked a red card. It is publicly announced that Martin does not know whether Judith picked a red card. It is publicly announced that Martin does not know whether or not everyone picked a red card. It is publicly announced that Judith knows whether Fay picked a red card. It is publicly announced that Barbara does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agenta knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Judith can now know whether Martin picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judith","Martin","Barbara","Fay"],"index":43655,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9560236931,"difficulty":0.0439763069}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Joseph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta: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":"Frankie can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Abel","Joseph","Frankie"],"index":45894,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9427005053,"difficulty":0.0572994947}
+{"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 or not everyone is thirsty. It is publicly announced that Peter does not know whether Barbara is thirsty. It is publicly announced that Barbara knows whether or not everyone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Peter can now know that Barbara is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Barbara","Peter","James"],"index":59891,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9347669482,"difficulty":0.0652330518}
+{"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 Greg. Cynthia's card is shown to Sharon. Cynthia's card is shown to Gregory. Sharon's card is shown to Gregory. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:3 Agentb:1 Agentc:1,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Cynthia can now know that Sharon can know that nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cynthia","Greg","Sharon","Gregory"],"index":10425,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990404248,"difficulty":0.0009595752}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria knows whether Leo's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agentc knows that (1|2|3))","n_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":"Kimberly can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Leo","Gloria","Kimberly"],"index":61835,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994434714,"difficulty":0.0005565286}
+{"premise":"There are two persons. Everyone is visible 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. It is publicly announced that Dennis'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|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":"Justin can now know that Dennis can know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Dennis","Justin"],"index":6396,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9990021586,"difficulty":0.0009978414}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Jose's card is shown to Jose. Billy's card is shown to Jose. Tommie's card is shown to Tommie. Billy's card is shown to Tommie. Jose's card is shown to Billy. Tommie's card is shown to Billy. It is publicly announced that someone picked a red card. It is publicly announced that Jose knows whether someone picked a red card. It is publicly announced that Billy picked a red card. It is publicly announced that someone picked a red card. It is publicly announced that Jose does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,3 Agentb:2,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Tommie can now know whether Billy picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jose","Tommie","Billy"],"index":20867,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.8794214129,"difficulty":0.1205785871}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ellen does not know whether Frank 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|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":"Ada can now know whether someone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Frank","Ellen","Ada"],"index":47865,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994131327,"difficulty":0.0005868673}
+{"premise":"There are three persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Samantha's card is shown to Kathleen. Anna's card is shown to Samantha. Samantha's card is shown to Anna. It is publicly announced that someone picked a red card. It is publicly announced that Kathleen knows whether someone picked a red card. It is publicly announced that Samantha does not know whether Kathleen picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2 Agentb:3 Agentc:2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Kathleen can now know that nobody picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathleen","Samantha","Anna"],"index":61419,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.9990296364,"difficulty":0.0009703636}
+{"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 (1&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 everyone is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Dorothy","Earl"],"index":55347,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.998927176,"difficulty":0.001072824}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Alonzo does not know whether or not everyone is thirsty. It is publicly announced that Alonzo does not know whether Ronald is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 2) ] Agentb knows 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)) ] [ ! ~(Agenta knows whether 2) ] 0","hypothesis":"Ronald can now know that Alonzo can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Alonzo","Ronald"],"index":27476,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9994963408,"difficulty":0.0005036592}
+{"premise":"There are two 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 someone is thirsty. It is publicly announced that someone is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Margie can now know whether Paul is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margie","Paul"],"index":25745,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.9867396355,"difficulty":1.9867396355}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that James knows whether James is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Joan can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patrick","Joan","James"],"index":22200,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9989354014,"difficulty":0.0010645986}
+{"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. Jessica's card is shown to Aurea. 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 Jessica does not know whether Deborah picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(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 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 1) ] 0","hypothesis":"Deborah can now know that someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Deborah","Jessica","Aurea"],"index":15348,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994602799,"difficulty":0.0005397201}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Michelle is thirsty. It is publicly announced that Gregory 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 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":"Rafael can now know that nobody is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rafael","Michelle","Enrique","Gregory"],"index":28716,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9990497231,"difficulty":0.0009502769}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene's forehead is 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 (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) ] [ ! ~(3) ] 0","hypothesis":"Cory can now know that Eugene can know whether Dale's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cory","Elizabeth","Eugene","Dale"],"index":43992,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.999425292,"difficulty":0.000574708}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Karen's card is shown to Karen. Wallace's card is shown to Karen. Harold's card is shown to Karen. Harold's card is shown to Billie. Karen's card is shown to Wallace. Karen's card is shown to Harold. It is publicly announced that someone picked a red card. It is publicly announced that Billie 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)) ] Agentd knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,3,4 Agentb:4 Agentc:1 Agentd:1 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Harold can now know that Karen can know that Karen picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Karen","Billie","Wallace","Harold"],"index":63147,"s-l":"explicit-0","deberta_pred":0,"deberta_confidence":0.6117781401,"difficulty":0.3882218599}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Reginald's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Ruby can now know that Reginald can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ruby","Reginald"],"index":62626,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989832044,"difficulty":0.0010167956}
+{"premise":"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 or not everyone's forehead is muddy. It is publicly announced that Lawrence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Lawrence can now know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lawrence","Teresa","Lucia"],"index":4288,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807016253,"difficulty":0.0192983747}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Karin knows whether someone is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Jack can now know that Constance can know that Karin is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Constance","Jack","Karin"],"index":52002,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.9979711175,"difficulty":0.0020288825}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that George is not thirsty. It is publicly announced that George does not know whether Maria is thirsty. It is publicly announced that Donna does not know whether Roger is thirsty. It is publicly announced that Donna does not know whether Roger is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] Agentc knows whether (Agentd knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agenta knows whether 4) ] [ ! ~(Agenta knows whether 4) ] 0","hypothesis":"George can now know whether Roger can know that Donna is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Maria","George","Roger"],"index":42701,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.9803532362,"difficulty":0.0196467638}
+{"premise":"There are four persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Percy knows whether Percy's forehead is muddy. It is publicly announced that Bobbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] Agenta knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Percy can now know that Norma can know whether Hilary's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Percy","Norma","Bobbie","Hilary"],"index":11182,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994138479,"difficulty":0.0005861521}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Ernesto does not know whether John 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 John 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) ] [ ! ~(Agentc knows whether 2) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 2) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows 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":"Alice can now know whether Ernesto can know that someone is thirsty.","setup":"internal","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Alice","John","Ernesto","Robert"],"index":32075,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.999471128,"difficulty":0.000528872}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony's forehead is muddy. It is publicly announced that Anthony knows whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 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:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Teresa can now know whether Anthony can know whether Teresa's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Reid","Teresa","Anthony"],"index":22225,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9994605184,"difficulty":0.0005394816}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Ryan's card is shown to Randy. Ryan's card is shown to Ryan. David's card is shown to Ryan. It is publicly announced that someone picked a red card. It is publicly announced that Randy does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2 Agentb:2,4 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Ryan can now know that everyone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Randy","Ryan","Anne","David"],"index":61363,"s-l":"explicit-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). Rosemarie's card is shown to Rosemarie. Brandon's card is shown to Rosemarie. Rosemarie's card is shown to Brandon. It is publicly announced that someone picked a red card. It is publicly announced that Brandon 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&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":"Brandon can now know whether Rosemarie can know whether or not everyone picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rosemarie","Brandon"],"index":63013,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.6401367188,"difficulty":0.3598632812}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Richard knows whether Richard is thirsty.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 Agentd:4 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 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 2) ] 0","hypothesis":"Richard can now know that Richard is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marie","Richard","Christine","Donald"],"index":5478,"s-l":"internal-0","deberta_pred":0,"deberta_confidence":0.7930884957,"difficulty":0.2069115043}
+{"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 (~(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":"Jennifer can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ginger","Jennifer","Steven"],"index":23814,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983512163,"difficulty":0.0016487837}
+{"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. Joann's card is shown to Carol. Jerry's card is shown to Joann. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2 Agentb:3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Carol can now know whether Joann can know that Jerry picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Carol","Joann","Jerry"],"index":21290,"s-l":"explicit-0","deberta_pred":1,"deberta_confidence":0.9180250168,"difficulty":1.9180250168}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Dalton does not know whether Lindsay is thirsty. It is publicly announced that Lindsay does not know whether Dalton is thirsty. It is publicly announced that Ricardo does not know whether or not everyone is thirsty. It is publicly announced that Ricardo is thirsty.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1 Agentb:2 Agentc:3 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 1) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] (Agentb knows 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) ] [ ! ~(Agenta knows whether 3) ] [ ! ~(Agentb knows whether (1&2&3)) ] [ ! 2 ] 0","hypothesis":"Ricardo can now know that Ricardo is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Lindsay","Ricardo","Dalton"],"index":47863,"s-l":"internal-1","deberta_pred":1,"deberta_confidence":0.6813864112,"difficulty":0.3186135888}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Melvin's card is shown to Malika. Gary's card is shown to Malika. Malika's card is shown to Melvin. Gary's card is shown to Gary. It is publicly announced that someone picked a red card.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3 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:2,3 Agentb:1 Agentc:3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Malika can now know whether Gary can know whether or not nobody picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Malika","Melvin","Gary","Leonora"],"index":24341,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9993553758,"difficulty":0.0006446242}
+{"premise":"There are two persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Barbara's card is shown to Keri. Keri's card is shown to Barbara. It is publicly announced that someone picked a red card. It is publicly announced that Keri does not know whether or not everyone picked a red card.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether (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":"Barbara can now know whether someone picked a red card.","setup":"explicit","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Keri","Barbara"],"index":50572,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9994499087,"difficulty":0.0005500913}
+{"premise":"There are four persons. Everyone is visible to others. Each person draws a card, face unrevealed (red or black). Eura's card is shown to Deborah. Deborah's card is shown to David. Eura's card is shown to David. David's card is shown to Nellie. Deborah's card is shown to Eura. Nellie's card is shown to Eura. It is publicly announced that someone picked a red card. It is publicly announced that Eura does not know whether Eura picked a red card. It is publicly announced that Deborah knows whether or not nobody picked a red card. It is publicly announced that Nellie 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) ] Agenta knows whether (Agentc knows whether 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":"Deborah can now know whether Nellie can know whether Eura picked a red card.","setup":"explicit","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Deborah","David","Nellie","Eura"],"index":67249,"s-l":"explicit-1","deberta_pred":1,"deberta_confidence":0.9989263415,"difficulty":0.0010736585}
+{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Erin can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["William","Erin","Harold"],"index":28518,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990215302,"difficulty":0.0009784698}
+{"premise":"There are four persons. Everyone is visible 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.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:1,2,3,4 Agentb:1,2,3,4 Agentc:1,2,3,4 Agentd:1,2,3,4 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:1,2,3,4 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":"Hazel can now know that Mildred's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":4,"label":0,"names":["James","Hazel","Daniel","Mildred"],"index":26626,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9982313514,"difficulty":0.0017686486}
+{"premise":"There are three persons. Everyone is visible 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 William'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 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":"Donald can now know whether Freddie can know that William's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Freddie","William","Donald"],"index":62477,"s-l":"forehead_mirror-1","deberta_pred":1,"deberta_confidence":0.9993951321,"difficulty":0.0006048679}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether 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 (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Anthony can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Anthony","Pamela"],"index":27328,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989575148,"difficulty":0.0010424852}
+{"premise":"There are three persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:1,2,3 Agentb:1,2,3 Agentc:1,2,3 VALID? [ ! (1|2|3) ] 0","hypothesis":"Priscilla can now know that Patsy can know that everyone's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anna","Priscilla","Patsy"],"index":47300,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9988749623,"difficulty":0.0011250377}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica'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 (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Monica can now know that Vanessa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Vanessa","Gabriela","Monica","Bonnie"],"index":49513,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994744658,"difficulty":0.0005255342}
+{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone is thirsty. It is publicly announced that Angela knows whether or not everyone is thirsty. It is publicly announced that Calvin is thirsty.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1 Agentb:2 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Angela can now know that Angela is thirsty.","setup":"internal","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Calvin","Angela"],"index":44563,"s-l":"internal-0","deberta_pred":1,"deberta_confidence":0.8401734233,"difficulty":1.8401734233}
+{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ashley knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jason can now know that Richard can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jason","Richard","Ashley","Maria"],"index":5435,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996137917,"difficulty":0.003862083}
+{"premise":"There are two persons. Everyone is visible to others. There is a mirror in the room. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda's forehead is not muddy. It is publicly announced that Daniella knows whether Daniella's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:1,2 Agentb:1,2 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Linda can now know that nobody's forehead is muddy.","setup":"forehead_mirror","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Linda","Daniella"],"index":45581,"s-l":"forehead_mirror-0","deberta_pred":0,"deberta_confidence":0.9989473224,"difficulty":0.0010526776}