diff --git "a/data/test-forehead.jsonl" "b/data/test-forehead.jsonl"
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+++ /dev/null
@@ -1,932 +0,0 @@
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether or not everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Alice can now know whether Christine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alice","Christine"],"index":35351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994251728,"difficulty":0.0005748272}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michael","Phillip"],"index":12191,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9109317064,"difficulty":0.0890682936}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine knows whether someone's forehead is muddy. It is publicly announced that Vanessa does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Vanessa can now know that Catherine can know whether Vanessa's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Vanessa","Catherine"],"index":25024,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991545677,"difficulty":0.0008454323}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether Kimberly's forehead is muddy. It is publicly announced that Elizabeth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Elizabeth can now know that Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kimberly","Elizabeth"],"index":36753,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940788746,"difficulty":0.0059211254}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie does not know whether or not everyone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"William can now know whether Thomas can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Thomas","Rodney","William","Stephanie"],"index":32078,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9735162258,"difficulty":0.0264837742}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Betty can now know whether Kimberly can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Betty","Kimberly","Kevin"],"index":50622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9612755775,"difficulty":0.0387244225}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred knows whether Steve's forehead is muddy. It is publicly announced that Willie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Steve can now know that Alfred can know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alfred","Sara","Steve","Willie"],"index":67681,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5743825436,"difficulty":0.4256174564}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agenta knows that (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Justin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Justin","Mark","Jeffrey"],"index":39374,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997492433,"difficulty":0.0002507567}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether Eric's forehead is muddy. It is publicly announced that Eric does not know whether Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Marsha can now know that William can know that Marsha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Marsha","William","Eric"],"index":19822,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958395958,"difficulty":0.0041604042}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Dora can now know whether Thomas can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Eileen","Dora","Thomas"],"index":43067,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997739196,"difficulty":0.0002260804}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deloise knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Deloise can now know whether Deloise's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cody","Deloise","Jennifer"],"index":25937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.829285562,"difficulty":0.170714438}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Barbara can now know that Stephen can know that Stephen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Barbara","Stephen","Tara"],"index":53062,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9960029721,"difficulty":0.0039970279}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Lee","Joann"],"index":34682,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997795224,"difficulty":0.0002204776}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia knows whether or not everyone's forehead is muddy. It is publicly announced that Anita does not know whether Anita's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Patricia can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alexis","Patricia","Mario","Anita"],"index":31382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8408505321,"difficulty":0.1591494679}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mark can now know that Taryn can know whether Sam's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Taryn","Mark","Sam","Dorothy"],"index":16620,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996221066,"difficulty":0.0003778934}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danny knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"James can now know that Kimberly can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kimberly","James","Danny"],"index":6061,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992602468,"difficulty":0.0007397532}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Betty can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Frank","Betty"],"index":27958,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978913665,"difficulty":0.0021086335}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Chad does not know whether Chad's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2&3&4) ] 0","hypothesis":"Nicholas can now know whether Nicholas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Juanita","Chad","Richard","Nicholas"],"index":66864,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9883298874,"difficulty":0.0116701126}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco's forehead is not muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Francisco can now know that Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joan","Francisco","Monty"],"index":8088,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992434144,"difficulty":0.007565856}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Linda can now know that Jackie can know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Elizabeth","Jackie","Linda"],"index":15537,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996046424,"difficulty":0.0003953576}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christy knows whether someone's forehead is muddy. It is publicly announced that Carolyn knows whether Christy's forehead is muddy. It is publicly announced that Rob does not know whether Rob's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Rob can now know whether Christy can know whether Christy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Rob","Christy"],"index":40039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5623679161,"difficulty":0.4376320839}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy. It is publicly announced that Frank knows whether Dianne's forehead is muddy. It is publicly announced that Bryan does not know whether Bryan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Frank can now know whether John can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dianne","Frank","Bryan","John"],"index":3641,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997127652,"difficulty":0.0002872348}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Gina can now know whether Marta's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Janet","Marta","Gina","Donna"],"index":67422,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995583892,"difficulty":0.0004416108}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Israel does not know whether Israel's forehead is muddy. It is publicly announced that Christian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christian can now know that Israel can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Israel","Christian","Carolyn"],"index":60514,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997758269,"difficulty":0.0002241731}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mario does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Mario can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Mario","Rose","Ardath"],"index":38195,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9718791842,"difficulty":1.9718791842}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaac does not know whether Isaac's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Isaac can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Isaac"],"index":37831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997686744,"difficulty":0.0002313256}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Michael can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Carl","Edwin","Nikki","Michael"],"index":37156,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9760933518,"difficulty":0.0239066482}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold does not know whether or not everyone's forehead is muddy. It is publicly announced that Harold knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mary can now know that Harold can know that Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Keith","Jerry","Mary"],"index":36955,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5730167627,"difficulty":0.4269832373}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Laura can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Laura","Olive"],"index":30307,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9713094234,"difficulty":1.9713094234}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether someone's forehead is muddy. It is publicly announced that Erin knows whether Sharon's forehead is muddy. It is publicly announced that Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] Agenta knows that (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentc knows whether 1) ] [ ! 1 ] 0","hypothesis":"Sharon can now know that Louis can know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Louis","Erin"],"index":15244,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6094961762,"difficulty":0.3905038238}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alberta's forehead is not muddy. It is publicly announced that Steven knows whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Alberta can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alberta","Nathaniel","Steven","Rudolph"],"index":60861,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985166192,"difficulty":0.0014833808}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce knows whether Richard's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Joyce can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Richard","Joyce","John"],"index":55155,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997457862,"difficulty":0.0002542138}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Luther can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willie","Stephen","Luther","Timothy"],"index":7956,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995482564,"difficulty":0.0004517436}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"John can now know whether Nona can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Nona","William","John"],"index":55644,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995383024,"difficulty":0.0004616976}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows whether (Agenta knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Henry can now know whether William can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["William","Tracy","Wayne","Henry"],"index":61585,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99975878,"difficulty":0.00024122}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that John knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Mary","John","Wanda","Georgina"],"index":37282,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997141957,"difficulty":0.0002858043}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"John can now know that Brian can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","John","Mary","Brian"],"index":58794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972794652,"difficulty":0.0027205348}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph does not know whether Ralph's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Kristen can now know that Kristen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristen","Ralph","Chad"],"index":66356,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971996546,"difficulty":0.0028003454}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin knows whether or not nobody's forehead is muddy. It is publicly announced that Erin's forehead is muddy. It is publicly announced that Denise's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Earl","Erin","Denise","Charles"],"index":40695,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8786183,"difficulty":0.1213817}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna does not know whether Edna's forehead is muddy. It is publicly announced that Daisy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Daisy can now know that Edna can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Daisy","Edna"],"index":32489,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985057116,"difficulty":0.0014942884}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henry's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy. It is publicly announced that Henry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Kevin can now know that William can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Henry","Kevin","William"],"index":57184,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977617264,"difficulty":0.0022382736}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Guadalupe can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Nicholas","Linda","Kent","Guadalupe"],"index":23603,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.997399807,"difficulty":1.997399807}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Eric can now know that Sallie can know that Paulette's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Paulette","Mia","Eric","Sallie"],"index":50844,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985659719,"difficulty":0.0014340281}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hector knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows whether (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Virginia can now know whether Julie can know that Virginia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hector","Julie","Mark","Virginia"],"index":28504,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9343715906,"difficulty":0.0656284094}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beatriz knows whether Leona's forehead is muddy. It is publicly announced that Beatriz does not know whether or not everyone's forehead is muddy. It is publicly announced that Leona knows whether or not everyone's forehead is muddy. It is publicly announced that Leona knows whether Beatriz's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Beatriz can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Beatriz","Leona"],"index":10939,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977904558,"difficulty":0.0022095442}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jorge does not know whether Jorge's forehead is muddy. It is publicly announced that Collette knows whether or not everyone's forehead is muddy. It is publicly announced that Jorge's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Collette can now know whether Collette's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Collette","Jennifer","Erik","Jorge"],"index":18159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7250282764,"difficulty":0.2749717236}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jason does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Jason can now know that Joe can know that Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Sarah","Joe","Jason"],"index":64612,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5390765071,"difficulty":1.5390765071}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mark can now know whether Kevin can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Kevin","Mark"],"index":50700,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999774158,"difficulty":0.000225842}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"James can now know whether Meredith can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Meredith","James"],"index":27601,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9143453836,"difficulty":1.9143453836}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Katharine can now know that Grace's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Katharine","Grace","John","Christopher"],"index":43382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998318553,"difficulty":0.001681447}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brooke does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Brooke can now know whether Joseph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mathew","Brooke","Joseph"],"index":52852,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997738004,"difficulty":0.0002261996}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Mary knows whether Robbie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Mary can now know whether Robbie can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Robbie","Sandra"],"index":33862,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970818162,"difficulty":0.0029181838}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Catherine can now know that Richard can know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Robert","Richard","Catherine"],"index":22258,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995471835,"difficulty":0.0004528165}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christine's forehead is not muddy. It is publicly announced that Lee does not know whether Lee's forehead is muddy. It is publicly announced that Lee knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lee can now know whether John can know that Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Christine","Lee","John"],"index":10989,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7927607298,"difficulty":1.7927607298}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia does not know whether Cynthia's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Eric can now know whether Dwayne can know that Dwayne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eric","Dwayne","James","Cynthia"],"index":53836,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9356104136,"difficulty":0.0643895864}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jason can now know that Richard can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Jason","Richard"],"index":26886,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983801842,"difficulty":0.0016198158}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether Leroy's forehead is muddy. It is publicly announced that Mary does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Leroy can now know that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Leroy"],"index":21012,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997183681,"difficulty":0.0002816319}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rogelio's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (~(1&2)) ] 0","hypothesis":"Rogelio can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Rogelio","Willis"],"index":66798,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997314811,"difficulty":0.0002685189}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether Kimberly's forehead is muddy. It is publicly announced that Linda knows whether or not everyone's forehead is muddy. It is publicly announced that Lindsey knows whether Kimberly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kimberly can now know whether Lindsey can know whether Lindsey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Kimberly","Lindsey","Thomas"],"index":20056,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.767677784,"difficulty":0.232322216}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Grace knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Grace can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ignacio","David","Grace","Michael"],"index":33335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985060692,"difficulty":0.0014939308}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mattie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Clarence can now know that Mattie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Mattie","Clarence"],"index":45086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972324967,"difficulty":0.0027675033}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelton does not know whether or not everyone's forehead is muddy. It is publicly announced that Shelton does not know whether Shelton's forehead is muddy. It is publicly announced that Shelton does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Shelton can now know whether John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Shelton","John"],"index":11123,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9164233208,"difficulty":0.0835766792}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edna's forehead is not muddy. It is publicly announced that Howard's forehead is muddy. It is publicly announced that Edna knows whether Edna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Howard can now know that Ralph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edna","Howard","Ralph"],"index":2653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979788661,"difficulty":0.0020211339}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly knows whether someone's forehead is muddy. It is publicly announced that Curtis knows whether Kimberly's forehead is muddy. It is publicly announced that Irma does not know whether Irma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kimberly can now know that Irma can know whether Kimberly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Curtis","Irma","Kimberly"],"index":57363,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994261265,"difficulty":0.0005738735}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elaine does not know whether Elaine's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jennifer can now know that Elaine can know whether Jennifer's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jennifer","Elaine"],"index":16419,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994576573,"difficulty":0.0005423427}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Joan can now know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Robert","Joan","Joey"],"index":57596,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995737672,"difficulty":0.0004262328}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wendell does not know whether Wendell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows whether (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Omar can now know whether Wendell can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melissa","Omar","Joann","Wendell"],"index":48356,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994545579,"difficulty":0.0005454421}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jacqueline knows whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jacqueline can now know whether Louie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacqueline","Joseph","Louie","Miguel"],"index":13316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995318651,"difficulty":0.0004681349}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Barbara can now know that Michael can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Barbara","Michael","Helen"],"index":17045,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9942329526,"difficulty":0.0057670474}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachelle's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Rachelle can now know that Anita can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Anita","Rachelle"],"index":21014,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7161663175,"difficulty":1.7161663175}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Myrtle knows whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Myrtle can now know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Myrtle","Mary"],"index":25324,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995580316,"difficulty":0.0004419684}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Steven can now know that Dolores can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helena","Dolores","Judy","Steven"],"index":47765,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.968434751,"difficulty":1.968434751}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Norman can now know whether Gregory's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gregory","Thomas","Melanie","Norman"],"index":22742,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993312359,"difficulty":0.0006687641}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise knows whether or not everyone's forehead is muddy. It is publicly announced that Anthony does not know whether Anthony's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Anthony can now know that Anthony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["George","Louise","Thomas","Anthony"],"index":8259,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7192512155,"difficulty":0.2807487845}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether or not nobody's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lillian can now know whether Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Lillian","Scott"],"index":60157,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9663050175,"difficulty":1.9663050175}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Eugene's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Brian can now know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["German","Kevin","Eugene","Brian"],"index":62948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929233789,"difficulty":0.0070766211}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stanley knows whether Shameka's forehead is muddy. It is publicly announced that Shameka does not know whether or not everyone's forehead is muddy. It is publicly announced that Stanley knows whether Dennis's forehead is muddy. It is publicly announced that Stanley knows whether Esmeralda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agenta knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Stanley can now know whether Shameka's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Stanley","Dennis","Esmeralda","Shameka"],"index":51932,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993533492,"difficulty":0.0006466508}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Brian can now know whether Heather's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Brian","Heather"],"index":26039,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994268417,"difficulty":0.0005731583}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy does not know whether Tracy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Philip can now know that Nevada can know that Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Carolyn","Tracy","Nevada"],"index":44534,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977261424,"difficulty":0.0022738576}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Mary can now know whether Richard can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Richard","Mary"],"index":54952,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8904061317,"difficulty":0.1095938683}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Paul can now know whether Bertha can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kimberly","Richard","Paul","Bertha"],"index":62509,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999781549,"difficulty":0.000218451}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Charles can now know whether Ruby can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Charles","Ruby"],"index":20820,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823983312,"difficulty":0.0176016688}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mildred knows whether Patrice's forehead is muddy. It is publicly announced that Barbara does not know whether Barbara's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrice knows whether Patrice's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Patrice can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Patrice","Barbara","Mildred"],"index":10347,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983984828,"difficulty":0.0016015172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaclyn knows whether someone's forehead is muddy. It is publicly announced that Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] (Agentc knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! 3 ] 0","hypothesis":"Sara can now know whether Jackie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jaclyn","James","Sara","Jackie"],"index":51702,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995334148,"difficulty":0.0004665852}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Michael can now know whether Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Esther","Gail","Michael","Lee"],"index":49955,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995385408,"difficulty":0.0004614592}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Louis can now know whether Virgil can know whether Virgil's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Elaine","Pamela","Virgil","Louis"],"index":45312,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9851065874,"difficulty":0.0148934126}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa does not know whether Lisa's forehead is muddy. It is publicly announced that Lisa does not know whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Alvin can now know whether Alvin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lynne","Lisa","Alvin","Andrew"],"index":20480,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9300078154,"difficulty":0.0699921846}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa does not know whether Theresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lisa can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Theresa","Miriam","Lisa"],"index":14034,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986126423,"difficulty":0.0013873577}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know whether Buffy can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arthur","John","Buffy","Gail"],"index":14316,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963327646,"difficulty":0.0036672354}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Diane knows whether or not nobody's forehead is muddy. It is publicly announced that Judith's forehead is not muddy. It is publicly announced that Diane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agentb knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Stacey can now know that Diane can know whether Diane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Judith","Stacey","Rose","Diane"],"index":63979,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.778788507,"difficulty":0.221211493}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jerome can now know whether Scott can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Jerome","Kimberly"],"index":7815,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997768998,"difficulty":0.0002231002}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Josie knows whether someone's forehead is muddy. It is publicly announced that Toby's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] [ ! ~(2) ] 0","hypothesis":"Toby can now know that Josie can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Josie","Toby"],"index":11042,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997796416,"difficulty":0.0002203584}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Shantelle can now know that Lucy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Shantelle","Evelyn","Lucy","Vickie"],"index":28951,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982250333,"difficulty":0.0017749667}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether Florence's forehead is muddy. It is publicly announced that Lakesha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Lakesha can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Florence","Fred","Lakesha","Curtis"],"index":59241,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977891445,"difficulty":0.0022108555}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Carol's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Jason can now know whether Raymond can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Raymond","Jason","Carol"],"index":19918,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995597005,"difficulty":0.0004402995}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy. It is publicly announced that Keith knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Christopher can now know whether Christopher's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Keith","Christopher","Ashley"],"index":65033,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8679227829,"difficulty":1.8679227829}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rene knows whether Carlton's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Rene can now know whether Carlton can know that Rene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Rene","Carlton"],"index":14774,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9765352607,"difficulty":0.0234647393}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juanita does not know whether or not everyone's forehead is muddy. It is publicly announced that Alejandro knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Valerie can now know that Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Juanita","Valerie","Alejandro"],"index":40245,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.647742331,"difficulty":1.647742331}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carla knows whether Henry's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Carla can now know that Henry can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Henry","Carla"],"index":45286,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983133078,"difficulty":0.0016866922}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marsha knows whether someone's forehead is muddy. It is publicly announced that Marsha knows whether or not everyone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lela can now know that Marsha can know that Marsha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Lela","Marsha","Tia"],"index":65895,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8847057223,"difficulty":0.1152942777}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma knows whether Dwight's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwight's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Thelma can now know whether Thelma's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thelma","Terry","Gary","Dwight"],"index":51500,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8810533881,"difficulty":0.1189466119}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Brandon can now know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Stephanie","Brandon"],"index":62390,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9658574462,"difficulty":0.0341425538}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kirk knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Karl can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Billy","Kirk","Karl"],"index":6117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9783475399,"difficulty":0.0216524601}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Scott can now know that Anthony can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Anthony","Thomas","Scott"],"index":18977,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973406196,"difficulty":0.0026593804}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel knows whether Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Albert can now know that Victoria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Daniel","Victoria","Albert"],"index":34179,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983286262,"difficulty":0.0016713738}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas does not know whether Douglas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Paul can now know that Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Douglas","Michael"],"index":59243,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978144169,"difficulty":0.0021855831}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karmen knows whether or not nobody's forehead is muddy. It is publicly announced that Karmen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Gary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christine","Gary","Julia","Karmen"],"index":64085,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980908036,"difficulty":0.0019091964}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arthur knows whether Melissa's forehead is muddy. It is publicly announced that Gerald knows whether Melissa's forehead is muddy. It is publicly announced that Melissa does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Melissa can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Melissa","Gerald","Arthur"],"index":59433,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997127652,"difficulty":0.0002872348}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bernice knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Bernice can now know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Bernice","Elizabeth","Andrea"],"index":50897,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995678067,"difficulty":0.0004321933}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Dorothy can now know whether Johnny can know that Johnny's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Mary","Dorothy","Johnny"],"index":66786,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9219531417,"difficulty":0.0780468583}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra does not know whether or not everyone's forehead is muddy. It is publicly announced that Sandra's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Sandra can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Sandra","Nora"],"index":26948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9813350439,"difficulty":0.0186649561}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Angela can now know that Mike can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mike","Angela","John"],"index":57863,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6503105164,"difficulty":0.3496894836}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda knows whether Pauline's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Linda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pauline","Linda"],"index":36274,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998457551,"difficulty":0.001542449}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] Agenta knows whether (Agentb knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Alan can now know whether Robert can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alan","Robert","Richard"],"index":27599,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997832179,"difficulty":0.0002167821}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tyler does not know whether Tyler's forehead is muddy. It is publicly announced that Tyler does not know whether Tyler's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Gary can now know that Tyler can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Tyler","Gary"],"index":34359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983987212,"difficulty":0.0016012788}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy. It is publicly announced that Larry's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Stacy can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Stacy","Larry","Anthony"],"index":39986,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999610126,"difficulty":0.000389874}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ricardo's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Rhonda can now know that Rhonda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricardo","Rhonda","Alberta","Stephanie"],"index":248,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.96161443,"difficulty":0.03838557}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime knows whether Katherine's forehead is muddy. It is publicly announced that Jaime's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! 2 ] 0","hypothesis":"Katherine can now know that Jaime can know that Katherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Dorothy","Jaime","Katherine"],"index":63868,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6772735715,"difficulty":0.3227264285}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucia knows whether Joy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentd knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nancy can now know whether Lucia can know that Greta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lucia","Joy","Greta","Nancy"],"index":1027,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976477027,"difficulty":0.0023522973}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Hugo can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Asa","David","Hugo"],"index":26949,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962189794,"difficulty":0.0037810206}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Leo can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ethel","Robert","Leo"],"index":21865,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981587529,"difficulty":0.0018412471}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Una does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Anglea can now know whether Stephen can know whether Peggie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Stephen","Peggie","Anglea","Una"],"index":25440,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992150068,"difficulty":0.0007849932}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether someone's forehead is muddy. It is publicly announced that Joshua's forehead is muddy. It is publicly announced that Jerry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 3 ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Jerry can now know that Joshua can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jose","Jerry","Joshua"],"index":51299,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981151819,"difficulty":0.0018848181}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patty does not know whether or not everyone's forehead is muddy. It is publicly announced that Walton knows whether Patty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Edward can now know that Walton can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Walton","Edward","Griselda","Patty"],"index":6679,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997152686,"difficulty":0.0002847314}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver knows whether Johnny's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Johnny can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Johnny","Oliver","Roberto"],"index":40548,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999682188,"difficulty":0.000317812}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Philip can now know that Joann can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joann","Jim","Veronica","Philip"],"index":11586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5927280784,"difficulty":0.4072719216}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jon's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Betty can now know that James can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bobby","Betty","Jon","James"],"index":58077,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983845949,"difficulty":0.0016154051}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earlene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Joseph can now know whether Jacqueline can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gail","Jacqueline","Earlene","Joseph"],"index":48945,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6178340316,"difficulty":1.6178340316}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Ethel can now know that Paul can know whether Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ethel","Paul"],"index":28723,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6181416512,"difficulty":0.3818583488}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether Martha's forehead is muddy. It is publicly announced that Shaniqua knows whether Martha's forehead is muddy. It is publicly announced that Shaniqua does not know whether Shaniqua's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Martha can now know whether Shaniqua can know whether Christy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Harold","Christy","Shaniqua","Martha"],"index":13695,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993711114,"difficulty":0.0006288886}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail does not know whether Gail's forehead is muddy. It is publicly announced that Jorge knows whether Jorge's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Jorge can now know whether Gail can know that Jorge's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jorge","Gail"],"index":49663,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6921615005,"difficulty":1.6921615005}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy. It is publicly announced that Carmen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Carmen can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Sara","Carmen"],"index":37572,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9950866103,"difficulty":0.0049133897}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie does not know whether Willie's forehead is muddy. It is publicly announced that Hilda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(4) ] 0","hypothesis":"Joseph can now know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Willie","Joseph","Jack","Hilda"],"index":63810,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9779637456,"difficulty":0.0220362544}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cathleen does not know whether Cathleen's forehead is muddy. It is publicly announced that Dale does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Cathleen can now know whether Rozanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dale","Rozanne","Cathleen","Christine"],"index":56011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992190599,"difficulty":0.0007809401}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Caroline knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Linda can now know whether Caroline can know whether Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shirley","Linda","Don","Caroline"],"index":59395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9963267446,"difficulty":0.0036732554}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Shelley can now know whether Shelley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bruce","Robert","Shelley","Lillie"],"index":42178,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8636279106,"difficulty":0.1363720894}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"William can now know that Donald can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Crystal","William","Donald"],"index":189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9934853911,"difficulty":0.0065146089}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marvin's forehead is muddy. It is publicly announced that Ursula does not know whether Ursula's forehead is muddy. It is publicly announced that Ursula knows whether Abraham's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Marvin can now know that Aaron can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marvin","Abraham","Aaron","Ursula"],"index":46397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9723165035,"difficulty":0.0276834965}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether Cheryl's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Jonathan can now know whether Robert can know whether Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Martha","Cheryl","Jonathan"],"index":54228,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994834661,"difficulty":0.0005165339}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Freda can now know whether Liz can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Freda","Liz","Kelsey","Sheila"],"index":63795,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9837964177,"difficulty":0.0162035823}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Gary's forehead is muddy. It is publicly announced that Gary knows whether Evelyn's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Evelyn can now know whether Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evelyn","Charles","Gary"],"index":15545,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9277757406,"difficulty":0.0722242594}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is not muddy. It is publicly announced that Jean does not know whether Jean's forehead is muddy. It is publicly announced that Jean knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Michelle can now know whether Edward can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Edward","Jean"],"index":347,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9099458456,"difficulty":0.0900541544}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin does not know whether Kevin's forehead is muddy. It is publicly announced that Florence's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentc knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Robert can now know whether Kevin can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kevin","Florence","Robert"],"index":62484,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997007847,"difficulty":0.0002992153}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria does not know whether Victoria's forehead is muddy. It is publicly announced that Alice knows whether or not nobody's forehead is muddy. It is publicly announced that Alice does not know whether Alice's forehead is muddy. It is publicly announced that Henry knows whether Victoria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Alice can now know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Victoria","Alice","Henry"],"index":33378,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.97606498,"difficulty":0.02393502}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ruth can now know whether Alethia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Norma","Alethia","Ruth","Teresa"],"index":54445,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996300936,"difficulty":0.0003699064}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Donna can now know whether Reuben can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Heather","Michael","Donna","Reuben"],"index":23460,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9881738424,"difficulty":0.0118261576}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda does not know whether Wanda's forehead is muddy. It is publicly announced that Wanda does not know whether Wanda's forehead is muddy. It is publicly announced that Wanda knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Wanda can now know that Dennis can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dennis","Wanda"],"index":48540,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997811913,"difficulty":0.0002188087}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joy does not know whether Joy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Benjamin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joy","Benjamin","Jenny","Clora"],"index":8633,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999740541,"difficulty":0.000259459}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Russell can now know that Leola can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joseph","Leola","Russell"],"index":701,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982652068,"difficulty":0.0017347932}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Irene does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Beulah can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jami","John","Irene","Beulah"],"index":13853,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6409822702,"difficulty":0.3590177298}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Cynthia can now know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cynthia","Judy","Gregory"],"index":32130,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993240118,"difficulty":0.006759882}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 2 ] 0","hypothesis":"Jackie can now know whether Jackie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jackie","Kenneth","Sandra"],"index":44409,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9725126028,"difficulty":0.0274873972}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Azzie knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Dino knows whether Azzie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentd knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Dino can now know whether Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marie","Azzie","Ola","Dino"],"index":22410,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994489551,"difficulty":0.0005510449}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven's forehead is not muddy. It is publicly announced that Annie does not know whether Annie's forehead is muddy. It is publicly announced that Annie knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Steven can now know that Annie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Steven","Annie","Anthony"],"index":21462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969763756,"difficulty":0.0030236244}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether someone's forehead is muddy. It is publicly announced that Patricia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(3) ] 0","hypothesis":"Stephen can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Andrew","Stephen","Patricia","Scott"],"index":43136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997776151,"difficulty":0.0002223849}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Vanessa can now know that Samuel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vanessa","Ted","Samuel","Frances"],"index":25920,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9946693778,"difficulty":0.0053306222}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norbert does not know whether Norbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Clifton can now know that Claudia can know whether Claudia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Claudia","Clifton","Norbert","Deborah"],"index":56219,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9861078262,"difficulty":0.0138921738}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Crystal knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kevin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Richard","Crystal","Kevin","Rodolfo"],"index":21055,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997740388,"difficulty":0.0002259612}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy. It is publicly announced that Troy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agenta knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Susan can now know that Kevin can know that Troy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Troy","Kevin"],"index":24128,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8434805274,"difficulty":0.1565194726}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Joseph can now know whether Ella's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Joseph","Ella"],"index":3051,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995445609,"difficulty":0.0004554391}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Scott can now know whether Danielle can know that Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Scott","Danielle","Larry"],"index":17936,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.955683887,"difficulty":0.044316113}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicole knows whether Marilyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marilyn can now know whether Nicole can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marilyn","Nicole","Kristin","Thomas"],"index":3111,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997622371,"difficulty":0.0002377629}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy. It is publicly announced that Timothy knows whether or not everyone's forehead is muddy. It is publicly announced that Charles's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Angela can now know that Timothy can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Paula","Timothy","Angela"],"index":5362,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9024373293,"difficulty":0.0975626707}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Catrina can now know that Robin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patrick","Catrina","Robin","Raymon"],"index":5962,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9692339897,"difficulty":0.0307660103}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sage can now know whether Sage's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Michelle","James","Sage"],"index":66524,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9669114947,"difficulty":1.9669114947}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Shannon can now know that Brianna can know that Shannon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Laura","Brianna","Shannon","Floyd"],"index":42680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998342514,"difficulty":0.001657486}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gail does not know whether Gail's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Gail can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Christina","Gail"],"index":27667,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9826034904,"difficulty":0.0173965096}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Louise does not know whether or not everyone's forehead is muddy. It is publicly announced that Louise does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Louise can now know whether Leonard can know whether Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Leonard","Louise"],"index":57273,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9972524047,"difficulty":0.0027475953}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter does not know whether or not everyone's forehead is muddy. It is publicly announced that Tracie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Tracie can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Katrina","James","Tracie"],"index":59613,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9732354283,"difficulty":0.0267645717}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank's forehead is not muddy. It is publicly announced that Frank's forehead is not muddy. It is publicly announced that Henry knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Henry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Henry","Joyce","Frank"],"index":67275,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983225465,"difficulty":0.0016774535}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Angela can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Debra","Angela","Larae"],"index":65658,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982402325,"difficulty":0.0017597675}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy. It is publicly announced that Dorothy's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Dorothy can now know whether Domingo can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Dorothy","Domingo"],"index":28585,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9706793427,"difficulty":0.0293206573}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Winnie knows whether someone's forehead is muddy. It is publicly announced that Winnie knows whether Ferdinand's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Charles can now know that Ferdinand can know that Ferdinand's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Charles","Philip","Ferdinand","Winnie"],"index":32406,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960600734,"difficulty":0.0039399266}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Marian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Marian can now know whether Mary can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Marian","Mary"],"index":18449,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9738143086,"difficulty":0.0261856914}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arturo knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Garrett can now know whether Arturo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Garrett","Shawn","Melinda","Arturo"],"index":12941,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999520421,"difficulty":0.000479579}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Eric can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Pedro","Eric"],"index":9341,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985327721,"difficulty":0.0014672279}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Michael can now know whether Daniel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Daniel","Stephen","Michael","Estell"],"index":40884,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996075034,"difficulty":0.0003924966}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Laura knows whether Amber's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Alisha can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Bradley","Amber","Alisha","Laura"],"index":30516,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997759461,"difficulty":0.0002240539}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Eliseo can now know that Kimberly can know whether Eliseo's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Eliseo","Donald","Kimberly","Michael"],"index":20387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995336533,"difficulty":0.0004663467}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Carol knows whether or not nobody's forehead is muddy. It is publicly announced that Carol knows whether Marguerite's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Marguerite can now know that Carol can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Marguerite","Carol"],"index":65945,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9917336702,"difficulty":0.0082663298}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daisy does not know whether or not everyone's forehead is muddy. It is publicly announced that Carl knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Austin can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Daisy","Austin","Carl"],"index":59820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997202754,"difficulty":0.0002797246}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rita knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Rita can now know whether Rita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kristy","Christopher","Rita"],"index":35959,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958075285,"difficulty":0.0041924715}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terri does not know whether Terri's forehead is muddy. It is publicly announced that Shirley knows whether Terri's forehead is muddy. It is publicly announced that Scott knows whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Shirley can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Scott","Terri","Shirley"],"index":26530,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998672843,"difficulty":0.001327157}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell knows whether Ann's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Laura can now know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Laura","Ann","Darrell","Barry"],"index":32015,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979870319,"difficulty":0.0020129681}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kendall's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Tommy can now know whether Kendall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carla","Kendall","Tommy"],"index":4855,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995959401,"difficulty":0.0004040599}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Karla can now know that Bonnie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bonnie","Gabriel","Karla"],"index":10469,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9702560902,"difficulty":0.0297439098}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erik knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Erik can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Matthew","Jay","Erik"],"index":23103,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997423291,"difficulty":0.0002576709}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris's forehead is not muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that James knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"James can now know whether Doris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Doris","James","Ola"],"index":55162,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997733235,"difficulty":0.0002266765}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eva knows whether Patricia's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Patricia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Patricia","Eva"],"index":8829,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947974682,"difficulty":0.0052025318}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Lenora can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elsie","Michael","Lenora"],"index":3029,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997629523,"difficulty":0.0002370477}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ethel's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"James can now know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Cynthia","James","Ethel","David"],"index":12072,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9956291914,"difficulty":0.0043708086}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stella's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Stella can now know whether Gary can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stella","Gary","Emma"],"index":47101,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997841716,"difficulty":0.0002158284}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ursula's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Michael can now know whether Darlene can know whether Darlene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Darlene","Michael","Ursula"],"index":51529,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.743899405,"difficulty":0.256100595}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Stephanie can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Lenore","Terry","Stephanie"],"index":57477,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978314042,"difficulty":0.0021685958}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynn knows whether someone's forehead is muddy. It is publicly announced that Lynn's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Mark can now know that Jayson can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lynn","Jayson","Mark"],"index":45397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976517558,"difficulty":0.0023482442}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darcy's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Darcy can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Darcy","Marcus"],"index":3574,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997801185,"difficulty":0.0002198815}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Jerry can now know whether Jose can know that Jonathan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jose","Jerry","Jonathan","Ralph"],"index":50903,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9943957329,"difficulty":0.0056042671}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy. It is publicly announced that Carla knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Charles can now know that Carla's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carla","Irma","Charles"],"index":63318,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.803881526,"difficulty":0.196118474}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas does not know whether Nicholas's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Nicholas can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ricky","Kathleen","Nicholas","Robert"],"index":15254,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924082756,"difficulty":0.0075917244}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether David's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Edgar can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["David","Edgar"],"index":45148,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9934421778,"difficulty":0.0065578222}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Clifford can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Clifford","Effie","Edward","Priscilla"],"index":41709,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9923138022,"difficulty":0.0076861978}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anabel knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agenta knows whether (Agentc knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Jean can now know whether Betty can know whether Anabel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jean","Anabel","Betty"],"index":47959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994359612,"difficulty":0.0005640388}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know that Patrick can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elizabeth","James","Patrick"],"index":11300,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979841709,"difficulty":0.0020158291}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall knows whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentd knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Nick can now know whether Randall can know that Brittney's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brittney","Gerald","Randall","Nick"],"index":8352,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979447722,"difficulty":0.0020552278}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah does not know whether or not everyone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Deborah can now know that John can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Deborah","John"],"index":47500,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997777343,"difficulty":0.0002222657}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Stephanie can now know that Kenneth can know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Roger","Stephanie","Helen"],"index":65198,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955897331,"difficulty":0.0044102669}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marshall does not know whether or not everyone's forehead is muddy. It is publicly announced that Christopher knows whether Christopher's forehead is muddy. It is publicly announced that Marshall knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Marshall can now know that Christopher can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Marshall","Christopher"],"index":65283,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9887652397,"difficulty":0.0112347603}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether or not nobody's forehead is muddy. It is publicly announced that Charles does not know whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Benjamin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Benjamin","Charles"],"index":18616,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Gilda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(2) ] 0","hypothesis":"Jessica can now know that Marion's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Gilda","Jessica","Travis"],"index":18464,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9872881174,"difficulty":0.0127118826}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elias knows whether Kellee's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Glen can now know whether Elias can know whether Elias's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andy","Elias","Glen","Kellee"],"index":12743,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.914983511,"difficulty":0.085016489}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that Joan knows whether Paula's forehead is muddy. It is publicly announced that Paula knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Robert can now know whether Joan can know that Joan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Joan","Sharon","Paula"],"index":985,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8758512139,"difficulty":1.8758512139}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia does not know whether Julia's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Julia can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Denny","Julia","John"],"index":44485,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976021647,"difficulty":0.0023978353}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy. It is publicly announced that Monica does not know whether Monica's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Laura knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Monica can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","James","Monica"],"index":24277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986568689,"difficulty":0.0013431311}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether someone's forehead is muddy. It is publicly announced that Nellie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agenta knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that Nellie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["John","Kari","Lawrence","Nellie"],"index":52245,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.565197587,"difficulty":0.434802413}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brittany can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Michael","Brittany","Dwight"],"index":22065,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5221931934,"difficulty":0.4778068066}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew does not know whether Andrew's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know whether Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","James","Andrew"],"index":59066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8855918646,"difficulty":0.1144081354}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edmund does not know whether Edmund's forehead is muddy. It is publicly announced that Oscar's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"Oscar can now know that Edmund can know whether Edmund's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Edmund","Jorge","Oscar"],"index":51722,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7963290215,"difficulty":0.2036709785}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy. It is publicly announced that Gary does not know whether or not everyone's forehead is muddy. It is publicly announced that Gary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"Gary can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Gary"],"index":56964,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8518058062,"difficulty":0.1481941938}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Billy can now know that Kelli's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kelli","Billy"],"index":27926,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980660081,"difficulty":0.0019339919}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Heather can now know that Roger can know that Roger's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roger","Rene","Heather","Natalie"],"index":49692,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984232187,"difficulty":0.0015767813}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows that (Agentb knows whether 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Evangelina can now know that Eugene can know whether Eugene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Evangelina","Eugene","Gene"],"index":64846,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9938759208,"difficulty":0.0061240792}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Eva does not know whether Eva's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Eva can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Ann","Eva"],"index":6301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9941447377,"difficulty":0.0058552623}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanie's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that George does not know whether George's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jeanie can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["George","Jeanie"],"index":44048,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8806032538,"difficulty":0.1193967462}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Richard can now know whether Angel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Angel","Richard"],"index":64919,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996153116,"difficulty":0.0003846884}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norman knows whether Chrissy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Esther can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Rocio","Esther","Chrissy","Norman"],"index":31192,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997503161,"difficulty":0.0002496839}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robin can now know whether Benjamin can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robin","Robert","Benjamin","Shelia"],"index":22685,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9846994281,"difficulty":0.0153005719}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Duane can now know whether Carolyn can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carolyn","Harold","Duane"],"index":43014,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999577105,"difficulty":0.000422895}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katherine's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Katherine can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Beth","Katherine","William"],"index":4915,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983983636,"difficulty":0.0016016364}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rose knows whether Rose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Jackqueline can now know that Lawrence can know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jackqueline","Lawrence","Peggy","Rose"],"index":62193,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983479977,"difficulty":0.0016520023}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Heidi can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Heidi","Michael"],"index":29382,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977738261,"difficulty":0.0022261739}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Levi can now know whether Marian can know whether Levi's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Linda","Levi","Marian","Maria"],"index":60931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991337657,"difficulty":0.0008662343}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tonya knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Debbie can now know that Jeffrey can know that Jeffrey's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Debbie","Tonya","Jeffrey","Wilma"],"index":58814,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99813205,"difficulty":0.00186795}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brandon does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Brandon can now know that Chad can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nancy","Brandon","Chad"],"index":41451,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977217317,"difficulty":0.0022782683}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Dorothea can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Susan","Dorothea","Michael","Lawrence"],"index":13730,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997785687,"difficulty":0.0002214313}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Rebecca can now know whether Denise can know whether Rebecca's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Marta","Rebecca","Denise","Lisa"],"index":41609,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9931771755,"difficulty":0.0068228245}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Agnes does not know whether Agnes's forehead is muddy. It is publicly announced that Rene knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Rene can now know whether Agnes can know that Rene's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Rene","Agnes"],"index":29917,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.885641098,"difficulty":1.885641098}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Evelyn knows whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Nickolas can now know that Evelyn can know that Evelyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Evelyn","Andrew","Nickolas","Susan"],"index":45316,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981769323,"difficulty":0.0018230677}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy. It is publicly announced that Gloria knows whether or not nobody's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Gloria knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Gloria can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Gloria"],"index":15331,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975575209,"difficulty":0.0024424791}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gail can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Gail","Carol","Charles"],"index":43427,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997343421,"difficulty":0.0002656579}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether someone's forehead is muddy. It is publicly announced that Dionne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agenta knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Dionne can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dionne","Debra"],"index":2359,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981709719,"difficulty":0.0018290281}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Thomas can now know that Alene's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Alene","Christopher","Thomas"],"index":29808,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971831441,"difficulty":0.0028168559}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows that (Agentd knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"William can now know that Charles can know whether Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tammy","William","Ron","Charles"],"index":49227,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995630383,"difficulty":0.0004369617}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy does not know whether Jeremy's forehead is muddy. It is publicly announced that Catalina knows whether Catalina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentd knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Pedro can now know that Jeremy can know that Jeremy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pedro","Carrie","Catalina","Jeremy"],"index":43562,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9936705828,"difficulty":0.0063294172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerry does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Katherine can now know whether Kerry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Eugene","Kerry","Katherine"],"index":45868,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997112155,"difficulty":0.0002887845}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Celeste does not know whether or not everyone's forehead is muddy. It is publicly announced that Enrique knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Enrique can now know that Celeste can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Celeste","Enrique"],"index":54442,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997732043,"difficulty":0.0002267957}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Andre does not know whether Andre's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] Agentc knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agenta knows whether 1) ] [ ! 3 ] 0","hypothesis":"John can now know whether Marie can know whether Andre's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Andre","Marie","John"],"index":62007,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994262457,"difficulty":0.0005737543}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Marci knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Samantha can now know that Clyde's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kenneth","Marci","Clyde","Samantha"],"index":15280,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977983236,"difficulty":0.0022016764}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Heather can now know whether Debbie can know whether Debbie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Debbie","Mabel","Heather"],"index":39325,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7343569398,"difficulty":1.7343569398}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe does not know whether Guadalupe's forehead is muddy. It is publicly announced that Winfred does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Felipa can now know that Winfred's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Guadalupe","Winfred","Felipa","John"],"index":3353,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.696323812,"difficulty":0.303676188}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Albert does not know whether or not everyone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Donna can now know whether Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Phillip","Donna","Albert"],"index":29165,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7454238534,"difficulty":1.7454238534}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott does not know whether or not everyone's forehead is muddy. It is publicly announced that Scott does not know whether Scott's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cesar can now know that Scott can know that Scott's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Scott","Cesar"],"index":36248,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9433261752,"difficulty":1.9433261752}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoinette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Antoinette can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Antoinette","Jesse"],"index":57766,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997435212,"difficulty":0.0002564788}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Steve can now know that Melissa can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steve","Dana","Melissa","Martha"],"index":37491,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6404103637,"difficulty":1.6404103637}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether or not everyone's forehead is muddy. It is publicly announced that Helen does not know whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Helen can now know whether Jane can know whether Jane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Helen","Jane"],"index":61750,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.77697891,"difficulty":0.22302109}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy. It is publicly announced that Gerald knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Linda can now know that Donna can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gerald","Donna","Joyce","Linda"],"index":53954,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997259974,"difficulty":0.0002740026}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Allen can now know that Sharon can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Sharon","Allen","Nathan"],"index":44458,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943321943,"difficulty":0.0056678057}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Alison can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elmer","Alison","Jason","James"],"index":22460,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997448325,"difficulty":0.0002551675}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"William can now know whether Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Mary","James","William"],"index":34523,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9818307757,"difficulty":0.0181692243}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether someone's forehead is muddy. It is publicly announced that Ann's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] Agenta knows that (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(1) ] 0","hypothesis":"Ann can now know that Jimmy can know whether Dane's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Ann","Jimmy","Dane"],"index":28707,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996061921,"difficulty":0.0003938079}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clarence does not know whether or not everyone's forehead is muddy. It is publicly announced that Mary knows whether Clarence's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentb knows that (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Eric can now know that Lenora can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mary","Eric","Lenora","Clarence"],"index":49840,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9482505918,"difficulty":0.0517494082}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jordan knows whether Larry's forehead is muddy. It is publicly announced that Larry does not know whether or not everyone's forehead is muddy. It is publicly announced that Jordan knows whether Dana's forehead is muddy. It is publicly announced that Jordan knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentd knows whether 4)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Larry can now know whether Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jordan","Dana","David","Larry"],"index":60247,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6385079622,"difficulty":1.6385079622}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Denise can now know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bryan","Denise","Jose"],"index":63470,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978924394,"difficulty":0.0021075606}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria's forehead is muddy. It is publicly announced that Maria knows whether someone's forehead is muddy. It is publicly announced that Tom knows whether Kenneth's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentd knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Tom can now know that Maria can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Tom","Michael","Maria"],"index":31139,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9266370535,"difficulty":0.0733629465}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debbie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"John can now know whether Donald can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Debbie","Susan","John"],"index":26874,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9956788421,"difficulty":0.0043211579}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Debra knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Debra can now know whether Wilbur can know whether Wilbur's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wilbur","Debra","Lonnie"],"index":33924,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5651780963,"difficulty":1.5651780963}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Esther knows whether Nick's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Nick can now know whether Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tina","Nick","Robert","Esther"],"index":23728,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9555981159,"difficulty":0.0444018841}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agenta knows whether (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Dona can now know whether Clara can know that Clara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Dona","Charles","Virginia","Clara"],"index":21401,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8228590488,"difficulty":0.1771409512}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (~(1&2&3)) ] 0","hypothesis":"Clarence can now know whether Sadie can know that Sadie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Kenneth","Sadie","Clarence"],"index":60877,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9938150644,"difficulty":0.0061849356}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Darrell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Robert can now know that Helen can know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrell","Robert","Amy","Helen"],"index":28575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994570613,"difficulty":0.0005429387}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul does not know whether Paul's forehead is muddy. It is publicly announced that Fred does not know whether Fred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Fred can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Evan","Paul","Fred"],"index":24178,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984323382,"difficulty":0.0015676618}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Roberto can now know that Jeri can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberto","Jeri","Ruben","Deloris"],"index":40203,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945105314,"difficulty":0.0054894686}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows whether (Agentc knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Otis can now know whether Jamie can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Otis","Lee","Jamie","Michael"],"index":12823,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995123148,"difficulty":0.0004876852}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francis knows whether Miguel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] Agentd knows that (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Letha can now know that Francis can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","Janis","Miguel","Letha"],"index":37871,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9879202843,"difficulty":0.0120797157}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Julia knows whether Michael's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael knows whether Julia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Michael can now know whether Julia can know that Julia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Julia","Michael"],"index":43239,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8139616251,"difficulty":0.1860383749}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Mary can now know that Floyd can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Patricia","Floyd","Karen","Mary"],"index":58942,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921675324,"difficulty":0.0078324676}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"Michael can now know that Catherine can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Catherine","Michael"],"index":45942,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9605673552,"difficulty":0.0394326448}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether Ellen's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ellen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Ellen"],"index":45630,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947012663,"difficulty":0.0052987337}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emory does not know whether or not everyone's forehead is muddy. It is publicly announced that Helga knows whether or not everyone's forehead is muddy. It is publicly announced that Emory does not know whether Emory's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agenta knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Emory can now know that William can know that Emory's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Helga","Sheila","Emory"],"index":34673,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8304300308,"difficulty":1.8304300308}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that John knows whether Stephen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentd knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"John can now know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Shawn","Stephen","Patricia","John"],"index":15674,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967051148,"difficulty":0.0032948852}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"John can now know whether Leroy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["John","Leroy"],"index":61710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997107387,"difficulty":0.0002892613}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentd knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Paula can now know whether Beulah can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Michael","Beulah","Henry","Paula"],"index":17113,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9985249639,"difficulty":0.0014750361}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barry does not know whether Barry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"William can now know that Barry can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Barry","Peggy","William"],"index":8566,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9914585948,"difficulty":0.0085414052}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Charles knows whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Robert can now know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Robert","Michael"],"index":62717,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959237576,"difficulty":0.0040762424}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Becky's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Robert can now know that Nathan can know whether Nathan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Doris","Nathan","Becky","Robert"],"index":23568,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9683747292,"difficulty":0.0316252708}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy. It is publicly announced that Glenn knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Robert","Raymond","Glenn"],"index":21475,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998113513,"difficulty":0.001886487}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lauren knows whether or not everyone's forehead is muddy. It is publicly announced that Lauren does not know whether Lauren's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Stan can now know that Lauren can know that Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lauren","Stan","Gloria"],"index":21037,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7319129705,"difficulty":1.7319129705}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows whether (Agentc knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Suzan can now know whether Taylor can know whether Suzan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Suzan","Sheila","Taylor","Willis"],"index":64522,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981356859,"difficulty":0.0018643141}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Robyn can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Vincent","Tyra","Robyn"],"index":61673,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912988544,"difficulty":0.0087011456}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Margaret can now know that Cory can know that Kelly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kelly","Margaret","David","Cory"],"index":63126,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984070659,"difficulty":0.0015929341}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alex does not know whether or not everyone's forehead is muddy. It is publicly announced that Pauline knows whether someone's forehead is muddy. It is publicly announced that Alex does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Pauline can now know whether Melissa can know that Pauline's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Melissa","Alex","Pauline","Robert"],"index":62567,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7932018042,"difficulty":0.2067981958}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Eric knows whether or not nobody's forehead is muddy. It is publicly announced that Eric knows whether Roy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Eric can now know whether Roy can know whether Roy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roy","Eric"],"index":56720,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9935786724,"difficulty":0.0064213276}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Jerry can now know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Todd","Jerry"],"index":40160,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986126423,"difficulty":0.0013873577}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Henrietta knows whether Henrietta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Irene can now know whether Henrietta can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Irene","Nestor","Henrietta"],"index":63025,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997352958,"difficulty":0.0002647042}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward's forehead is muddy. It is publicly announced that Barbara knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Barbara can now know that Edward can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Edward","Barbara"],"index":29835,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9859879613,"difficulty":0.0140120387}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that Timothy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Timothy can now know that Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Annie","Timothy","Gail"],"index":16626,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9743767381,"difficulty":0.0256232619}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Vicki can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Robin","Vicki","Linda"],"index":51448,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Paula can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Paula","James"],"index":30767,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5290341377,"difficulty":0.4709658623}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] 0","hypothesis":"James can now know whether Sherilyn can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["James","Sherilyn"],"index":44699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988534451,"difficulty":0.0011465549}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hoa does not know whether Hoa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Richard can now know that Hoa can know that Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Hoa","Joanne"],"index":9866,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974631071,"difficulty":0.0025368929}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beatriz knows whether or not nobody's forehead is muddy. It is publicly announced that Beatriz knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Beatriz can now know whether Beatriz's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Max","Kenneth","Sharon","Beatriz"],"index":17897,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6257203221,"difficulty":0.3742796779}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Israel can now know that David can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Israel","David","Joseph","Charles"],"index":64681,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997839272,"difficulty":0.002160728}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vernon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Richard can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Vernon","Marcus"],"index":64320,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5140815973,"difficulty":1.5140815973}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pearl does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Jong can now know that Carol can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jong","Pearl","Paul","Carol"],"index":12241,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7184535861,"difficulty":1.7184535861}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan's forehead is not muddy. It is publicly announced that Ann knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Micah","Daniel","Susan","Ann"],"index":19744,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982705116,"difficulty":0.0017294884}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Joseph can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Joseph","Charles","Mary"],"index":47821,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997230172,"difficulty":0.0002769828}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether James's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lisa can now know that Linda can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","Lisa","Linda"],"index":4834,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9916709661,"difficulty":0.0083290339}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ollie does not know whether Ollie's forehead is muddy. It is publicly announced that Boris knows whether Ollie's forehead is muddy. It is publicly announced that Boris does not know whether Boris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentb knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Nick can now know that Diane can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Nick","Diane","Boris","Ollie"],"index":7305,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983496666,"difficulty":0.0016503334}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deann knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows whether (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Gail can now know whether Deann can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deann","Stephen","Gail","Joseph"],"index":14776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894633293,"difficulty":0.0105366707}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2) ] 0","hypothesis":"Michelle can now know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Michelle","Tina"],"index":40776,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944185019,"difficulty":0.0055814981}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edward does not know whether Edward's forehead is muddy. It is publicly announced that Billy does not know whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Edward can now know that Billy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Billy","Vera","Edward"],"index":52662,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984437823,"difficulty":0.0015562177}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Francisco knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Francisco can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Kathleen","Francisco"],"index":19746,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955703616,"difficulty":0.0044296384}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly does not know whether Holly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Holly can now know that Robert can know that Wendy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wendy","Robert","Roger","Holly"],"index":11710,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979288578,"difficulty":0.0020711422}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Marjorie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Barbara","Marjorie","Teresa"],"index":51175,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996830225,"difficulty":0.0003169775}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nettie knows whether Nettie's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Nettie can now know that Sharon can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sharon","Nettie","Dana"],"index":36822,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8604218364,"difficulty":1.8604218364}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jerome can now know that Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tiffany","Jacqueline","Willie","Jerome"],"index":16924,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983152151,"difficulty":0.0016847849}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Benjamin can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elvira","James","In","Benjamin"],"index":60117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997727275,"difficulty":0.0002272725}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephan's forehead is muddy. It is publicly announced that Amanda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] (Agentb knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! ~(1) ] 0","hypothesis":"Kenneth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Amanda","Kenneth","Maria","Stephan"],"index":55767,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6324570179,"difficulty":1.6324570179}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Philip can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sylvia","Philip","Awilda","Beth"],"index":46704,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9929056168,"difficulty":0.0070943832}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Earl does not know whether Earl's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Christopher can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Earl","Christopher","Shirley"],"index":3602,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997567534,"difficulty":0.0002432466}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tina knows whether or not everyone's forehead is muddy. It is publicly announced that Tina knows whether someone's forehead is muddy. It is publicly announced that Tina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Tina can now know that Garry can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["James","Garry","Tina"],"index":23867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997203946,"difficulty":0.0002796054}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Lois can now know whether Priscilla can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lois","Priscilla","Robert"],"index":28510,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9970040917,"difficulty":1.9970040917}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arturo knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentd knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Arturo can now know whether Charles can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Charles","James","Arturo"],"index":6138,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6753363609,"difficulty":0.3246636391}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Kathleen's forehead is muddy. It is publicly announced that Kathleen knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] Agentc knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kathleen can now know that Linda can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Linda","Robert","Kathleen","Andra"],"index":42817,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970415235,"difficulty":0.0029584765}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] 0","hypothesis":"Melissa can now know that Ray's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Robert","Melissa","William","Ray"],"index":63367,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970672727,"difficulty":0.0029327273}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lawrence knows whether or not nobody's forehead is muddy. It is publicly announced that Lawrence's forehead is muddy. It is publicly announced that Lawrence knows whether Lawrence's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! 1 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Lawrence can now know whether Francisco can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lawrence","Francisco"],"index":32010,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8470034599,"difficulty":0.1529965401}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Andrew knows whether or not nobody's forehead is muddy. It is publicly announced that Andrew does not know whether Andrew's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["John","Andrew"],"index":34949,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9940299988,"difficulty":1.9940299988}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert knows whether Allison's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agenta knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Robert can now know whether Richard can know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Thomas","Richard","Allison"],"index":28301,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9960816503,"difficulty":0.0039183497}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bethany knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Mary can now know that Bethany can know whether Bethany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Bethany","Mary"],"index":37164,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960617423,"difficulty":0.0039382577}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Christopher can now know that Lisa can know that Hector's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Hector","Michael","Christopher","Lisa"],"index":14574,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983820915,"difficulty":0.0016179085}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roseann knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Arturo can now know that James can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Roseann","Arturo","James"],"index":63061,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997779727,"difficulty":0.0002220273}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Della knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentc knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Valerie can now know whether John can know whether Valerie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Della","Valerie"],"index":43175,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9987536669,"difficulty":0.0012463331}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Ryan can now know whether Timothy can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Ryan","Timothy"],"index":42297,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984592199,"difficulty":0.0015407801}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that Edith's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 2 ] 0","hypothesis":"John can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["John","Edith"],"index":53547,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967632294,"difficulty":0.0032367706}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Kimberly can now know that Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesus","Kimberly","Margaret","Danielle"],"index":24747,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9713203311,"difficulty":0.0286796689}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nelson's forehead is not muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Sharon can now know whether Randy can know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nelson","Sharon","Randy"],"index":30848,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5281413794,"difficulty":1.5281413794}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Roberto's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agentb knows whether (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"David can now know whether Roberto can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Roberto","David"],"index":44927,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996721745,"difficulty":0.0003278255}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that April knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Raymond can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Raymond","Eli","April"],"index":51716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983347058,"difficulty":0.0016652942}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Judith knows whether or not everyone's forehead is muddy. It is publicly announced that Judith knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Judith can now know whether Norman can know whether Judith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Norman","Judith"],"index":16196,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9970911741,"difficulty":0.0029088259}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Joseph can now know that Randall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Bruce","Joseph","Randall"],"index":38832,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5650698543,"difficulty":1.5650698543}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pauline does not know whether or not everyone's forehead is muddy. It is publicly announced that Pauline does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Pauline can now know that Pauline's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Betty","Pauline"],"index":19297,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9690208435,"difficulty":1.9690208435}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Danielle knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Kathleen can now know whether Danielle can know whether Danielle's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kyle","Danielle","Kathleen"],"index":64184,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6338926554,"difficulty":0.3661073446}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold knows whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"James can now know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Bridgett","Harold","Brent","James"],"index":20403,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6949520707,"difficulty":0.3050479293}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether or not everyone's forehead is muddy. It is publicly announced that Royce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 1 ] 0","hypothesis":"Royce can now know that Marjorie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Royce","Robert","Marjorie","Alice"],"index":61624,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6042386293,"difficulty":0.3957613707}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruth does not know whether Ruth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ruth can now know whether Colleen can know that Colleen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Colleen","Reginald","Ruth"],"index":32899,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9509444237,"difficulty":1.9509444237}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is muddy. It is publicly announced that Raymond does not know whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Raymond can now know that Brian can know whether Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Raymond","Brian"],"index":16548,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983276725,"difficulty":0.0016723275}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karyn does not know whether Karyn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Karyn can now know whether Dwight can know that Karyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Katherine","Simone","Dwight","Karyn"],"index":55670,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8710438609,"difficulty":0.1289561391}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecile does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sherman can now know that Pamela can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Pamela","Cecile","Sherman"],"index":10338,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977241158,"difficulty":0.0022758842}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether Charles's forehead is muddy. It is publicly announced that Charles knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Timothy can now know whether Timothy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Charles","Lorretta","Timothy","Paula"],"index":33753,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5354222655,"difficulty":1.5354222655}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane's forehead is not muddy. It is publicly announced that Jane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Alvina can now know that Alvina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alvina","Thomas","Sam","Jane"],"index":60052,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992251575,"difficulty":0.007748425}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Catherine can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Catherine","James","Chris","Steven"],"index":22600,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9902362227,"difficulty":1.9902362227}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nina knows whether Mark's forehead is muddy. It is publicly announced that Norma does not know whether Norma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Norma can now know that Nina can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Mark","Nina"],"index":7694,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9651437998,"difficulty":0.0348562002}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Thomas can now know that Kathryn can know that David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["David","Thomas","Kathryn","Cecilia"],"index":63968,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984480143,"difficulty":0.0015519857}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dawn's forehead is muddy. It is publicly announced that Lori's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] Agentd knows that (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Doris can now know that Dawn can know whether Doris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Edward","Dawn","Lori","Doris"],"index":46723,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992077947,"difficulty":0.0007922053}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary does not know whether Gary's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Gary can now know whether Gary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peggy","Gary","Jack"],"index":47790,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9650467634,"difficulty":0.0349532366}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Mary can now know that Jackie can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mary","Jackie"],"index":65674,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982973933,"difficulty":0.0017026067}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Michael can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Mary","Michelle","Michael"],"index":67543,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977205396,"difficulty":0.0022794604}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colleen does not know whether Colleen's forehead is muddy. It is publicly announced that Colleen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Patricia can now know that Colleen can know that Patricia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Colleen","Patricia"],"index":18794,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8000805974,"difficulty":0.1999194026}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jessica knows whether Betty's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Stanley can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victoria","Betty","Stanley","Jessica"],"index":62182,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9924713373,"difficulty":0.0075286627}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] [ ! 3 ] 0","hypothesis":"Christopher can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ronald","John","Christopher"],"index":29311,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9545680881,"difficulty":0.0454319119}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Lois can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Terrance","Fred","Sonny","Lois"],"index":16671,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984656572,"difficulty":0.0015343428}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daina does not know whether Daina's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Ralph can now know that Joe can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joe","Daina","Ralph"],"index":22794,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9449759126,"difficulty":0.0550240874}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan knows whether or not nobody's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Dan can now know that Clint can know whether Dan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Clint","Dan","Diane"],"index":4517,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999327302,"difficulty":0.000672698}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen does not know whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Francis can now know that Thomas can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Francis","Helen","Robert","Thomas"],"index":37306,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984412789,"difficulty":0.0015587211}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor does not know whether Eleanor's forehead is muddy. It is publicly announced that Mary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Eleanor can now know whether Mary can know whether Eleanor's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eleanor","Mary"],"index":15087,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979196191,"difficulty":0.0020803809}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy. It is publicly announced that Sharita's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(2) ] 0","hypothesis":"Sharita can now know whether Christopher can know that Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Betty","Sharita","Christopher"],"index":63302,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9841775894,"difficulty":0.0158224106}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether James's forehead is muddy. It is publicly announced that James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] [ ! 2 ] 0","hypothesis":"Anna can now know that Anna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Anna","James","Ross","Kevin"],"index":42411,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8322613239,"difficulty":0.1677386761}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melissa does not know whether Melissa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Addie can now know whether Ann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Melissa","Ann","Christina","Addie"],"index":29387,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996019006,"difficulty":0.0003980994}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ella does not know whether or not everyone's forehead is muddy. It is publicly announced that Ella knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agenta knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Amanda can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Amanda","Ella"],"index":51705,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997771382,"difficulty":0.0002228618}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether Karen's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] Agentb knows that (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (1&2) ] 0","hypothesis":"Karen can now know that Tiffany can know whether Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Tiffany","Karen"],"index":15028,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.990378499,"difficulty":0.009621501}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosetta does not know whether Rosetta's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Dorothy knows whether or not everyone's forehead is muddy. It is publicly announced that Dorothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] Agentd knows that (Agentc knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! 2 ] 0","hypothesis":"Sandra can now know that Rosetta can know whether Rosetta's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andrew","Dorothy","Rosetta","Sandra"],"index":60622,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7801039219,"difficulty":1.7801039219}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida knows whether someone's forehead is muddy. It is publicly announced that Patricia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Seth can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Ida","Seth","Bill","Patricia"],"index":60439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997804761,"difficulty":0.0002195239}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michele knows whether Michele's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Eric can now know whether Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Eric","Sherry","Patrick","Michele"],"index":318,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999566257,"difficulty":0.000433743}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy does not know whether Timothy's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Libby knows whether Timothy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Libby can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Timothy","Michael","Libby"],"index":35262,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995112419,"difficulty":0.0004887581}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Michael can now know that Janet can know whether Janet's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Michael","Janet","Rex","Robert"],"index":65122,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9930968881,"difficulty":0.0069031119}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Demetrius's forehead is not muddy. It is publicly announced that Milan knows whether Milan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Milan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Demetrius","Sylvia","Milan","Gary"],"index":54443,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998481214,"difficulty":0.001518786}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin knows whether Robin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 4) ] 0","hypothesis":"Robin can now know whether Tommy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Dolores","Phyllis","Tommy","Robin"],"index":30194,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994723201,"difficulty":0.0005276799}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anneliese knows whether Anneliese's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Nancy can now know whether Stacy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nancy","Stacy","Anneliese"],"index":53397,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995927215,"difficulty":0.0004072785}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne does not know whether Wayne's forehead is muddy. It is publicly announced that Lori's forehead is muddy. It is publicly announced that Carmen knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 1 ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Wayne can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lori","Carmen","Margaret","Wayne"],"index":43978,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981302619,"difficulty":0.0018697381}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Daniel can now know that Frank can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Frank","Javier","Daniel","John"],"index":13954,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999706924,"difficulty":0.000293076}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"David can now know that Krystyna can know whether Krystyna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Robert","Krystyna","David","Rene"],"index":65264,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6618156433,"difficulty":1.6618156433}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Isidro does not know whether Isidro's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Isidro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Clifford","James","Isidro"],"index":58591,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9888640642,"difficulty":0.0111359358}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoine knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Dena knows whether Dena's forehead is muddy. It is publicly announced that Antoine knows whether Dena's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Dena can now know whether Lois can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lois","Dena","Antoine"],"index":2030,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997040629,"difficulty":0.0002959371}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pedro does not know whether Pedro's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agenta knows whether (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Mark can now know whether Pedro can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mark","Lorraine","Misty","Pedro"],"index":23654,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996911287,"difficulty":0.0003088713}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew knows whether Elliott's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Roy can now know that Elliott can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Matthew","Elliott","Roy"],"index":8014,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9915456176,"difficulty":0.0084543824}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nathaniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"Nathaniel can now know whether Brendan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Nathaniel","Brendan","Sherri"],"index":63558,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994904995,"difficulty":0.0005095005}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Christine can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Daniel","David","Sarah","Christine"],"index":9640,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980667233,"difficulty":0.0019332767}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynette's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] 0","hypothesis":"Philip can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Lynette","Philip"],"index":49003,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998509109,"difficulty":0.001490891}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmine does not know whether Carmine's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Amy can now know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Carmine","Sylvia","Amy"],"index":36645,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9768291116,"difficulty":0.0231708884}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentb knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lino can now know whether Eduardo can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lino","Eduardo","Peter","David"],"index":51568,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995415211,"difficulty":0.0004584789}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robin does not know whether Robin's forehead is muddy. It is publicly announced that Kenneth's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(2) ] 0","hypothesis":"Lucia can now know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Michael","Kenneth","Robin","Lucia"],"index":67564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9996092916,"difficulty":0.0003907084}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Virginia can now know whether Kathy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Virginia","Thomas","Kathy","Teresa"],"index":49645,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994192123,"difficulty":0.0005807877}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Lawrence can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Nan","Eloise","Janet","Lawrence"],"index":59252,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985914826,"difficulty":0.0014085174}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cyril knows whether Cyril's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Cyril can now know that Danielle can know that Cyril's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Danielle","Bradley","Cyril"],"index":30057,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9973831773,"difficulty":1.9973831773}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kate does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Tania can now know that Young's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Young","Nancy","Tania","Kate"],"index":27388,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.795085907,"difficulty":0.204914093}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alyssa's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] (Agentb knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Alyssa can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Russell","Alyssa"],"index":49803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997288585,"difficulty":0.0002711415}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James's forehead is muddy. It is publicly announced that Stephanie does not know whether Stephanie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donna can now know that James can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Stephanie","Donna","James"],"index":58480,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99977988,"difficulty":0.00022012}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Sandra can now know that Rose can know that Lester's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lester","Sandra","Rose"],"index":8212,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9981684685,"difficulty":0.0018315315}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Debrah can now know that William can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Elizabeth","Debrah","William"],"index":28410,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997802377,"difficulty":0.0002197623}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillian knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jean can now know that Mariela's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mariela","Lillian","Jean"],"index":53304,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6589118242,"difficulty":0.3410881758}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Michael can now know whether Alvaro can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Michael","Alvaro"],"index":40768,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9986365438,"difficulty":0.0013634562}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia knows whether someone's forehead is muddy. It is publicly announced that Virginia knows whether or not everyone's forehead is muddy. It is publicly announced that Margarite's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Juliet can now know that Virginia can know that Margarite's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margarite","Juliet","Virginia","Grace"],"index":40238,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8862134814,"difficulty":0.1137865186}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tommy does not know whether Tommy's forehead is muddy. It is publicly announced that Gregory does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Gregory can now know that Tommy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Tommy","Gregory","Erika","Archie"],"index":39020,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.791200757,"difficulty":0.208799243}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shane's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Shane can now know that Shane's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","Robert","Shane","Kevin"],"index":67349,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.849301517,"difficulty":0.150698483}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genevieve knows whether someone's forehead is muddy. It is publicly announced that Heather knows whether Joseph's forehead is muddy. It is publicly announced that Joseph knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentb knows that (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Heather can now know that Joseph can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Genevieve","Heather","Hortensia","Joseph"],"index":27123,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984334111,"difficulty":0.0015665889}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agentb knows whether (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Letitia can now know whether William can know whether Letitia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["William","Letitia"],"index":66066,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958484173,"difficulty":0.0041515827}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Audrey's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Audrey can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Dewey","Audrey"],"index":22244,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9944387674,"difficulty":0.0055612326}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela does not know whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jamie can now know whether Angela can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Lottie","Jamie","Felica"],"index":29461,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954990745,"difficulty":0.0045009255}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian knows whether Chad's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Chad can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Marian","Chad"],"index":21819,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982414246,"difficulty":0.0017585754}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell knows whether Lynn's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Brian can now know whether Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Lynn","Brian","Darrell"],"index":57553,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927154183,"difficulty":0.0072845817}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paulette knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows whether (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Charles can now know whether Russell can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Charles","Paulette","Russell"],"index":13608,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9629603028,"difficulty":0.0370396972}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd does not know whether Todd's forehead is muddy. It is publicly announced that Justin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! 1 ] 0","hypothesis":"Justin can now know that Todd can know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Justin","Todd"],"index":38552,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7830030918,"difficulty":0.2169969082}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ona does not know whether Ona's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Ona can now know whether Helen can know that Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Helen","Ona","John"],"index":58865,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9499140382,"difficulty":1.9499140382}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Johnetta does not know whether Johnetta's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Travis can now know whether Johnetta can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Travis","Johnetta"],"index":45898,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997662902,"difficulty":0.0002337098}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Lee can now know whether Mildred can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lee","Richard","Mildred","Hobert"],"index":9326,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9791101813,"difficulty":0.0208898187}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesus knows whether Barry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Barry can now know that Dortha's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jesus","Barry","Dortha","Caroline"],"index":15595,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983022213,"difficulty":0.0016977787}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sanford knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentb knows whether (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Jeanne can now know whether Calvin can know that Brandy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sanford","Jeanne","Brandy","Calvin"],"index":26020,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979793429,"difficulty":0.0020206571}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregory's forehead is not muddy. It is publicly announced that Gregory's forehead is not muddy. It is publicly announced that Dwight knows whether Gregory's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Dwight can now know that April's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Dwight","April","Gregory"],"index":17345,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9194930792,"difficulty":0.0805069208}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Arthur can now know that Yvonne can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Arthur","Cristy","John","Yvonne"],"index":29893,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979838133,"difficulty":0.0020161867}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Santiago does not know whether Santiago's forehead is muddy. It is publicly announced that Santiago's forehead is muddy. It is publicly announced that Andrew's forehead is muddy. It is publicly announced that Henry's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! 1 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Santiago can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Santiago","Henry","Andrew","Guillermo"],"index":155,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6964222789,"difficulty":0.3035777211}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lois knows whether someone's forehead is muddy. It is publicly announced that Lois knows whether someone's forehead is muddy. It is publicly announced that Elijah knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] (Agenta knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Elijah can now know whether Elijah's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elijah","Lois"],"index":60265,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7262375951,"difficulty":1.7262375951}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shawn knows whether Shawn's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] Agentd knows that (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Mark can now know that Shawn can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shawn","Anna","Stephen","Mark"],"index":40012,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992194176,"difficulty":0.0007805824}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joshua can now know that Angela can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angela","Joshua","Patricia","Arlene"],"index":18690,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997529387,"difficulty":0.0002470613}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dolores's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] (Agenta knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] 0","hypothesis":"Dolores can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dolores","James"],"index":41865,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984048009,"difficulty":0.0015951991}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wenona knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Bernard can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jacob","Wenona","Bernard","James"],"index":33948,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999697566,"difficulty":0.000302434}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Christie can now know that Christie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michael","Christie","David","Daniel"],"index":15159,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7017980814,"difficulty":0.2982019186}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"John can now know that Paul can know that Keith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Keith","Paul","John","Hester"],"index":6908,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9392620921,"difficulty":0.0607379079}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephanie's forehead is muddy. It is publicly announced that Stephanie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Stephanie can now know that Sherri can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Stephanie","Sherri"],"index":49320,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.518330276,"difficulty":1.518330276}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"James can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["James","Mary"],"index":3762,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997035861,"difficulty":0.0002964139}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul knows whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that Patrick knows whether Marion's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marion","Patrick","Paul","James"],"index":18683,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9985089898,"difficulty":0.0014910102}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Timothy can now know that Carmelo can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["James","Karen","Timothy","Carmelo"],"index":46216,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995778203,"difficulty":0.0004221797}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Omar does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Omar can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Omar","Dale","Morris"],"index":6464,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997723699,"difficulty":0.0002276301}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Thomas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Jose can now know whether Thomas can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Jose","Norma"],"index":25592,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997164607,"difficulty":0.0002835393}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentd knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Josephine can now know whether Jessica can know that Martha's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donald","Jessica","Martha","Josephine"],"index":59710,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9952690005,"difficulty":0.0047309995}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether or not everyone's forehead is muddy. It is publicly announced that Andrew knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Richard can now know that Andrew can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Richard","Andrew"],"index":39988,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993033409,"difficulty":0.0006966591}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Benjamin knows whether someone's forehead is muddy. It is publicly announced that Leonor's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Benjamin can now know that Kathaleen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Benjamin","Peggy","Kathaleen","Leonor"],"index":12841,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928990602,"difficulty":0.0071009398}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Paula can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sandra","Paula","Scott"],"index":60094,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983152151,"difficulty":0.0016847849}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"John can now know that Christopher can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Juana","Johanna","John","Christopher"],"index":3058,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992413521,"difficulty":0.0007586479}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy. It is publicly announced that Jerome knows whether Christopher's forehead is muddy. It is publicly announced that Jerome does not know whether Jerome's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agentc knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Jerome can now know that Dale can know that Dale's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeanne","Dale","Jerome","Christopher"],"index":36333,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898236394,"difficulty":0.0101763606}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Jerry knows whether Jerry's forehead is muddy. It is publicly announced that Wayne knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] Agentc knows whether (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (1&2&3) ] [ ! (Agentb knows whether 2) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Wayne can now know whether Jerry can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Edward","Jerry","Wayne"],"index":57246,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9959962368,"difficulty":0.0040037632}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela's forehead is muddy. It is publicly announced that Rebecca's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] Agentd knows whether (Agentb knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Richard can now know whether Angela can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Angela","Rebecca","Richard"],"index":18571,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7322888374,"difficulty":0.2677111626}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucia knows whether someone's forehead is muddy. It is publicly announced that Lucia knows whether David's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Katie can now know whether Ana can know that Ana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ana","Katie","David","Lucia"],"index":2962,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5881006718,"difficulty":0.4118993282}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paula's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Paula can now know that Haywood's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Haywood","Brenda","Charles","Paula"],"index":36414,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9927500486,"difficulty":0.0072499514}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys does not know whether Gladys's forehead is muddy. It is publicly announced that Larry knows whether or not everyone's forehead is muddy. It is publicly announced that Larry knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Larry can now know that Gladys's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Gladys","Larry"],"index":64806,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.595692873,"difficulty":0.404307127}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie knows whether or not everyone's forehead is muddy. It is publicly announced that Harry knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Bonnie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Jerry","Harry","Bonnie"],"index":1900,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997197986,"difficulty":0.0002802014}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jessie's forehead is not muddy. It is publicly announced that Cynthia knows whether Katherine's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Jessie can now know whether Katherine can know whether Cynthia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cynthia","Katherine","Jessie","Helen"],"index":10321,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983987212,"difficulty":0.0016012788}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy. It is publicly announced that Reid knows whether Reid's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Daniel can now know whether Reid can know that Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Reid","Daniel"],"index":7186,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.5839731097,"difficulty":0.4160268903}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Susan does not know whether Susan's forehead is muddy. It is publicly announced that Ashley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ashley can now know that Jack can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Susan","Ashley","Jack"],"index":65963,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978430271,"difficulty":0.0021569729}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy. It is publicly announced that Xiao's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] Agentb knows whether (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(2) ] 0","hypothesis":"Xiao can now know whether Susan can know that Xiao's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Xiao","Susan"],"index":58211,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8466256857,"difficulty":0.1533743143}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey does not know whether Jeffrey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Loretta can now know whether Jeffrey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Loretta","Kathy","Jeffrey"],"index":3860,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994695783,"difficulty":0.0005304217}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Zachary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Michael can now know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kristie","Eric","Zachary","Michael"],"index":34877,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983307719,"difficulty":0.0016692281}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Glen's forehead is not muddy. It is publicly announced that Glen knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] 0","hypothesis":"Avis can now know whether Glen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Avis","Glen","Laura"],"index":31358,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995326996,"difficulty":0.0004673004}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scotty does not know whether Scotty's forehead is muddy. It is publicly announced that Lisa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Lisa can now know that Scotty's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Christopher","Scotty","Lisa"],"index":20161,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5191722512,"difficulty":1.5191722512}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy. It is publicly announced that Kimberly knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Donald can now know whether Donald's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Eric","Donald","Kimberly"],"index":23855,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5306899548,"difficulty":1.5306899548}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Paul's forehead is muddy. It is publicly announced that Marielle does not know whether or not everyone's forehead is muddy. It is publicly announced that Marielle does not know whether Marielle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Marielle can now know whether Paul can know whether Paul's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Paul","Marielle"],"index":46476,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9419451356,"difficulty":0.0580548644}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lynda does not know whether or not everyone's forehead is muddy. It is publicly announced that Lynda knows whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Peter can now know that Daniel can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lynda","Leon","Daniel","Peter"],"index":28680,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978821874,"difficulty":0.0021178126}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"James can now know whether Jessie can know that Donna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Donna","Jessie","James","Keith"],"index":63987,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9980211258,"difficulty":0.0019788742}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Emma can now know that Elizabeth can know that Emma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["George","Elizabeth","Emma"],"index":20950,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9790070057,"difficulty":0.0209929943}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lena does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Virginia can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Richard","Virginia","Gregory","Lena"],"index":1373,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977982044,"difficulty":0.0022017956}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frankie's forehead is muddy. It is publicly announced that Lilian knows whether someone's forehead is muddy. It is publicly announced that Frankie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agenta knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Jeanna can now know that Frankie can know that Lilian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Frankie","Jeanna","Lilian"],"index":38735,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9727553129,"difficulty":0.0272446871}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alex's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Alex can now know that Gina can know whether Gina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Wilfredo","Alex","Gina","Nancy"],"index":62418,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742544889,"difficulty":0.0257455111}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy. It is publicly announced that James's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"James can now know whether David can know whether James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Tracy","David","James","Vincent"],"index":36309,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993189573,"difficulty":0.0006810427}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raphael's forehead is muddy. It is publicly announced that Ashley does not know whether Ashley's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Raphael can now know whether Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Raphael","Steven","Charles","Ashley"],"index":63579,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994755387,"difficulty":0.0005244613}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michael can now know that Janet's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Janet"],"index":5366,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8237550855,"difficulty":1.8237550855}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Harry knows whether Peter's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (~(1&2&3)) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Peter can now know whether Ralph can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Peter","Ralph"],"index":67396,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997778535,"difficulty":0.0002221465}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lisa knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Angelina can now know whether Karen can know whether Mark's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Karen","Mark","Lisa","Angelina"],"index":27468,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999542594,"difficulty":0.000457406}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather does not know whether Heather's forehead is muddy. It is publicly announced that Heather does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Heather can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joshua","James","Heather"],"index":48583,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978017211,"difficulty":0.0021982789}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether Rebecca's forehead is muddy. It is publicly announced that James's forehead is not muddy. It is publicly announced that Raymond knows whether Raymond's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agentc knows whether (Agentb knows whether (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Rebecca can now know whether Christopher can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Christopher","Rebecca","James"],"index":54810,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8125815988,"difficulty":1.8125815988}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anthony knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Anthony can now know that Linda can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Phillip","Ralph","Linda"],"index":13474,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997532964,"difficulty":0.0002467036}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Charles knows whether someone's forehead is muddy. It is publicly announced that Jack does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows that (Agentb knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Jack can now know that Peggy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jack","Peggy","Charles"],"index":58317,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9997794032,"difficulty":0.0002205968}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Bertha can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Bertha","Robert"],"index":20145,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9334014654,"difficulty":1.9334014654}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christie knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Shirley can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Shirley","Christie","Joe"],"index":42421,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891405106,"difficulty":0.0108594894}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Joe can now know whether Rebecca can know that Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rebecca","Daniel","Joe"],"index":42140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9419466853,"difficulty":0.0580533147}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delbert does not know whether Delbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Delbert can now know whether Betty can know whether Betty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Delbert","Betty","Blanca"],"index":30841,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.91276896,"difficulty":1.91276896}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas does not know whether Nicholas's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (~(1&2)) ] 0","hypothesis":"Eula can now know that Nicholas can know that Eula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nicholas","Eula"],"index":38217,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9955910444,"difficulty":1.9955910444}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] (Agentb knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"David can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andre","David"],"index":33215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9984454513,"difficulty":0.0015545487}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn knows whether Eric's forehead is muddy. It is publicly announced that Eric knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows whether (Agentb knows whether (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Eric can now know whether Kathryn can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Eric","Kathryn"],"index":46721,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994540811,"difficulty":0.0005459189}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Faye does not know whether Faye's forehead is muddy. It is publicly announced that Jon's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agenta knows whether (Agentc knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"James can now know whether Anne can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Faye","Anne","Jon"],"index":33829,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7107486129,"difficulty":1.7107486129}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentd knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Harry can now know whether Sarah can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gregory","Clara","Sarah","Harry"],"index":57682,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9394689202,"difficulty":0.0605310798}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Kenneth can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Joseph","Blake","Ryan"],"index":11480,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992123842,"difficulty":0.0007876158}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy. It is publicly announced that Claude knows whether Claude's forehead is muddy. It is publicly announced that Robert knows whether Claude's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Robert can now know whether Claude can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Claude"],"index":8097,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9891377091,"difficulty":0.0108622909}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard knows whether or not everyone's forehead is muddy. It is publicly announced that Richard knows whether someone's forehead is muddy. It is publicly announced that Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! 3 ] 0","hypothesis":"Vincent can now know that Thomas can know whether Vincent's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vincent","Thomas","Richard"],"index":30382,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984818101,"difficulty":0.0015181899}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ralph knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Thelma can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Ralph","Thelma","William"],"index":16107,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988045692,"difficulty":0.0011954308}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Juana can now know that Connie can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Connie","Ann","Juana"],"index":48609,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988325238,"difficulty":0.0011674762}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amanda does not know whether Amanda's forehead is muddy. It is publicly announced that Maxine knows whether or not everyone's forehead is muddy. It is publicly announced that Amanda's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2)) ] [ ! ~(2) ] 0","hypothesis":"Amanda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Maxine","Amanda"],"index":16884,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976750016,"difficulty":0.0023249984}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Clifton can now know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Clifton","Scott","Sylvia"],"index":14696,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990261793,"difficulty":0.0009738207}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Shirley can now know whether Alice can know whether Alice's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Alice","Stephanie"],"index":40322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967036843,"difficulty":0.0032963157}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eric's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Eric can now know that Patricia can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Helen","Eric","Patricia","Angie"],"index":19351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994887114,"difficulty":0.0005112886}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Robert can now know that Andrew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michelle","Andrew","Robert"],"index":27754,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9629219174,"difficulty":0.0370780826}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Burton knows whether Charles's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Susan can now know whether Susan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Burton","Susan","Charles"],"index":18919,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.993008256,"difficulty":0.006991744}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lorna knows whether Aaron's forehead is muddy. It is publicly announced that Aaron does not know whether Aaron's forehead is muddy. It is publicly announced that Aaron does not know whether Aaron's forehead is muddy. It is publicly announced that Aaron knows whether Lorna's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Aaron can now know that Lorna can know that Lorna's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lorna","Aaron"],"index":47451,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9007114768,"difficulty":1.9007114768}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1|2|3))","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Lauren can now know whether Mary can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Jeanne","Lauren"],"index":10995,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994056225,"difficulty":0.0005943775}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cornell knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows whether (Agentb knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Vernon can now know whether Stephan can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Vernon","Stephan","Cornell"],"index":58666,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993751645,"difficulty":0.0006248355}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agenta knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Randall can now know that Madeleine can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Madeleine","Randall","David","Delbert"],"index":36497,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993921518,"difficulty":0.0006078482}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry does not know whether Harry's forehead is muddy. It is publicly announced that Ignacio knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Ignacio can now know whether Harry can know that Harry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ignacio","Harry"],"index":3256,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7053913474,"difficulty":0.2946086526}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Kate can now know whether Tony can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["David","Tony","Jose","Kate"],"index":65119,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9984663725,"difficulty":0.0015336275}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle's forehead is muddy. It is publicly announced that Gerald does not know whether Gerald's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michelle can now know whether Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Gerald","Melanie","Michelle"],"index":60515,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.81378901,"difficulty":0.18621099}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (1&2)) ] [ ! (~(1&2)) ] 0","hypothesis":"Robert can now know whether Anthony can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Robert","Anthony"],"index":14079,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993548989,"difficulty":0.0006451011}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carmela knows whether Carmela's forehead is muddy. It is publicly announced that Susan knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Susan can now know whether Cyrus can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Carmela","Cyrus","Susan"],"index":34920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992540479,"difficulty":0.0007459521}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Douglas knows whether Douglas's forehead is muddy. It is publicly announced that Douglas's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] Agentd knows that (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! ~(3) ] 0","hypothesis":"Brian can now know that Edward can know that Douglas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Edward","Shawn","Douglas","Brian"],"index":46843,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.983716011,"difficulty":0.016283989}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeffrey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Brandi can now know that Leon can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["William","Jeffrey","Leon","Brandi"],"index":66625,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998927772,"difficulty":0.001072228}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billy knows whether Billy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Linda can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Billy","Cynthia","Lulu","Linda"],"index":63532,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9348654747,"difficulty":1.9348654747}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lee does not know whether Lee's forehead is muddy. It is publicly announced that Jerry does not know whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Lee can now know that Jerry can know that Lee's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Tammy","Lee"],"index":64311,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9821106791,"difficulty":0.0178893209}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Russell can now know that Aaron can know that Aaron's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brian","Aaron","Kenneth","Russell"],"index":35763,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970061183,"difficulty":0.0029938817}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cheryl knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Cheryl can now know that Cheryl's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Cynthia","Cheryl","Edna"],"index":52594,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.963588655,"difficulty":0.036411345}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Floyd does not know whether Floyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Kevin can now know that Lillie can know whether Floyd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Lillie","Floyd","Kevin","Betty"],"index":23537,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.998950839,"difficulty":0.001049161}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas does not know whether Thomas's forehead is muddy. It is publicly announced that Daniel does not know whether Daniel's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Megan can now know that Thomas can know that Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Daniel","Laura","Thomas","Megan"],"index":55335,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962355494,"difficulty":0.0037644506}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gwendolyn knows whether Toby's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Carry can now know whether Alan can know that Toby's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carry","Alan","Toby","Gwendolyn"],"index":62250,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.943380475,"difficulty":0.056619525}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy. It is publicly announced that John does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Craig can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Craig","John"],"index":4785,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994702935,"difficulty":0.0005297065}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dan does not know whether Dan's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Cody can now know whether Matthew can know whether Dan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Dan","Cody","Matthew"],"index":42996,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991588593,"difficulty":0.0008411407}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Michael can now know whether William can know that Louise's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Carolyn","Michael","William","Louise"],"index":7575,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9870142937,"difficulty":0.0129857063}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentd knows that (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Amanda can now know that Martha can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Martha","Thomas","Amanda"],"index":55888,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894743562,"difficulty":0.0105256438}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilma knows whether or not everyone's forehead is muddy. It is publicly announced that Wilma does not know whether Wilma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Wilma can now know that Christy's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wilma","Christy","Tammy"],"index":41246,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9807434678,"difficulty":0.0192565322}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom does not know whether or not everyone's forehead is muddy. It is publicly announced that Tom knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Tom can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Joseph","Helen","Tom","Rex"],"index":14472,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990488887,"difficulty":0.0009511113}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Bradley can now know that Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bradley","Robert"],"index":64715,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9754604697,"difficulty":0.0245395303}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Billie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Willie can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Andrew","Willie","Billie"],"index":42056,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994575381,"difficulty":0.0005424619}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Arturo knows whether Ronald's forehead is muddy. It is publicly announced that Malika's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] Agentc knows whether (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Malika can now know whether Arturo can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Arturo","Amanda","Malika","Ronald"],"index":24199,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993374944,"difficulty":0.0006625056}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether William's forehead is muddy. It is publicly announced that Tarah knows whether or not everyone's forehead is muddy. It is publicly announced that Roger knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] Agentb knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] [ ! (Agenta knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"William can now know that Agustin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Tarah","William","Roger","Agustin"],"index":67581,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990353584,"difficulty":0.0009646416}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas knows whether Philip's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentc knows that (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Thomas can now know that Philip can know that Philip's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Timothy","Thomas","Isaac"],"index":19675,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9846950173,"difficulty":0.0153049827}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Michael's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Jason can now know that Carla can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Carla","Jason"],"index":25511,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999317646,"difficulty":0.000682354}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jane knows whether Victoria's forehead is muddy. It is publicly announced that Jane knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Victoria can now know whether Jane can know that Victoria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Victoria","Jane"],"index":61133,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7783370614,"difficulty":0.2216629386}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frank knows whether or not everyone's forehead is muddy. It is publicly announced that Frank knows whether Frank's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Frank can now know that Chris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Chris","Frank"],"index":34035,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994766116,"difficulty":0.0005233884}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Jill can now know that Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Jill","Thomas","James"],"index":63628,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971154928,"difficulty":0.0028845072}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Reba can now know that Antonio's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Peter","Michael","Antonio","Reba"],"index":5636,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963650703,"difficulty":0.0036349297}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Seymour knows whether or not everyone's forehead is muddy. It is publicly announced that Seymour does not know whether Seymour's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Janice can now know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Seymour","Steven","Janice"],"index":32131,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9847220778,"difficulty":0.0152779222}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bridget does not know whether Bridget's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentc knows whether (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Kelly can now know whether Bridget can know that Bridget's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bridget","Ann","Kelly"],"index":61536,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.670168817,"difficulty":1.670168817}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilber knows whether Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Wilber can now know that Niki can know that Wilber's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wilber","Angela","Niki"],"index":22022,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9974488616,"difficulty":0.0025511384}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luana does not know whether Luana's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Luana can now know whether Lizzie can know that Luana's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lizzie","Luana","Kenneth"],"index":21575,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8651457429,"difficulty":0.1348542571}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"William can now know whether Latasha can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tasha","Latasha","William"],"index":14120,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9623618722,"difficulty":0.0376381278}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nichole knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Nichole can now know that Lazaro's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Berenice","Nichole","Lazaro"],"index":34321,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980475903,"difficulty":0.0019524097}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Joel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Joel can now know that Albert can know that Joel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Albert","Joel"],"index":28057,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9806885719,"difficulty":0.0193114281}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Russell's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agenta knows that (Agentd knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"James can now know that Russell can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["James","Darlene","Brian","Russell"],"index":28691,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989350438,"difficulty":0.0010649562}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candace knows whether Candace's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Candace can now know that Candace's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Linda","Candace","Evelyn","Kerry"],"index":14649,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9594967961,"difficulty":1.9594967961}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Teresa knows whether Teresa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Susan can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Teresa","Raymond","Kenneth","Susan"],"index":54217,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989216328,"difficulty":0.0010783672}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sabra does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Sabra can now know whether Rafael can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sabra","Kim","Carol","Rafael"],"index":43489,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7188408971,"difficulty":0.2811591029}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremy does not know whether Jeremy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Margaret can now know whether Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Jeremy","Margaret"],"index":23351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7241882086,"difficulty":0.2758117914}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lessie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Lessie can now know whether Carlota's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["John","Lessie","Carlota"],"index":16859,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991946816,"difficulty":0.0008053184}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lillie does not know whether Lillie's forehead is muddy. It is publicly announced that Donna does not know whether Donna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Donna can now know that Lillie can know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Donna","Julie","Edward","Lillie"],"index":33864,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9970914125,"difficulty":0.0029085875}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentc knows whether (Agentb knows whether 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Bridgette can now know whether Timothy can know whether Lori's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mollie","Timothy","Bridgette","Lori"],"index":66950,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991649389,"difficulty":0.0008350611}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven knows whether Jewell's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agentb knows whether (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Jewell can now know whether Steven can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Herbert","Jewell","Steven"],"index":45910,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992911816,"difficulty":0.0007088184}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ken knows whether Lonnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agentb knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Matthew can now know that Lonnie can know whether Lonnie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lonnie","Matthew","Ken"],"index":62653,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9701254964,"difficulty":0.0298745036}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Melba can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joyce","Melba","Daniel","Joshua"],"index":7687,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994231462,"difficulty":0.0005768538}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karla's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Bill can now know that John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Bill","Emelda","John","Karla"],"index":15013,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8293312788,"difficulty":0.1706687212}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gordon does not know whether or not everyone's forehead is muddy. It is publicly announced that Victor knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Victor can now know that Gordon can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Gordon","Victor"],"index":8324,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994547963,"difficulty":0.0005452037}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Isabel knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Isabel can now know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["George","David","Ethel","Isabel"],"index":46149,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9952175617,"difficulty":0.0047824383}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] Agentd knows that (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Karen can now know that Patricia can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","Shannon","Patricia","Karen"],"index":63002,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9868572354,"difficulty":0.0131427646}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harold's forehead is not muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Michael knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Patty can now know whether Harold can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Patty","Harold","Michael"],"index":9055,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9867292643,"difficulty":0.0132707357}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theresa does not know whether Theresa's forehead is muddy. It is publicly announced that Theresa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Theresa can now know whether Pearl can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Pearl","Lonnie","Theresa"],"index":25278,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9878314137,"difficulty":0.0121685863}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Annie can now know that Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Annie","Susie","David"],"index":41370,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9868817329,"difficulty":0.0131182671}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dennis does not know whether Dennis's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Gary can now know that Dennis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gary","Dennis","Aaron","Brandon"],"index":41791,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9912762642,"difficulty":0.0087237358}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sandra knows whether Jerry's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Jerry can now know whether Sandra can know whether Sandra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jerry","Ruth","Sandra"],"index":29586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7922455668,"difficulty":0.2077544332}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Mary can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Laura","Mary","Karen","Sandra"],"index":30627,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993593097,"difficulty":0.0006406903}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Issac does not know whether Issac's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Issac can now know whether Tiffany can know that Tiffany's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Royce","Lisa","Tiffany","Issac"],"index":48567,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9908379912,"difficulty":1.9908379912}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack does not know whether Jack's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Christina can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jack","Rey","Christina","James"],"index":10927,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9801415205,"difficulty":0.0198584795}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gayla does not know whether Gayla's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Gayla","Helen","Robert","George"],"index":37582,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990119934,"difficulty":0.0009880066}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Millie does not know whether Millie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Michele can now know that Angela can know that Millie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Angela","Michele","Millie"],"index":28859,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969453216,"difficulty":0.0030546784}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Lisette can now know whether John can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Lisette","John"],"index":34036,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989971519,"difficulty":0.0010028481}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Russell's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Russell can now know that Vincent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Vincent","Russell"],"index":14427,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9978606105,"difficulty":1.9978606105}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Roberta can now know that Rubie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Roberta","Rubie","Joseph","Alicia"],"index":64588,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976066351,"difficulty":0.0023933649}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Christopher can now know that Howard can know whether Brandon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Christopher","Howard","Brandon"],"index":63139,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999266088,"difficulty":0.000733912}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catharine's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] Agentb knows whether (Agenta knows whether (1|2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Catharine can now know whether Michael can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michael","Catharine"],"index":45571,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994698167,"difficulty":0.0005301833}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agenta knows whether (Agentb knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Leroy can now know whether Matthew can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Leroy","Matthew","Donna"],"index":67506,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9724444151,"difficulty":0.0275555849}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jesse's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentc knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Charles can now know that Jesse can know that Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Wesley","Charles","Jesse"],"index":50783,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976673126,"difficulty":0.0023326874}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Willie's forehead is muddy. It is publicly announced that Katherine's forehead is muddy. It is publicly announced that Luana does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Willie can now know that Luana can know whether Jacob's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Willie","Katherine","Jacob","Luana"],"index":48378,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999324441,"difficulty":0.000675559}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Esther's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Christina can now know whether Esther can know whether Esther's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Esther","Christina","Ethel"],"index":8007,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9930348396,"difficulty":0.0069651604}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Mary can now know that Marian can know whether Marian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shirley","Marian","Mary"],"index":16909,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6765496135,"difficulty":1.6765496135}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kristen does not know whether Kristen's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (1|2|3) ] 0","hypothesis":"Sherry can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Sherry","Kristen","Jane"],"index":31193,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99899894,"difficulty":0.00100106}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Emmett knows whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Elizabeth can now know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Danelle","Elizabeth","Emmett"],"index":30091,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9624332786,"difficulty":0.0375667214}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lloyd knows whether William's forehead is muddy. It is publicly announced that Lloyd knows whether Lloyd's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Lloyd can now know that William can know whether Lloyd's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Lloyd","Elizabeth"],"index":48642,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9074786305,"difficulty":0.0925213695}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Carol can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Carol","Kimberly"],"index":64860,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998662591,"difficulty":0.001337409}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather does not know whether Heather's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Brenda can now know that Sharon can know whether Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carolyn","Brenda","Sharon","Heather"],"index":8979,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931069016,"difficulty":0.0068930984}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patty's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Eric can now know that Patty can know that Patty's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Eric","Patty","Terri","Ann"],"index":51983,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958317876,"difficulty":0.0041682124}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond's forehead is not muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Raymond knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agentd knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Hannah can now know that Sean can know whether Hannah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Raymond","Hannah","Morris","Sean"],"index":29718,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982126951,"difficulty":0.0017873049}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether Norma's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Norma can now know that Jessica can know that Caterina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Pamela","Norma","Caterina","Jessica"],"index":26647,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969627261,"difficulty":0.0030372739}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy. It is publicly announced that James does not know whether James's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"James can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["James","Terry"],"index":60523,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6840852499,"difficulty":0.3159147501}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether Brian's forehead is muddy. It is publicly announced that Brian does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentc knows whether (Agentb knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Harold can now know whether Karey can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brian","Karey","Harold","Nell"],"index":22933,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994516969,"difficulty":0.0005483031}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"George can now know that Michael can know whether Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kenneth","William","George","Michael"],"index":65694,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5304114223,"difficulty":1.5304114223}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Tammy's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] Agenta knows whether (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1&2) ] [ ! 2 ] 0","hypothesis":"Walter can now know whether Tammy can know whether Tammy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Walter","Tammy"],"index":42787,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9914035201,"difficulty":0.0085964799}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lewis's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Vincent can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jeremiah","Lewis","Vincent"],"index":23121,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989441037,"difficulty":0.0010558963}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amada knows whether or not nobody's forehead is muddy. It is publicly announced that Clinton's forehead is muddy. It is publicly announced that Eric does not know whether or not everyone's forehead is muddy. It is publicly announced that Eric's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agenta knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Eric can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eric","Amada","Clinton","Jesse"],"index":48558,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989901185,"difficulty":0.0010098815}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tanisha knows whether Juan's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Juan can now know whether Anthony can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Greg","Anthony","Tanisha","Juan"],"index":47301,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9705462456,"difficulty":0.0294537544}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] 0","hypothesis":"David can now know that Freddie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","David","Freddie"],"index":65953,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9928190112,"difficulty":0.0071809888}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Vivian can now know that Andrea can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emmanuel","Andrea","John","Vivian"],"index":41167,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753988981,"difficulty":0.0246011019}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentc knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Lucretia can now know whether Kelly can know whether Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Richard","Kelly","Lucretia"],"index":5172,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992300272,"difficulty":0.0007699728}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elisabeth does not know whether Elisabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows that (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Terrence can now know that Amy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Elisabeth","Terrence","Amy"],"index":49054,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989773035,"difficulty":0.0010226965}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Randall does not know whether Randall's forehead is muddy. It is publicly announced that Randall does not know whether Randall's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Randall can now know whether Randall's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Elizabeth","Randall"],"index":50095,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9897603393,"difficulty":0.0102396607}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victoria knows whether someone's forehead is muddy. It is publicly announced that Victoria knows whether Donald's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"George can now know that Victoria can know that Angie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Angie","Donald","Victoria"],"index":38052,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967204928,"difficulty":0.0032795072}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Carolyn can now know whether Carol can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anthony","Carolyn","Carol"],"index":23339,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7092048526,"difficulty":0.2907951474}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose knows whether Carrie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Steven can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Jose","Carrie","Steven","Robert"],"index":44835,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975300431,"difficulty":0.0024699569}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma's forehead is muddy. It is publicly announced that Lillian knows whether someone's forehead is muddy. It is publicly announced that Norma knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows that 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Norma can now know that Lillian can know that Lillian's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Norma","Gerry","Lillian"],"index":40505,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9815903306,"difficulty":0.0184096694}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Grace knows whether Merrill's forehead is muddy. It is publicly announced that Joanne knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows that 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Pamela can now know that Joanne's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Grace","Pamela","Merrill","Joanne"],"index":2108,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960307479,"difficulty":0.0039692521}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether Martin's forehead is muddy. It is publicly announced that Martin knows whether Ronald's forehead is muddy. It is publicly announced that Ronald's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether 2) ] [ ! ~(2) ] 0","hypothesis":"Martin can now know whether Ronald can know that Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Martin","Ronald","James"],"index":18445,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8829094172,"difficulty":1.8829094172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agentb knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Juan can now know that Preston can know that Juan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Emma","Preston","Juana","Juan"],"index":23068,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978172779,"difficulty":0.0021827221}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Samuel does not know whether Samuel's forehead is muddy. It is publicly announced that Samuel does not know whether Samuel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Samuel can now know whether Sean's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Samuel","Lillian","Sean","Karen"],"index":13820,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999112308,"difficulty":0.000887692}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy. It is publicly announced that Kate's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentd knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Kate can now know whether Daniel can know whether Daniel's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Mabel","Jeffrey","Daniel","Kate"],"index":52204,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8916656971,"difficulty":0.1083343029}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alan knows whether or not nobody's forehead is muddy. It is publicly announced that Alan does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Scott can now know whether Alan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Alan","Scott"],"index":67677,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9983452559,"difficulty":0.0016547441}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Meagan's forehead is not muddy. It is publicly announced that John's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] [ ! ~(2) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Janie","John","Claudia","Meagan"],"index":31798,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9771407843,"difficulty":0.0228592157}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Candace does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agenta knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Jean can now know whether Candace can know whether Jean's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jean","Candace"],"index":53037,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9982940555,"difficulty":0.0017059445}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret's forehead is muddy. It is publicly announced that Mark does not know whether Mark's forehead is muddy. It is publicly announced that Ryan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! ~(Agentc knows whether 3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Mark can now know that Ryan's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Margaret","Ryan","Mark"],"index":32239,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9921326041,"difficulty":0.0078673959}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] 0","hypothesis":"Grace can now know that Raymond's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Raymond","Ronald","Grace","Geneva"],"index":36140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979422688,"difficulty":0.0020577312}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renna does not know whether or not everyone's forehead is muddy. It is publicly announced that Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] (Agentd knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Kelly can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Stephane","Renna","Todd","Kelly"],"index":65079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988834262,"difficulty":0.0011165738}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bradley does not know whether or not everyone's forehead is muddy. It is publicly announced that Bradley does not know whether Bradley's forehead is muddy. It is publicly announced that Antonia's forehead is muddy. It is publicly announced that Antonia knows whether Bradley's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] (Agenta knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Bradley can now know that Antonia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Bradley","Antonia"],"index":13870,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5288889408,"difficulty":0.4711110592}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether Bernice's forehead is muddy. It is publicly announced that Helene knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Bernice can now know whether Bernice's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Robert","Christopher","Bernice","Helene"],"index":50575,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9858152866,"difficulty":0.0141847134}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelley knows whether Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Karen can now know whether Shelley can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["John","Shelley","Thomas","Karen"],"index":44255,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7272988558,"difficulty":0.2727011442}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David knows whether Darcy's forehead is muddy. It is publicly announced that Darcy does not know whether Darcy's forehead is muddy. It is publicly announced that Darcy does not know whether Darcy's forehead is muddy. It is publicly announced that Darcy knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"David can now know that Darcy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["David","Darcy"],"index":45386,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990813732,"difficulty":0.0009186268}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Hattie does not know whether Hattie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Hattie can now know that Linda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Lillie","Alan","Linda","Hattie"],"index":65618,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971277118,"difficulty":0.0028722882}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ed does not know whether or not everyone's forehead is muddy. It is publicly announced that Carey knows whether or not nobody's forehead is muddy. It is publicly announced that Ed does not know whether Ed's forehead is muddy. It is publicly announced that Carey knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether 1)","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Carey can now know whether Ed's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Ed","Carey"],"index":67115,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979400039,"difficulty":0.0020599961}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether someone's forehead is muddy. It is publicly announced that Beverly's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! ~(3) ] 0","hypothesis":"Beverly can now know that Robert can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Robert","Beverly"],"index":42586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990072846,"difficulty":0.0009927154}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mitchell does not know whether Mitchell's forehead is muddy. It is publicly announced that Lisa knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Mitchell can now know that Lisa can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mitchell","Lisa"],"index":40718,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994834661,"difficulty":0.0005165339}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Helen knows whether Helen's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Earl can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Helen","Earl","Marylee","Tiffany"],"index":6624,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9085158706,"difficulty":1.9085158706}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Richard can now know that Beth can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Richard","Eric","Beth"],"index":36065,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9955848455,"difficulty":0.0044151545}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Inez can now know whether Donald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Brooke","Donald","Inez","Kimberly"],"index":32545,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994357228,"difficulty":0.0005642772}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Dorothy can now know whether Robert can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Robert","Mona","Dorothy"],"index":18516,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9642881751,"difficulty":0.0357118249}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Eric can now know that Lucy can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Eric","Lucy","Stephen"],"index":65630,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99941957,"difficulty":0.00058043}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geneva does not know whether Geneva's forehead is muddy. It is publicly announced that Geneva does not know whether Geneva's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Mildred can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Geneva","Mildred"],"index":5112,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989460111,"difficulty":0.0010539889}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald knows whether Cassandra's forehead is muddy. It is publicly announced that Donald knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that (1&2&3))","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Donald can now know that Donna can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Donald","Donna","Cassandra"],"index":13024,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989008904,"difficulty":0.0010991096}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Antoine does not know whether or not everyone's forehead is muddy. It is publicly announced that Antoine knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Antoine can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Malcolm","Jim","Antoine","John"],"index":10556,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5861070752,"difficulty":1.5861070752}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelica knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agenta knows whether (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Angelica can now know whether Janet can know that Tracie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Angelica","Kenneth","Janet","Tracie"],"index":43825,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9526171088,"difficulty":0.0473828912}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Shelley can now know that John can know whether Shelley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["April","Shelley","John"],"index":41294,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9383623004,"difficulty":0.0616376996}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elena knows whether someone's forehead is muddy. It is publicly announced that Elena knows whether Michael's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Richard can now know whether Michael can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Betty","Richard","Michael","Elena"],"index":40227,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9871270657,"difficulty":0.0128729343}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Beverley does not know whether Beverley's forehead is muddy. It is publicly announced that Margaret does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Beverley can now know that Andrew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Beverley","Margaret","Andrew","Richard"],"index":27254,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8585059047,"difficulty":0.1414940953}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steve does not know whether Steve's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] Agentd knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Timothy can now know whether Charles can know whether Steve's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Charles","William","Steve","Timothy"],"index":30017,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991735816,"difficulty":0.0008264184}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Scott's forehead is muddy. It is publicly announced that Martin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] Agenta knows whether (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"June can now know whether Martin can know whether Martin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["June","Scott","Martin","Stephine"],"index":23223,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9919576645,"difficulty":0.0080423355}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Lucille can now know that Bessie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Angela","Bessie","Lucille","Beatrice"],"index":67438,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9937931299,"difficulty":0.0062068701}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] (Agentc knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Ryan can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Michael","Ryan","Napoleon"],"index":45424,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994783998,"difficulty":0.0005216002}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alejandro does not know whether Alejandro's forehead is muddy. It is publicly announced that Alejandro knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] Agentc knows whether (Agentd knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether (~(1|2|3|4))) ] 0","hypothesis":"Don can now know whether Amy can know whether Amy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alejandro","Shawn","Don","Amy"],"index":42480,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9451264739,"difficulty":0.0548735261}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Norma knows whether or not nobody's forehead is muddy. It is publicly announced that Norma's forehead is muddy. It is publicly announced that Elbert's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] (Agentc knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 2 ] [ ! ~(3) ] 0","hypothesis":"Elbert can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Pedro","Norma","Elbert","Christopher"],"index":61051,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987712502,"difficulty":0.0012287498}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Heather knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Roxanne can now know that Steve can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steve","Roxanne","Heather"],"index":56027,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993713498,"difficulty":0.0006286502}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeremiah knows whether Sara's forehead is muddy. It is publicly announced that Sara knows whether someone's forehead is muddy. It is publicly announced that Sara's forehead is muddy. It is publicly announced that Jeremiah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! 1 ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Jeremiah can now know that Mary can know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sara","Mary","Jeremiah"],"index":61699,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9289800525,"difficulty":0.0710199475}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Aaron knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] Agenta knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Joshua can now know that Aaron can know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Joshua","Ruth","Aaron"],"index":33917,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9975681901,"difficulty":0.0024318099}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy. It is publicly announced that Alexander knows whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth does not know whether Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Annie can now know that Doris can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Annie","Alexander","Doris","Elizabeth"],"index":31171,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994730353,"difficulty":0.0005269647}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jeanne knows whether Jeanne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Richard can now know that Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mark","Jeanne","Richard","Tina"],"index":23226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969272017,"difficulty":0.0030727983}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 4)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Janet can now know that Jenna can know that Patrick's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jenna","Janet","John","Patrick"],"index":16580,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969047904,"difficulty":0.0030952096}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Vivian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Valda can now know that Valda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Vivian","Carol","Kareem","Valda"],"index":43223,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9619244337,"difficulty":0.0380755663}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Bret can now know that Juan can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Debora","Bret","Juan"],"index":3124,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993047714,"difficulty":0.0006952286}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tiffany knows whether someone's forehead is muddy. It is publicly announced that Robert knows whether Tiffany's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Paul","Robert","Tiffany"],"index":17262,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9331991076,"difficulty":0.0668008924}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"John can now know that Carolyn can know whether Carolyn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Mitchell","Carolyn"],"index":57928,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9958288074,"difficulty":0.0041711926}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Leo can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Karen","Robert","Leo","Eugenia"],"index":21100,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994568229,"difficulty":0.0005431771}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerri's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Krista can now know whether Gerri's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gerri","Floyd","Stuart","Krista"],"index":60860,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989776611,"difficulty":0.0010223389}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacie knows whether someone's forehead is muddy. It is publicly announced that Louis does not know whether or not everyone's forehead is muddy. It is publicly announced that Stacie knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agenta knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Louis can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Louis","Stacie"],"index":28580,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.557918787,"difficulty":1.557918787}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Timothy can now know whether Edith can know that Edith's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Arnold","Edith","Timothy"],"index":59853,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995443821,"difficulty":0.004556179}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erica knows whether Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] Agentd knows whether (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] 0","hypothesis":"Mildred can now know whether Michael can know that Gina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Erica","Gina","Michael","Mildred"],"index":9356,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9727368355,"difficulty":0.0272631645}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eugene knows whether someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agenta knows that (Agentc knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"William can now know that Eugene can know whether William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Lorraine","Eugene"],"index":52136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8263214827,"difficulty":0.1736785173}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Victor knows whether someone's forehead is muddy. It is publicly announced that Irene's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Victor can now know that Victor's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Victor","Enrique","Christina","Irene"],"index":19059,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976297617,"difficulty":0.0023702383}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Margaret knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether (~(1|2))) ] 0","hypothesis":"Margaret can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Margaret","Pamela"],"index":15947,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989848733,"difficulty":0.0010151267}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maegan knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Jeffrey can now know that Deloris can know that Deloris's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jeffrey","Deloris","Maegan"],"index":33733,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959449172,"difficulty":0.0040550828}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Barbara can now know that Mary can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mary","Barbara","Janna","Shawn"],"index":43455,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9945947528,"difficulty":0.0054052472}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cody knows whether Ami's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Cody knows whether Cody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 3) ] [ ! ~(4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Cody can now know that Robert can know that Lauren's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cody","Lauren","Ami","Robert"],"index":6274,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971354008,"difficulty":0.0028645992}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary does not know whether Mary's forehead is muddy. It is publicly announced that Jennifer knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Jennifer can now know whether Mary can know whether Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Mary","Jennifer"],"index":5925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9793014526,"difficulty":0.0206985474}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yesenia does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Barbara can now know whether Kimberly can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Barbara","Kimberly","Yesenia","John"],"index":41085,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.6892459989,"difficulty":0.3107540011}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Maria can now know that Betty can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Maria","Joanne","John","Betty"],"index":40854,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988725781,"difficulty":0.0011274219}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether Dorothy's forehead is muddy. It is publicly announced that Luke does not know whether Luke's forehead is muddy. It is publicly announced that Dorothy knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"James can now know that Dorothy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Luke","James","Dorothy","Mark"],"index":47545,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990531802,"difficulty":0.0009468198}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Quinn can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ronnie","Maurice","Robert","Quinn"],"index":38405,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994677901,"difficulty":0.0005322099}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kerrie does not know whether Kerrie's forehead is muddy. It is publicly announced that Jesus knows whether Kerrie's forehead is muddy. It is publicly announced that Jesus does not know whether Jesus's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] Agenta knows that (Agentd knows whether 4)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentc knows whether 4) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Deborah can now know that Kerrie can know whether Kerrie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Deborah","Thomas","Jesus","Kerrie"],"index":53063,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7174072266,"difficulty":1.7174072266}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen knows whether Karen's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Shannon can now know that Karen can know that Joy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Philip","Joy","Karen","Shannon"],"index":46838,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.992723763,"difficulty":0.007276237}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina knows whether Edmund's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Regina can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edmund","Flossie","Regina","Ronald"],"index":25247,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993861914,"difficulty":0.0006138086}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shirley's forehead is muddy. It is publicly announced that Shirley knows whether or not nobody's forehead is muddy. It is publicly announced that Numbers does not know whether Numbers's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Shirley can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Numbers","Richard","Shirley"],"index":49041,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990255833,"difficulty":0.0009744167}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gary's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Gary can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Don","Gary"],"index":16577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989649057,"difficulty":0.0010350943}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Violet knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bobby can now know that Violet can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Bobby","Robert","Violet"],"index":23818,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994457364,"difficulty":0.0005542636}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cecilia knows whether Alexander's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Cecilia can now know whether Cecilia's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Susan","Cecilia","Alexander","Kenneth"],"index":4165,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9891521931,"difficulty":0.0108478069}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentb knows that (Agentc knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Laura can now know that Gerald can know that Maria's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Maria","Laura","Gerald"],"index":21586,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960889816,"difficulty":0.0039110184}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows that (Agentb knows that 1)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Guadalupe can now know that Lyn can know that Katelynn's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Katelynn","Lyn","Guadalupe"],"index":65726,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943686128,"difficulty":0.0056313872}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michelle does not know whether or not everyone's forehead is muddy. It is publicly announced that Michelle does not know whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Michelle can now know that Denise can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Michelle","Denise"],"index":63652,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5852844715,"difficulty":1.5852844715}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know that Jarrett can know that Regina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Joseph","Jarrett","Evelyn","Regina"],"index":31449,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968675971,"difficulty":0.0031324029}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kathryn knows whether someone's forehead is muddy. It is publicly announced that Richard's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] (Agentb knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! ~(1) ] 0","hypothesis":"Kathryn can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Richard","Kathryn"],"index":48070,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988889098,"difficulty":0.0011110902}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jim's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agenta knows that (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Concetta can now know that Robert can know that Richard's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Concetta","Robert","Richard","Jim"],"index":19861,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963179827,"difficulty":0.0036820173}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Karen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Karen can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sean","Ruby","David","Karen"],"index":58622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989908338,"difficulty":0.0010091662}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"John can now know that Keith can know whether David's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","John","Keith"],"index":46005,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992640615,"difficulty":0.0007359385}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patricia does not know whether Patricia's forehead is muddy. It is publicly announced that William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! 2 ] 0","hypothesis":"Patricia can now know that William can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Patricia","William"],"index":51679,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5314003825,"difficulty":1.5314003825}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jere knows whether Michael's forehead is muddy. It is publicly announced that Jere knows whether or not everyone's forehead is muddy. It is publicly announced that Patrick does not know whether Patrick's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Patrick can now know whether Jere can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Michael","Patrick","Jere"],"index":7764,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994658828,"difficulty":0.0005341172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maureen does not know whether or not everyone's forehead is muddy. It is publicly announced that Joseph's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] Agentc knows that (Agentd knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Maureen can now know that Joseph can know whether Maureen's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Samuel","Eddie","Maureen","Joseph"],"index":40406,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.949339509,"difficulty":0.050660491}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Keith does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Maribel can now know whether James can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Maribel","Robert","Keith","James"],"index":5360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992020726,"difficulty":0.0007979274}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ida knows whether someone's forehead is muddy. It is publicly announced that Ida knows whether or not everyone's forehead is muddy. It is publicly announced that Jeffery's forehead is not muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] Agentc knows whether (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(1) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Ida can now know whether Patricia can know that Jeffery's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jeffery","Patricia","Ida","Ronald"],"index":20651,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9455251098,"difficulty":0.0544748902}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donna knows whether Jose's forehead is muddy. It is publicly announced that Melissa knows whether Jessica's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] (Agentb knows whether 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] [ ! (Agentd knows whether 1) ] 0","hypothesis":"Donna can now know whether Melissa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Donna","Jose","Melissa"],"index":29491,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992498755,"difficulty":0.0007501245}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Holly does not know whether Holly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Travis can now know that Holly can know that Holly's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Travis","Holly"],"index":38247,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9894984961,"difficulty":0.0105015039}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Ronnie does not know whether Ronnie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Charles can now know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Charles","Willie","Ronnie"],"index":60065,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963518381,"difficulty":0.0036481619}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lena does not know whether Lena's forehead is muddy. It is publicly announced that Aaron does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Aaron can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Aaron","Glenn","Lena"],"index":16935,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6369109154,"difficulty":1.6369109154}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tammy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Curtis can now know that Tammy can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sybil","Tammy","Curtis"],"index":66080,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994764924,"difficulty":0.0005235076}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne knows whether Suzanne's forehead is muddy. It is publicly announced that Ronni knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentb knows that (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Michelle can now know that Ronni can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Suzanne","Michelle","Ronni"],"index":36464,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9982158542,"difficulty":0.0017841458}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows that (~(1|2|3|4)))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Randy can now know whether Kevin can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Danielle","Randy","Kevin","Antoinette"],"index":7925,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991108775,"difficulty":0.0008891225}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] Agentb knows whether (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! 4 ] 0","hypothesis":"John can now know whether Janet can know whether Wm's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wm","John","Andres","Janet"],"index":28531,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993077517,"difficulty":0.0006922483}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] Agenta knows that (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Kerri can now know that Joe can know whether Joe's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Kerri","Wayne","Esther","Joe"],"index":28613,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.951074779,"difficulty":0.048925221}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erlene's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Erlene can now know that Edna's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Alan","Erlene","Benjamin","Edna"],"index":28195,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9979548454,"difficulty":0.0020451546}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura does not know whether or not everyone's forehead is muddy. It is publicly announced that Laura does not know whether Laura's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Laura can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Laura","Michael","Jerald"],"index":36236,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994565845,"difficulty":0.0005434155}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Maria can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Charles","Maria","William","David"],"index":52874,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987986088,"difficulty":0.0012013912}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentd knows whether (1&2&3&4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Carol can now know whether John can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jean","Carol","Silvia","John"],"index":13086,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9838482738,"difficulty":0.0161517262}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Nicholas knows whether or not nobody's forehead is muddy. It is publicly announced that Nicholas knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! (Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Jessica","Margaret","John","Nicholas"],"index":58427,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999494195,"difficulty":0.000505805}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Willie can now know that Brenda can know that Willie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Margaret","Willie","Debra","Brenda"],"index":52527,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9947321415,"difficulty":0.0052678585}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Genevieve knows whether or not nobody's forehead is muddy. It is publicly announced that Tony's forehead is muddy. It is publicly announced that Cheri does not know whether or not everyone's forehead is muddy. It is publicly announced that Cheri's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] (Agenta knows that 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (~(1|2|3|4))) ] [ ! 3 ] [ ! ~(Agenta knows whether (1&2&3&4)) ] [ ! ~(1) ] 0","hypothesis":"Cheri can now know that Tony's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Cheri","Genevieve","Tony","Richard"],"index":16531,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8236911297,"difficulty":0.1763088703}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that April's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] Agentc knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] 0","hypothesis":"Robbie can now know whether Terry can know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Terry","Pamela","Robbie","April"],"index":49117,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9879505634,"difficulty":0.0120494366}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jackie does not know whether Jackie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Thomas can now know whether Elizabeth can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Jackie","Thomas","Elizabeth"],"index":51479,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9749346972,"difficulty":0.0250653028}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leticia does not know whether Leticia's forehead is muddy. It is publicly announced that Leticia does not know whether Leticia's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Jennifer can now know that Leticia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Jennifer","Leticia"],"index":47584,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990562797,"difficulty":0.0009437203}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether Pauline's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] Agentb knows that (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Carol can now know that Pauline can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Helen","Carol","Pauline","Lauretta"],"index":3600,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990109205,"difficulty":0.0009890795}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gladys knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentb knows that (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Mildred can now know that Tom can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Gladys","Mildred","Tom","Robert"],"index":64717,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993770719,"difficulty":0.0006229281}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"John can now know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","John","Joseph","Deborah"],"index":27856,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9753981829,"difficulty":0.0246018171}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agenta knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Mark can now know that Betty can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Mark","Betty","Robert","David"],"index":66379,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989523888,"difficulty":0.0010476112}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ila's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"David can now know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Ila","David"],"index":4354,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9824038744,"difficulty":0.0175961256}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maribeth does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Maribeth can now know that Gloria can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Maribeth","Gloria"],"index":47036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998839438,"difficulty":0.001160562}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances does not know whether Frances's forehead is muddy. It is publicly announced that Frances's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] Agentd knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] 0","hypothesis":"Jesse can now know whether George can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Frances","George","Blanche","Jesse"],"index":54140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9763433337,"difficulty":0.0236566663}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Karen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] Agentc knows that (Agentb knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Johnathan can now know that Juan can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Karen","Juan","Johnathan"],"index":28369,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9919223785,"difficulty":0.0080776215}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy. It is publicly announced that Betty does not know whether Betty's forehead is muddy. It is publicly announced that Betty knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] Agenta knows that (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Edmund can now know that Betty can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Edmund","Betty"],"index":29568,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989262223,"difficulty":0.0010737777}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracy knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] Agentb knows that (Agenta knows that (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Tracy can now know that Robert can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Robert","Tracy"],"index":6729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989410043,"difficulty":0.0010589957}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Robert can now know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Sue","Robert"],"index":24790,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6730127335,"difficulty":1.6730127335}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Kyla can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kyla","Dolly","Barbara","Anne"],"index":34474,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989602566,"difficulty":0.0010397434}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Amy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Scott can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Willa","Scott","Amy","Anastasia"],"index":59509,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994636178,"difficulty":0.0005363822}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erin's forehead is not muddy. It is publicly announced that Erin knows whether someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tracey does not know whether Tracey's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agentb knows whether (1|2|3)) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Tracey can now know that Karen can know that Erin's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Tracey","Erin","Karen"],"index":25217,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.997497499,"difficulty":0.002502501}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] Agentd knows whether (Agenta knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Juan can now know whether Shantel can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Shantel","Monica","Margaret","Juan"],"index":56803,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9751944542,"difficulty":0.0248055458}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tom's forehead is muddy. It is publicly announced that Lorenza does not know whether Lorenza's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"James can now know that Anita's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tom","James","Anita","Lorenza"],"index":27638,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9926615953,"difficulty":0.0073384047}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alice does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether Alice can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kathryn","Sara","Robert","Alice"],"index":32942,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9369437099,"difficulty":0.0630562901}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lula's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agenta knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Lula can now know that Sean can know that Lula's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lula","Sean","Deborah"],"index":38298,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959949255,"difficulty":0.0040050745}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether someone's forehead is muddy. It is publicly announced that Twila's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether (1|2|3|4)) ] [ ! ~(4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joseph can now know whether Helen's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Joseph","Helen","Harriett","Twila"],"index":24395,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994136095,"difficulty":0.0005863905}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Janice knows whether or not everyone's forehead is muddy. It is publicly announced that Janice knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Janice can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Michael","Janice"],"index":43843,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9995028973,"difficulty":0.0004971027}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Sarah knows whether Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] [ ! ~(3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Marie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sarah","Marie","Robert"],"index":59658,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9628264308,"difficulty":0.0371735692}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether Vicky's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Lynne can now know whether Billy can know whether Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Vicky","Billy","Laura","Lynne"],"index":10462,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9948242903,"difficulty":0.0051757097}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anita's forehead is muddy. It is publicly announced that Anita knows whether Mildred's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] Agentc knows that (Agenta knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Anthony can now know that Anita can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Anita","Mildred","Anthony"],"index":45757,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994850159,"difficulty":0.0005149841}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kimberly does not know whether or not everyone's forehead is muddy. It is publicly announced that Kimberly knows whether Eleanor's forehead is muddy. It is publicly announced that Kimberly does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Donald can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Eleanor","Mattie","Kimberly","Donald"],"index":11468,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987457991,"difficulty":0.0012542009}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mercedes knows whether Mercedes's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] (Agentd knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 2) ] 0","hypothesis":"Angeles can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Gloria","Mercedes","Jason","Angeles"],"index":30333,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994607568,"difficulty":0.0005392432}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Greg knows whether Lindsey's forehead is muddy. It is publicly announced that Lindsey does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Greg can now know that Lindsey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Kathy","Greg","Lindsey"],"index":41858,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7543849349,"difficulty":1.7543849349}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda's forehead is muddy. It is publicly announced that Nelly does not know whether Nelly's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 2 ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Brenda can now know whether Nelly can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Nelly","Brenda"],"index":59098,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9767966866,"difficulty":0.0232033134}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether Joseph's forehead is muddy. It is publicly announced that Agustin knows whether Agustin's forehead is muddy. It is publicly announced that Agustin knows whether Agustin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether 3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Eileen can now know that Joseph can know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Eileen","Joseph","Agustin"],"index":36899,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9293938875,"difficulty":0.0706061125}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agentc knows that (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Brenda can now know that James can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["James","William","Brenda"],"index":65570,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960653186,"difficulty":0.0039346814}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angelica's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentd knows whether (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Frances can now know whether Angelica can know whether Amanda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amanda","Angelica","Alberto","Frances"],"index":31506,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992799163,"difficulty":0.0007200837}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that George's forehead is not muddy. It is publicly announced that Homer's forehead is muddy. It is publicly announced that George knows whether George's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] Agenta knows whether (Agentc knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] [ ! 2 ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"George can now know whether Charles can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["George","Homer","Charles"],"index":19924,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99931705,"difficulty":0.00068295}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jaime does not know whether Jaime's forehead is muddy. It is publicly announced that Vicki knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] (Agentb knows that (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether (1|2)) ] 0","hypothesis":"Vicki can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Jaime","Vicki"],"index":45878,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998906374,"difficulty":0.001093626}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Pamela knows whether Lisa's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Edith can now know whether Gabriel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edith","Lisa","Pamela","Gabriel"],"index":15867,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993752837,"difficulty":0.0006247163}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roosevelt knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Joyce can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Betty","Joyce","Bernice","Roosevelt"],"index":42066,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9909405708,"difficulty":0.0090594292}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alisha knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"William can now know that Alisha can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alisha","William","Anthony"],"index":24271,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994388223,"difficulty":0.0005611777}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Craig's forehead is muddy. It is publicly announced that Jennifer does not know whether or not everyone's forehead is muddy. It is publicly announced that Jennifer does not know whether Jennifer's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! 1 ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Craig can now know that Jennifer can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Craig","Jennifer"],"index":41510,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7008252144,"difficulty":1.7008252144}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Randal can now know whether Howard can know whether Randal's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Oscar","Howard","Randal"],"index":13780,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9377750754,"difficulty":0.0622249246}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy. It is publicly announced that Rudolph knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agenta knows that (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Dorothy can now know that Rudolph can know that Rudolph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Dorothy","Rudolph"],"index":40136,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8550742269,"difficulty":1.8550742269}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentc knows that (Agentb knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Betty can now know that Mark can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Mark","Betty"],"index":2515,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992989302,"difficulty":0.0007010698}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dana knows whether Dana's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agentb knows that (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Paul can now know that Dana can know that Monte's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Monte","Paul","Dana","Joel"],"index":60189,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9943833351,"difficulty":0.0056166649}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara does not know whether Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Melissa can now know that Roxann's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sara","Carlos","Melissa","Roxann"],"index":5337,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971297383,"difficulty":0.0028702617}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentd knows that (Agenta knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ernesto can now know that Herbert can know that Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Herbert","Elizabeth","Michael","Ernesto"],"index":5865,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9963430762,"difficulty":0.0036569238}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cesar does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know that Larry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marcelle","Cesar","Larry","Robert"],"index":931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9482272267,"difficulty":0.0517727733}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elise does not know whether Elise's forehead is muddy. It is publicly announced that Elise does not know whether Elise's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Janet can now know that Elise can know whether Janet's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Janet","Elise"],"index":4263,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9687350392,"difficulty":0.0312649608}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Peter's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Peter can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Maxwell","Peter","Karol","Joe"],"index":5011,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9505724311,"difficulty":0.0494275689}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether someone's forehead is muddy. It is publicly announced that Luke knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (1|2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Martha can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Luke","Martha"],"index":53729,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9887337685,"difficulty":0.0112662315}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Franklin does not know whether Franklin's forehead is muddy. It is publicly announced that Daniel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentc knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Josh can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Franklin","Daniel","Josh","Donald"],"index":42370,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994240999,"difficulty":0.0005759001}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth knows whether Marie's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! 2 ] 0","hypothesis":"Kenneth can now know that Marie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Marie","Kenneth"],"index":1577,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.5677478909,"difficulty":1.5677478909}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Terry knows whether or not everyone's forehead is muddy. It is publicly announced that Robbi's forehead is not muddy. It is publicly announced that Michiko knows whether Paul's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] (Agentb knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] [ ! ~(4) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Terry can now know whether Terry's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Michiko","Terry","Paul","Robbi"],"index":10749,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9821433425,"difficulty":0.0178566575}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stacie knows whether or not everyone's forehead is muddy. It is publicly announced that Michael does not know whether Michael's forehead is muddy. It is publicly announced that Stacie does not know whether Stacie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] Agentc knows that (Agenta knows that 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Howard can now know that Roberto can know that Michael's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Roberto","Michael","Howard","Stacie"],"index":31036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9833956957,"difficulty":0.0166043043}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows whether (Agentd knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Lawrence can now know whether Edith can know that Lawrence's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Steven","Robert","Lawrence","Edith"],"index":6226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9966509938,"difficulty":0.0033490062}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph knows whether or not nobody's forehead is muddy. It is publicly announced that Jaime knows whether or not nobody's forehead is muddy. It is publicly announced that Jaime does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Jaime can now know that Joseph can know whether Jaime's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jaime","Joseph"],"index":32132,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7438428402,"difficulty":0.2561571598}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] 0","hypothesis":"Rene can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rene","Rose","Kevin","Joshua"],"index":47183,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892514348,"difficulty":0.0107485652}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wilbur does not know whether Wilbur's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Amy can now know that Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ruth","Wilbur","Amy","Vada"],"index":700,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972923398,"difficulty":0.0027076602}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cesar does not know whether Cesar's forehead is muddy. It is publicly announced that Daniel knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentc knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Daniel can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Joseph","Cesar","Daniel"],"index":62969,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9983073473,"difficulty":0.0016926527}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carol knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] (Agenta knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] 0","hypothesis":"Carol can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Carol","Travis","Flora"],"index":26552,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994402528,"difficulty":0.0005597472}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Steven can now know that Dannette can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Steven","Jason","Dannette"],"index":51768,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999382019,"difficulty":0.000617981}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Len does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] [ ! (1|2|3) ] 0","hypothesis":"Len can now know whether Len's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Len","Robin","Sheridan"],"index":67504,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9892116785,"difficulty":0.0107883215}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Virginia's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Virginia can now know that William can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Timothy","Sharon","Virginia","William"],"index":49397,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998978138,"difficulty":0.001021862}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] Agentb knows that (Agenta knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Irma can now know that Annie can know whether Irma's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Annie","Irma"],"index":42923,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.8835327625,"difficulty":1.8835327625}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wayne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"April can now know that Wayne can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Wayne","April","Thomas","Stacy"],"index":42295,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994687438,"difficulty":0.0005312562}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Roxie knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Ronald can now know that Toni's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Toni","Ronald","Amanda","Roxie"],"index":9205,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977254272,"difficulty":0.0022745728}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] Agenta knows whether (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"Mack can now know whether Sarah can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Mack","Sarah"],"index":33929,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8785643578,"difficulty":1.8785643578}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Denise knows whether or not everyone's forehead is muddy. It is publicly announced that Connie does not know whether Connie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] Agentd knows that (Agentb knows whether (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1&2&3&4)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Denise can now know that Doug can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Dawn","Doug","Connie","Denise"],"index":22634,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994385839,"difficulty":0.0005614161}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christopher knows whether or not nobody's forehead is muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy. It is publicly announced that Christopher knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (1&2&3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Christopher can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Mary","Christopher","May"],"index":35281,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9980345368,"difficulty":0.0019654632}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agenta knows that (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Marie can now know that Mary can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Marie","John","Mary"],"index":34656,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994071722,"difficulty":0.0005928278}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Antonio knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] Agenta knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Lauren can now know that Antonio can know whether Antonio's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lauren","Antonio","Katherine"],"index":16618,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.90926373,"difficulty":0.09073627}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Todd's forehead is muddy. It is publicly announced that Philip knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Todd can now know whether Todd's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Philip","Christina","Todd","Bonnie"],"index":21217,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9613324404,"difficulty":0.0386675596}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon does not know whether Sharon's forehead is muddy. It is publicly announced that Ashley does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agentb knows whether (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Ashley can now know whether Sharon can know that Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Sharon","Ashley","Christine"],"index":59873,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6574962735,"difficulty":1.6574962735}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether Eva's forehead is muddy. It is publicly announced that Kenneth knows whether Marion's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kenneth can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Sharon","Marion","Kenneth","Eva"],"index":38319,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972116351,"difficulty":0.0027883649}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Guadalupe does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agenta knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know whether Darrin can know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Darrin","Guadalupe","Joseph","Catherine"],"index":49351,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991724491,"difficulty":0.0008275509}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ruby knows whether Bobby's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] Agenta knows whether (Agentb knows that (1|2))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (1&2) ] 0","hypothesis":"Bobby can now know whether Ruby can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Bobby","Ruby"],"index":64263,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994232655,"difficulty":0.0005767345}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Christopher does not know whether Christopher's forehead is muddy. It is publicly announced that Clarence knows whether Christopher's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] (Agentc knows whether 3)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Charles can now know whether Charles's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Christopher","Clarence","Charles","Leslie"],"index":54849,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9925774932,"difficulty":0.0074225068}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Milton knows whether someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] Agentb knows whether (Agentc knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Marvin can now know whether Robert can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Milton","Marvin","Robert"],"index":10308,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994530082,"difficulty":0.0005469918}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joel does not know whether or not everyone's forehead is muddy. It is publicly announced that Joel does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Joel can now know whether Joel's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Joel","Charles"],"index":49980,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8791248798,"difficulty":0.1208751202}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rachel knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] 0","hypothesis":"Sara can now know that Sara's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Darren","Sara","Rachel"],"index":32649,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968478084,"difficulty":0.0031521916}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gerald knows whether Gerald's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] Agenta knows that (Agentc knows that (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Richard can now know that Gerald can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Richard","Marilyn","Gerald","Harry"],"index":59774,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993329644,"difficulty":0.0006670356}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agenta knows that (Agentc knows whether (1|2|3|4))","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Sandy can now know that Sarah can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Sandy","Nathaniel","Sarah","James"],"index":50152,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.999392271,"difficulty":0.000607729}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] (Agentb knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Ronald can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Larry","Ronald","Daniel","Shari"],"index":60716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986544847,"difficulty":0.0013455153}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sheri knows whether or not nobody's forehead is muddy. It is publicly announced that Sheri does not know whether Sheri's forehead is muddy. It is publicly announced that Sheri knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Sheri can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Peter","Sheri","Perry"],"index":52381,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999047339,"difficulty":0.000952661}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agentd knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Helen can now know whether Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Marjorie","Linda","Bradley","Helen"],"index":46831,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992359877,"difficulty":0.0007640123}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Courtney knows whether Bradley's forehead is muddy. It is publicly announced that Courtney knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Bradley can now know that Bradley's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Elizabeth","Bradley","Courtney"],"index":53036,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9620041847,"difficulty":0.0379958153}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Wanda can now know whether Cecil can know that Cecil's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Wanda","Charles","Cecil"],"index":17907,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967409968,"difficulty":0.0032590032}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Elbert knows whether Lucy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agentd knows whether (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Elbert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["John","Lucy","Stanley","Elbert"],"index":16539,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9976332188,"difficulty":0.0023667812}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jonathan does not know whether Jonathan's forehead is muddy. It is publicly announced that Paul knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jonathan can now know whether Hilda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Kyle","Jonathan","Hilda","Paul"],"index":59698,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993382096,"difficulty":0.0006617904}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sidney does not know whether Sidney's forehead is muddy. It is publicly announced that Sidney does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Sidney can now know whether George can know that George's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Sidney","George"],"index":41621,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.6819629669,"difficulty":1.6819629669}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jack does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Jack can now know that Lisa can know that Jack's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Lisa","Mary","Jack"],"index":1186,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8052418828,"difficulty":1.8052418828}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wm does not know whether Wm's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Chong can now know that Joseph's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Kim","Chong","Joseph","Wm"],"index":26841,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9976201653,"difficulty":0.0023798347}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows that (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Jeanette can now know that Robert can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Veronica","Jeanette","Robert","Joseph"],"index":65562,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957142472,"difficulty":0.0042857528}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Rose can now know whether Patricia can know whether Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Patricia","Rose","Robert","Sarah"],"index":14362,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991624355,"difficulty":0.0008375645}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Viola's forehead is muddy. It is publicly announced that Maria knows whether or not everyone's forehead is muddy. It is publicly announced that Heather knows whether Viola's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] (Agentb knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3)) ] [ ! (Agentb knows whether 3) ] 0","hypothesis":"Heather can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maria","Heather","Viola"],"index":39310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994565845,"difficulty":0.0005434155}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Melanie does not know whether or not everyone's forehead is muddy. It is publicly announced that Keith knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] (Agenta knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (Agentc knows whether (~(1|2|3))) ] 0","hypothesis":"Melanie can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Melanie","Ivan","Keith"],"index":3172,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.579816103,"difficulty":1.579816103}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Christian's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] Agentd knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Christian can now know that Paula can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Thomas","John","Paula","Christian"],"index":39120,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986876845,"difficulty":0.0013123155}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Deborah knows whether Buddy's forehead is muddy. It is publicly announced that Annie knows whether Pamela's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Deborah can now know whether Annie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Deborah","Pamela","Annie","Buddy"],"index":54331,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992949963,"difficulty":0.0007050037}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Linda does not know whether Linda's forehead is muddy. It is publicly announced that Moises knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentc knows that 4)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Moises can now know that Audrey's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Linda","Shannon","Moises","Audrey"],"index":39048,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9968140721,"difficulty":0.0031859279}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert knows whether Albert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] Agentc knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 4) ] 0","hypothesis":"Spencer can now know that Albert can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Sherry","Robert","Spencer","Albert"],"index":25569,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972802401,"difficulty":0.0027197599}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentb knows that (Agentc knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Eddie can now know that Angela can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Eddie","Angela"],"index":67401,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994458556,"difficulty":0.0005541444}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Christine can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Christine","George","John"],"index":4015,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9939517379,"difficulty":0.0060482621}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Katerine knows whether someone's forehead is muddy. It is publicly announced that Gerald's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] (Agentc knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] [ ! ~(2) ] 0","hypothesis":"Katerine can now know whether Guillermo's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Guillermo","Gerald","Katerine","Robert"],"index":55054,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994024038,"difficulty":0.0005975962}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronald knows whether William's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"William can now know that Ronald can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["William","Ronald"],"index":47173,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990099669,"difficulty":0.0009900331}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jose does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Clark can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Ryan","James","Jose","Clark"],"index":27964,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988547564,"difficulty":0.0011452436}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin knows whether Kevin's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"John can now know that Michael can know whether John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["John","Michael","Kevin"],"index":21296,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991909862,"difficulty":0.0008090138}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jimmy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentc knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Pedro can now know that Jimmy can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jimmy","Dorothy","Pedro","Karla"],"index":12103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989675283,"difficulty":0.0010324717}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sara does not know whether Sara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agentb knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Larry can now know whether Fredrick can know that Sara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Sara","Larry","Fredrick"],"index":66322,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9403616786,"difficulty":0.0596383214}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mark knows whether someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Carlos knows whether Mark's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] (Agenta knows that (1&2&3&4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] [ ! (1&2&3&4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Regina can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Regina","Mark","Gary","Carlos"],"index":37999,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9958835244,"difficulty":0.0041164756}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Larry can now know whether Eric can know that Joyce's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Peter","Joyce","Larry","Eric"],"index":36136,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9479919076,"difficulty":0.0520080924}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Erik knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"James can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Laura","Erik","James"],"index":66719,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988289475,"difficulty":0.0011710525}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rosemary knows whether Rosemary's forehead is muddy. It is publicly announced that Ashley knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Ashley can now know that Richard can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Rosemary","Richard","Ashley"],"index":19277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990377426,"difficulty":0.0009622574}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Madonna's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Alva can now know that Madonna can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Madonna","Patricia","Alva"],"index":60313,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.99947685,"difficulty":0.00052315}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darla knows whether Talia's forehead is muddy. It is publicly announced that Jimmie does not know whether Jimmie's forehead is muddy. It is publicly announced that Mattie knows whether Talia's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] Agentd knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Jimmie can now know whether Talia can know whether Talia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Talia","Mattie","Darla","Jimmie"],"index":55503,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989959598,"difficulty":0.0010040402}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sterling knows whether Anna's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead is muddy. It is publicly announced that Anna does not know whether Anna's forehead is muddy. It is publicly announced that Anna knows whether Sterling's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] Agentb knows that (Agenta knows that (~(1|2)))","n_announcements":4,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agenta knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Anna can now know that Sterling can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Sterling","Anna"],"index":65758,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.999088645,"difficulty":0.000911355}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bryan knows whether Barbara's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] Agenta knows that (Agentb knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] 0","hypothesis":"Kelley can now know that Barbara can know that Bryan's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kelley","Barbara","Bryan"],"index":60879,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9971541166,"difficulty":0.0028458834}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Theodore knows whether or not everyone's forehead is muddy. It is publicly announced that Theodore does not know whether Theodore's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Rebecca can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Earnest","Rebecca","Theodore"],"index":64196,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990625978,"difficulty":0.0009374022}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether Brian's forehead is muddy. It is publicly announced that Fannie does not know whether Fannie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] Agentc knows whether (Agentb knows that (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"James can now know whether Fannie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brian","Fannie","James"],"index":36695,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994356036,"difficulty":0.0005643964}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Joe's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] [ ! 2 ] 0","hypothesis":"Kerry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Joe","Kerry"],"index":61341,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954622388,"difficulty":0.0045377612}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Olga knows whether Viola's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] Agenta knows that (Agentd knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Viola can now know that Paul can know that Olga's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Viola","Olga","Elsa","Paul"],"index":60182,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972983003,"difficulty":0.0027016997}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maria knows whether someone's forehead is muddy. It is publicly announced that Maria does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentb knows that (Agenta knows that (~(1|2|3|4)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Rex can now know that Earl can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Earl","Rex","Eunice","Maria"],"index":65603,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987108707,"difficulty":0.0012891293}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn knows whether someone's forehead is muddy. It is publicly announced that Diane does not know whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] Agentb knows that (Agenta knows that (1|2|3))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1|2|3) ] 0","hypothesis":"Troy can now know that Diane can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Diane","Troy","Carolyn"],"index":21047,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994713664,"difficulty":0.0005286336}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agenta knows whether (Agentd knows whether 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Barbara can now know whether Carol can know whether Carol's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Barbara","Carla","Courtney","Carol"],"index":43501,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.995064199,"difficulty":0.004935801}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Juan knows whether Brenda's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] 0","hypothesis":"Brenda can now know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Brenda","Juan"],"index":58,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9760277271,"difficulty":0.0239722729}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"William can now know whether Jesus can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Daniel","Jesus","William"],"index":49229,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.5975600481,"difficulty":0.4024399519}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Angela knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] (Agenta knows that (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Angela can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Angela","Aurelio","Rosa"],"index":1328,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988724589,"difficulty":0.0011275411}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Clyde's forehead is muddy. It is publicly announced that Clyde knows whether someone's forehead is muddy. It is publicly announced that Alberto knows whether Elizabeth's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] Agentb knows whether (Agentc knows whether 2)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 4 ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Alberto can now know whether Richard can know whether Alberto's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Elizabeth","Alberto","Richard","Clyde"],"index":26295,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9977699518,"difficulty":0.0022300482}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Harry knows whether Kim's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agenta knows that (Agentb knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"Harry can now know that Kim can know whether Harry's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Harry","Kim","Darci"],"index":4921,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9954093099,"difficulty":0.0045906901}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fernando does not know whether Fernando's forehead is muddy. It is publicly announced that Jose does not know whether Jose's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] (Agentd knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Ann can now know whether Fernando's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Fernando","Joyce","Jose","Ann"],"index":57920,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9979034662,"difficulty":0.0020965338}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agentc knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Joyce can now know that Becky can know that John's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jonathan","John","Becky","Joyce"],"index":46156,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9530969858,"difficulty":0.0469030142}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentd knows that (Agentc knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Annabel can now know that Teresa can know that Nicole's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Nicole","Teresa","Annabel"],"index":5622,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9939869642,"difficulty":0.0060130358}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] Agentb knows whether (Agentc knows whether 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Christine can now know whether Billy can know whether Billy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["George","Christine","Billy","Mary"],"index":26830,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994260788,"difficulty":0.005739212}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Betty knows whether or not everyone's forehead is muddy. It is publicly announced that Betty's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(1) ] 0","hypothesis":"Francis can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Betty","Virginia","Francis"],"index":18170,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990259409,"difficulty":0.0009740591}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mike does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] Agentb knows that (Agenta knows whether (~(1|2)))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Mike can now know that Jack can know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Jack","Mike"],"index":63320,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994599223,"difficulty":0.0005400777}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joseph does not know whether or not everyone's forehead is muddy. It is publicly announced that Jennifer knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] Agentc knows that (Agentb knows whether 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether (1|2|3|4)) ] 0","hypothesis":"Wanda can now know that Kristy can know whether Kristy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Jennifer","Kristy","Wanda","Joseph"],"index":9465,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.5130884051,"difficulty":1.5130884051}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Frances knows whether Rachel's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] (Agentc knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentb knows whether 1) ] [ ! (1|2|3) ] 0","hypothesis":"Kenneth can now know whether Kenneth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rachel","Frances","Kenneth"],"index":41821,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9898277521,"difficulty":0.0101722479}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Yvonne does not know whether or not everyone's forehead is muddy. It is publicly announced that Yvonne does not know whether Yvonne's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Yvonne can now know whether Vincent's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Yvonne","James","Vincent"],"index":26810,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989321828,"difficulty":0.0010678172}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James knows whether Andy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] Agentd knows that (Agenta knows whether 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Pamela can now know that Andy can know whether Andy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Andy","Patricia","James","Pamela"],"index":64577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.7395863533,"difficulty":0.2604136467}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janie does not know whether or not everyone's forehead is muddy. It is publicly announced that Janie does not know whether or not everyone's forehead is muddy. It is publicly announced that Thomas knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] Agentb knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Janie can now know whether Thomas can know whether Thomas's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Thomas","Janie"],"index":59914,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.524274826,"difficulty":0.475725174}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Darrell knows whether someone's forehead is muddy. It is publicly announced that Darrell knows whether Dale's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (Agentd knows whether 3) ] [ ! (1|2|3|4) ] 0","hypothesis":"Frank can now know that Jeanne can know that Jeanne's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jeanne","Frank","Dale","Darrell"],"index":20765,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972321391,"difficulty":0.0027678609}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ernest's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] Agenta knows whether (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Shannon can now know whether Ernest can know that Ernest's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shannon","Rachel","Ernest"],"index":6682,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9898938537,"difficulty":0.0101061463}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Delma knows whether or not everyone's forehead is muddy. It is publicly announced that Delma does not know whether Delma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sharon can now know that Sharon's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Delma","Chris","Sharon"],"index":10215,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9691187739,"difficulty":0.0308812261}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kelly's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 2 ] 0","hypothesis":"Kelly can now know that Luther's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michael","Kelly","Luther"],"index":24103,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9787422419,"difficulty":0.0212577581}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gertrude does not know whether Gertrude's forehead is muddy. It is publicly announced that Brenda does not know whether Brenda's forehead is muddy. It is publicly announced that Gertrude knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] Agentc knows that (Agentd knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether 3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Gertrude can now know that Sara can know that Brenda's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Brenda","Patricia","Gertrude","Sara"],"index":36074,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9965923429,"difficulty":0.0034076571}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Travis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] (Agentc knows whether (~(1|2|3)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(3) ] 0","hypothesis":"Travis can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Betty","Jack","Travis"],"index":15909,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994562268,"difficulty":0.0005437732}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Luis's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(4) ] 0","hypothesis":"Luis can now know that Luis's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brad","Anthony","Justin","Luis"],"index":50399,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9953332543,"difficulty":0.0046667457}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Annie knows whether James's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] Agentb knows that (Agenta knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 2) ] 0","hypothesis":"James can now know that Annie can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Annie","James","Dianne"],"index":3866,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994427562,"difficulty":0.0005572438}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Fred knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] Agenta knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1|2|3|4)) ] 0","hypothesis":"Jennifer can now know that William can know that William's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Tracey","Fred","William"],"index":24350,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994740665,"difficulty":0.005259335}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Jerome does not know whether Jerome's forehead is muddy. It is publicly announced that Jerome does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] (Agentb knows whether (1|2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether (1&2)) ] 0","hypothesis":"Jerome can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Guy","Jerome"],"index":36931,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994531274,"difficulty":0.0005468726}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Isaiah does not know whether Isaiah's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agenta knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Elizabeth can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Elizabeth","Patricia","Jan","Isaiah"],"index":48786,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993738532,"difficulty":0.0006261468}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] Agentc knows whether (Agentb knows that 3)","n_announcements":0,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] 0","hypothesis":"Pamela can now know whether Kurt can know that Pamela's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Kurt","Pamela"],"index":48290,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9410943389,"difficulty":0.0589056611}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sharon knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] (Agentd knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Hannah can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Judy","Sharon","Dinah","Hannah"],"index":56132,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990235567,"difficulty":0.0009764433}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that David's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] (Agentb knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(1) ] 0","hypothesis":"Lue can now know whether Lue's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["David","Lue","Peter","Traci"],"index":27020,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.991483748,"difficulty":0.008516252}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian's forehead is muddy. It is publicly announced that David knows whether Brian's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Brian can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Carmen","Brian","Richard","David"],"index":59948,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987745881,"difficulty":0.0012254119}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Lucille does not know whether Lucille's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Lucille can now know that Lucille's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Marvin","Paul","Yvonne","Lucille"],"index":39226,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9892302155,"difficulty":0.0107697845}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Catherine's forehead is not muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(1) ] [ ! (1|2) ] 0","hypothesis":"Thomas can now know whether Catherine's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Catherine","Thomas"],"index":66542,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992644191,"difficulty":0.0007355809}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Bonnie knows whether David's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] Agentd knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 3) ] 0","hypothesis":"Bonnie can now know whether Lillie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["John","Lillie","David","Bonnie"],"index":37983,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994412065,"difficulty":0.0005587935}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentb knows that (Agenta knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Joey can now know that Nancy can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Nancy","Joey","Barbara","Andres"],"index":27959,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993816614,"difficulty":0.0006183386}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joshua knows whether or not nobody's forehead is muddy. It is publicly announced that Esther knows whether or not nobody's forehead is muddy. It is publicly announced that Esther does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] Agenta knows that (Agentb knows that (1|2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether (~(1|2))) ] [ ! (Agenta knows whether (~(1|2))) ] [ ! ~(Agenta knows whether (1&2)) ] 0","hypothesis":"Esther can now know that Joshua can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Esther","Joshua"],"index":58560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994421601,"difficulty":0.0005578399}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth does not know whether or not everyone's forehead is muddy. It is publicly announced that Elizabeth's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] (Agentb knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! 1 ] 0","hypothesis":"Mark can now know whether Elizabeth's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","Mark"],"index":1357,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9989174604,"difficulty":0.0010825396}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Donald does not know whether Donald's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentd knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Donald can now know that Harold can know that Walter's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Walter","Tammy","Harold","Donald"],"index":13381,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9972873926,"difficulty":0.0027126074}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Justin knows whether or not everyone's forehead is muddy. It is publicly announced that Ruth knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agenta knows whether 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Caitlyn can now know whether Caitlyn's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Caitlyn","Ruth","Justin"],"index":24592,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9823964834,"difficulty":0.0176035166}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] Agentd knows whether (Agentb knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"Carol can now know whether William can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Amber","William","Sadie","Carol"],"index":9046,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9978271127,"difficulty":0.0021728873}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Anne's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agentb knows whether (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Robin can now know whether James can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Anne","Robin","James","Renee"],"index":40596,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.8148954511,"difficulty":1.8148954511}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cindy's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] Agenta knows whether (Agentb knows that (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] 0","hypothesis":"Cindy can now know whether Sarah can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Cindy","Sarah","Jesus","Ernest"],"index":30631,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994847775,"difficulty":0.0005152225}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that James does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] Agenta knows that (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether (1&2&3)) ] 0","hypothesis":"Jean can now know that James can know that James's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Jean","James","Doris"],"index":55619,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.7564204931,"difficulty":1.7564204931}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwin's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] (Agenta knows that (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] [ ! 2 ] 0","hypothesis":"Erik can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Erik","Edwin"],"index":50793,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987506866,"difficulty":0.0012493134}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that John does not know whether John's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] Agenta knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"John can now know that Jorge can know that Jorge's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["John","Martha","Jorge"],"index":41811,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9959852695,"difficulty":0.0040147305}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Alfred does not know whether or not everyone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] [ ! (1&2&3) ] 0","hypothesis":"John can now know whether Alfred can know whether Tina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Alfred","John","Tina"],"index":32974,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993020296,"difficulty":0.0006979704}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colleen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentd knows whether (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Charles can now know whether Lillie can know that Lillie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Robert","Lillie","Colleen","Charles"],"index":25519,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9940438867,"difficulty":0.0059561133}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brenda knows whether or not nobody's forehead is muddy. It is publicly announced that Ashley's forehead is not muddy. It is publicly announced that Brenda's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] Agenta knows that (Agentb knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (~(1|2|3|4))) ] [ ! ~(1) ] [ ! ~(4) ] 0","hypothesis":"Ashley can now know that Scott can know whether Ashley's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Ashley","Scott","Jo","Brenda"],"index":59966,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992092252,"difficulty":0.0007907748}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edwina knows whether or not everyone's forehead is muddy. It is publicly announced that Edwina does not know whether Edwina's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Wilma can now know that Edwina's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Wilma","William","Edwina"],"index":9234,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9414023161,"difficulty":0.0585976839}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Eleanor does not know whether or not everyone's forehead is muddy. It is publicly announced that Margie knows whether Eleanor's forehead is muddy. It is publicly announced that Margie knows whether Eleanor's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] Agenta knows whether (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Margie can now know whether Thomas can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Margie","Karen","Eleanor","Thomas"],"index":66812,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994693398,"difficulty":0.0005306602}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William does not know whether or not everyone's forehead is muddy. It is publicly announced that William knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] (Agentb knows whether (~(1|2)))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agentb knows whether (1&2)) ] [ ! (Agentb knows whether (~(1|2))) ] 0","hypothesis":"William can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":1,"names":["Elizabeth","William"],"index":8225,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994552732,"difficulty":0.0005447268}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Robert does not know whether Robert's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Kathleen does not know whether Kathleen's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] Agentb knows that (Agenta knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(Agentb knows whether 2) ] [ ! ~(2) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Robert can now know that Brad can know that Brad's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Brad","Robert","Kathleen"],"index":4237,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.9968727231,"difficulty":1.9968727231}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] 0","hypothesis":"Lizette can now know whether Mary can know that Valerie's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Lizette","Mary","Valerie"],"index":55564,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9865292311,"difficulty":0.0134707689}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Edgar does not know whether or not everyone's forehead is muddy. It is publicly announced that Suzanna's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] (Agenta knows whether (1|2|3|4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! 3 ] 0","hypothesis":"Everett can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Everett","Mollie","Suzanna","Edgar"],"index":30193,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994800687,"difficulty":0.0005199313}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Krista knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] (Agentc knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! (Agentb knows whether (1&2&3)) ] 0","hypothesis":"Mark can now know that Jessie's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Jessie","Krista","Mark"],"index":7716,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9781980515,"difficulty":0.0218019485}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Wanda's forehead is muddy. It is publicly announced that Wanda's forehead is muddy. It is publicly announced that Thomas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] (Agentc knows that (~(1|2|3|4)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! 3 ] [ ! 2 ] 0","hypothesis":"Wanda can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Tiffany","Thomas","Wanda","Keith"],"index":7122,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989732504,"difficulty":0.0010267496}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carolyn does not know whether Carolyn's forehead is muddy. It is publicly announced that Edward knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Donna can now know that Edward's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Donna","Carolyn","Edward"],"index":54577,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9789284468,"difficulty":0.0210715532}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Matthew does not know whether Matthew's forehead is muddy. It is publicly announced that Matthew knows whether Kimberley's forehead is muddy. It is publicly announced that Matthew knows whether or not everyone's forehead is muddy. It is publicly announced that Kimberley's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] (Agentb knows that 1)","n_announcements":4,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agenta knows whether 3) ] [ ! (Agenta knows whether (1&2&3)) ] [ ! ~(3) ] 0","hypothesis":"Norma can now know that Matthew's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Matthew","Norma","Kimberley"],"index":3679,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.985182941,"difficulty":0.014817059}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gennie knows whether Gennie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] Agentc knows whether (Agenta knows that (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Gennie can now know whether Walter can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Walter","Robert","Gennie"],"index":59627,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9672124982,"difficulty":0.0327875018}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Janet's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentc knows whether (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Janet can now know whether Jeffrey can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Anthony","Jeffrey","Janet","Iris"],"index":43591,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992797971,"difficulty":0.0007202029}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Peggy does not know whether Peggy's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] (Agentb knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (~(1&2&3)) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Tenisha can now know that Brian's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Brian","Tenisha","Peggy"],"index":46327,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9960557222,"difficulty":0.0039442778}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentc knows that (Agentd knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Larry can now know that Samuel can know that Lucia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Lucia","Ester","Larry","Samuel"],"index":41913,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903880954,"difficulty":0.0096119046}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Modesta's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] Agentb knows that (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(2) ] 0","hypothesis":"Modesta can now know that Barbara can know that Rudolph's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Rudolph","Modesta","Barbara","Robert"],"index":15818,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9977472425,"difficulty":0.0022527575}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Maurine knows whether Elmer's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elmer does not know whether Elmer's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows whether (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether 3) ] [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"Maurine can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Maurine","David","Elmer"],"index":41538,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994220734,"difficulty":0.0005779266}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Robert does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] (Agentc knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentc knows whether (1&2&3&4)) ] 0","hypothesis":"Robert can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Erika","Tracy","Robert","Gail"],"index":48287,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.6020358801,"difficulty":1.6020358801}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Timothy's forehead is not muddy. It is publicly announced that Mary knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] (Agentb knows whether 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(2) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Timothy can now know whether Lois's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Mary","Timothy","Lois"],"index":26523,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9993031025,"difficulty":0.0006968975}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Valerie knows whether Valerie's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] Agentc knows that (Agentd knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 3) ] 0","hypothesis":"Valerie can now know that Margaret can know that Margaret's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jim","Maggie","Valerie","Margaret"],"index":67624,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.994297564,"difficulty":0.005702436}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thomas's forehead is muddy. It is publicly announced that Earl knows whether someone's forehead is muddy. It is publicly announced that Thomas knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agenta knows whether (Agentb knows that (~(1|2|3)))","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 1 ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Thomas can now know whether Carolyn can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Thomas","Carolyn","Earl"],"index":59775,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994158745,"difficulty":0.0005841255}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Sharon can now know that Lora can know that Lora's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Carmelina","Jesse","Lora","Sharon"],"index":26624,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931806326,"difficulty":0.0068193674}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] (Agenta knows that (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1|2|3) ] [ ! (1|2|3) ] 0","hypothesis":"Richard can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Richard","Elaine","Megan"],"index":32601,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989566803,"difficulty":0.0010433197}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sarah does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agenta knows whether (Agentd knows whether 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Audrey can now know whether Anne can know whether Sarah's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Audrey","Sarah","Maria","Anne"],"index":53148,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9990665317,"difficulty":0.0009334683}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Seth knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] (Agenta knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (1|2|3)) ] 0","hypothesis":"Seth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Seth","Annie","Brittney"],"index":50204,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9877891541,"difficulty":0.0122108459}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thurman does not know whether Thurman's forehead is muddy. It is publicly announced that Dorothy does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Thurman can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Thurman","Dorothy","Patrick","Milan"],"index":61950,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9978495836,"difficulty":0.0021504164}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kevin's forehead is not muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] Agentc knows whether (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(1) ] 0","hypothesis":"Bryant can now know whether Kevin can know that Bryant's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Kevin","Sue","Bryant"],"index":33910,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.6150203347,"difficulty":0.3849796653}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Doris does not know whether Doris's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] (Agentc knows whether (1|2|3|4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Angela can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Edward","Doris","Angela","Gerald"],"index":13560,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994427562,"difficulty":0.0005572438}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Brian does not know whether Brian's forehead is muddy. It is publicly announced that Kenton knows whether or not everyone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that William does not know whether William's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] (Agentb knows that (1&2&3&4))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agenta knows whether 1) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! (~(1&2&3&4)) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"William can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Brian","William","Kenton","Ronald"],"index":62031,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9973762035,"difficulty":0.0026237965}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mabel does not know whether Mabel's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] Agentc knows whether (Agentb knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Ruth can now know whether Michael can know whether Ruth's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Johnny","Michael","Ruth","Mabel"],"index":30676,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9967904687,"difficulty":0.0032095313}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Zachary does not know whether or not everyone's forehead is muddy. It is publicly announced that Juana knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] Agentb knows whether (Agenta knows whether (1&2))","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether (1&2)) ] [ ! (Agentb knows whether (1&2)) ] 0","hypothesis":"Juana can now know whether Zachary can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Zachary","Juana"],"index":36370,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9767363071,"difficulty":0.0232636929}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria does not know whether Gloria's forehead is muddy. It is publicly announced that Stewart's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] (Agentd knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentd knows whether 4) ] [ ! 3 ] 0","hypothesis":"Gloria can now know that Stewart's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lauri","Adrian","Stewart","Gloria"],"index":57614,"s-l":"forehead-1","deberta_pred":0,"deberta_confidence":0.7839038968,"difficulty":1.7839038968}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Carrie knows whether Elbert's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] Agentb knows whether (Agenta knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether 4) ] 0","hypothesis":"Debra can now know whether Alice can know that Debra's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alice","Debra","Carrie","Elbert"],"index":10140,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9903967381,"difficulty":0.0096032619}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Barbara knows whether or not everyone's forehead is muddy. It is publicly announced that Marina does not know whether Marina's forehead is muddy. It is publicly announced that Jack knows whether Frank's forehead is muddy. It is publicly announced that Marina does not know whether Marina's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (1&2&3&4)) ] [ ! ~(Agentd knows whether 4) ] [ ! (Agentb knows whether 1) ] [ ! ~(Agentd knows whether 4) ] 0","hypothesis":"Jack can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Frank","Jack","Barbara","Marina"],"index":34593,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990659356,"difficulty":0.0009340644}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] (Agentd knows that 2)","n_announcements":0,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] 0","hypothesis":"Ronald can now know that Teresa's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Elmer","Teresa","Wanda","Ronald"],"index":13852,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962190986,"difficulty":0.0037809014}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Rashida knows whether Rashida's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] (Agentc knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 1) ] 0","hypothesis":"Harry can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Rashida","Clara","Harry","William"],"index":55089,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989192486,"difficulty":0.0010807514}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nancy's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] Agenta knows whether (Agentb knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (~(1&2)) ] [ ! ~(2) ] 0","hypothesis":"Ethel can now know whether Nancy can know that Nancy's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":1,"names":["Ethel","Nancy"],"index":25663,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.989341855,"difficulty":0.010658145}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Thelma's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] Agentb knows that (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! 3 ] 0","hypothesis":"Thomas can now know that Thelma can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["William","Thomas","Thelma"],"index":53590,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.7814698219,"difficulty":0.2185301781}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Dwight does not know whether Dwight's forehead is muddy. It is publicly announced that Dwight's forehead is not muddy. It is publicly announced that Dwight knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] (Agentb knows that (1&2))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(1) ] [ ! (Agenta knows whether (1|2)) ] 0","hypothesis":"Wanda can now know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Dwight","Wanda"],"index":63761,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9987506866,"difficulty":0.0012493134}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] (Agenta knows whether (1&2))","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (1|2) ] 0","hypothesis":"Andre can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Andre","Clara"],"index":15308,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.956392467,"difficulty":0.043607533}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sterling's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] Agentd knows whether (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] 0","hypothesis":"Susan can now know whether Sterling can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Alisa","Steven","Sterling","Susan"],"index":59859,"s-l":"forehead-0","deberta_pred":1,"deberta_confidence":0.9937864542,"difficulty":1.9937864542}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Sadie does not know whether Sadie's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] (Agenta knows that (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] 0","hypothesis":"Sadie can now know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Sadie","Thomas","Joseph"],"index":57439,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994441867,"difficulty":0.0005558133}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Suzanne does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Suzanne can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Eryn","Beverly","Suzanne"],"index":17417,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994702935,"difficulty":0.0005297065}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Cynthia knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] Agentb knows that (Agentc knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agenta knows whether (~(1|2|3))) ] 0","hypothesis":"Richard can now know that Eric can know whether Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Cynthia","Richard","Eric"],"index":55582,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9964717627,"difficulty":0.0035282373}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Joyce's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] (Agentb knows whether (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 2 ] 0","hypothesis":"Joyce can now know whether or not nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Lola","Joyce","Yvonne","Nella"],"index":55088,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994829893,"difficulty":0.0005170107}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ronnie knows whether someone's forehead is muddy. It is publicly announced that Ronnie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentd knows that (Agenta knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Ronnie can now know that Marna can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Marna","Zachary","Michelle","Ronnie"],"index":43079,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9907859564,"difficulty":0.0092140436}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that William knows whether someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] Agentd knows that (Agentb knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentb knows whether (1|2|3|4)) ] 0","hypothesis":"Rita can now know that William can know that Cecelia's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Cecelia","William","Kenneth","Rita"],"index":30030,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.996946156,"difficulty":0.003053844}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Patrick knows whether someone's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] Agentd knows that (Agentc knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether (1|2|3|4)) ] [ ! (~(1&2&3&4)) ] 0","hypothesis":"Patrick can now know that Eric can know that Eric's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ivan","Michael","Eric","Patrick"],"index":41785,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.99386096,"difficulty":0.00613904}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Renee's forehead is muddy. It is publicly announced that Mary knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] (Agentd knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 3 ] [ ! (Agenta knows whether (1&2&3&4)) ] 0","hypothesis":"Joseph can now know that Mary's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Mary","Brenda","Renee","Joseph"],"index":57334,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9523705244,"difficulty":0.0476294756}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Leanna does not know whether Leanna's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] Agentb knows whether (Agentc knows whether (1|2|3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Leanna can now know whether Darlene can know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Mary","Leanna","Darlene"],"index":35624,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994276166,"difficulty":0.0005723834}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Regina does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] Agenta knows whether (Agentc knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether (1&2&3)) ] 0","hypothesis":"Regina can now know whether Betsy can know that Regina's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Regina","Thelma","Betsy"],"index":24934,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.8963709474,"difficulty":0.1036290526}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Monica does not know whether Monica's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentb knows that (Agenta knows that 2)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Monica can now know that Megan can know that Monica's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Megan","Monica","Virginia"],"index":67356,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9954688549,"difficulty":0.0045311451}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] Agentc knows that (Agentb knows that 4)","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1|2|3|4) ] 0","hypothesis":"Luis can now know that Ralph can know that Barbara's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Ryan","Ralph","Luis","Barbara"],"index":64089,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9957593083,"difficulty":0.0042406917}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Kenneth's forehead is muddy. It is publicly announced that Edward's forehead is muddy. It is publicly announced that Susie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] Agentc knows that (Agentd knows that (1|2|3|4))","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! 2 ] [ ! ~(Agentd knows whether (1&2&3&4)) ] 0","hypothesis":"Julius can now know that Susie can know that someone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Kenneth","Edward","Julius","Susie"],"index":2347,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994763732,"difficulty":0.0005236268}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Mary knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentc knows whether (~(1|2|3|4))) ] 0","hypothesis":"Jesse can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":0,"names":["Colin","Jesse","Mary","Wendy"],"index":9233,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.998849988,"difficulty":0.001150012}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] (Agenta knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] 0","hypothesis":"William can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["William","Marilyn","Joseph","Alfred"],"index":48094,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9981075525,"difficulty":0.0018924475}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy. It is publicly announced that Alice's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] (Agenta knows that 1)","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (1&2&3&4) ] [ ! 3 ] 0","hypothesis":"Steven can now know that Steven's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Steven","Jeannette","Alice","Lisa"],"index":61153,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9914441705,"difficulty":0.0085558295}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Laura knows whether or not everyone's forehead is muddy. It is publicly announced that Gene knows whether or not nobody's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] (Agentc knows that (~(1|2|3)))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1&2&3)) ] [ ! (Agentb knows whether (~(1|2|3))) ] 0","hypothesis":"Laura can now know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Anita","Gene","Laura"],"index":39937,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990544915,"difficulty":0.0009455085}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Oliver knows whether or not nobody's forehead is muddy. It is publicly announced that Oliver knows whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] Agentc knows that (Agentb knows whether (1&2&3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (~(1|2|3))) ] [ ! (Agentc knows whether (1&2&3)) ] 0","hypothesis":"Oliver can now know that Mae can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Miguel","Mae","Oliver"],"index":16747,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9475747347,"difficulty":0.0524252653}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Shelton does not know whether Shelton's forehead is muddy. It is publicly announced that Robert's forehead is not muddy. It is publicly announced that Shelton's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] Agentc knows whether (Agenta knows whether 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agenta knows whether 1) ] [ ! ~(3) ] [ ! 1 ] 0","hypothesis":"Robert can now know whether Shelton can know whether Shelton's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["Shelton","Duane","Robert"],"index":13816,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9735352993,"difficulty":0.0264647007}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Artie knows whether Jose's forehead is muddy. It is publicly announced that Diane's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] Agentc knows that (Agentd knows that (1&2&3&4))","n_announcements":2,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! 3 ] 0","hypothesis":"Diane can now know that Jose can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Artie","Pete","Diane","Jose"],"index":6188,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9986073375,"difficulty":0.0013926625}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Richard does not know whether Richard's forehead is muddy. It is publicly announced that not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] Agentc knows that (Agenta knows that 3)","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentb knows whether 2) ] [ ! (~(1&2&3)) ] 0","hypothesis":"Robert can now know that Nicola can know that Robert's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Nicola","Richard","Robert"],"index":48603,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9962259531,"difficulty":0.0037740469}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Elizabeth knows whether Rebecca's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agentc knows whether (1&2&3))","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Elizabeth can now know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Rebecca","Betty","Elizabeth"],"index":41111,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9643954635,"difficulty":0.0356045365}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Tony knows whether Michelle's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] (Agenta knows that 1)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 1) ] 0","hypothesis":"Michelle can now know that Michelle's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["Michelle","Joseph","Tony"],"index":48513,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9742434025,"difficulty":0.0257565975}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Olive's forehead is not muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] (Agentb knows that 2)","n_announcements":1,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! ~(2) ] 0","hypothesis":"Olive can now know that Olive's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":2,"label":0,"names":["Delbert","Olive"],"index":48280,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9969153404,"difficulty":0.0030846596}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Stephen's forehead is not muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] Agentc knows that (Agentb knows that (~(1|2|3|4)))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(3) ] 0","hypothesis":"Stephen can now know that Cynthia can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Jennifer","Cynthia","Stephen","Novella"],"index":23941,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9989677668,"difficulty":0.0010322332}
-{"premise":"There are two persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Ann knows whether Ralph's forehead is muddy. It is publicly announced that Ralph knows whether or not everyone's forehead is muddy. It is publicly announced that someone's forehead is muddy.","smcdel_problem":"VARS 1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] Agenta knows that (Agentb knows that (~(1|2)))","n_announcements":3,"pbcheck":"VARS 0,1,2 LAW Top OBS Agenta:2 Agentb:1 VALID? [ ! (1|2) ] [ ! (Agentb knows whether 1) ] [ ! (Agenta knows whether (1&2)) ] [ ! (1|2) ] 0","hypothesis":"Ralph can now know that Ann can know that nobody's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":2,"label":0,"names":["Ralph","Ann"],"index":20880,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9990347624,"difficulty":0.0009652376}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Martha knows whether Gary's forehead is muddy. It is publicly announced that Martha does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] (Agentb knows whether (1|2|3))","n_announcements":2,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether 2) ] [ ! ~(Agentc knows whether (1&2&3)) ] 0","hypothesis":"Gary can now know whether someone's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":1,"names":["Anita","Gary","Martha"],"index":16215,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9994558692,"difficulty":0.0005441308}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Geneva knows whether Thomas's forehead is muddy. It is publicly announced that Thomas does not know whether or not everyone's forehead is muddy. It is publicly announced that Geneva knows whether Jeannette's forehead is muddy. It is publicly announced that Geneva knows whether Austin's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] (Agentb knows whether 3)","n_announcements":4,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agenta knows whether 4) ] [ ! ~(Agentd knows whether (1&2&3&4)) ] [ ! (Agenta knows whether 2) ] [ ! (Agenta knows whether 3) ] 0","hypothesis":"Jeannette can now know whether Austin's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":4,"label":1,"names":["Geneva","Jeannette","Austin","Thomas"],"index":22327,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9991718531,"difficulty":0.0008281469}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gregg knows whether someone's forehead is muddy. It is publicly announced that Juanita knows whether Gregg's forehead is muddy. It is publicly announced that Steven does not know whether Steven's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] Agenta knows that (Agentc knows that 1)","n_announcements":3,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (Agentc knows whether (1|2|3)) ] [ ! (Agenta knows whether 3) ] [ ! ~(Agentb knows whether 2) ] 0","hypothesis":"Juanita can now know that Gregg can know that Juanita's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":0,"names":["Juanita","Steven","Gregg"],"index":56277,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9967761636,"difficulty":0.0032238364}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Michael knows whether Linda's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] Agenta knows that (Agentc knows that (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! (Agentd knows whether 2) ] 0","hypothesis":"Danielle can now know that Courtney can know that everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":0,"names":["Danielle","Linda","Courtney","Michael"],"index":33685,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9988473654,"difficulty":0.0011526346}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Colleen's forehead is muddy. It is publicly announced that not everyone's forehead is muddy. It is publicly announced that Nicholas's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] Agentd knows that (Agenta knows whether 2)","n_announcements":3,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! 1 ] [ ! (~(1&2&3&4)) ] [ ! 4 ] 0","hypothesis":"Nicholas can now know that Colleen can know whether Laura's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Colleen","Laura","John","Nicholas"],"index":43310,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9988705516,"difficulty":0.0011294484}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] Agentb knows whether (Agenta knows whether 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! (1&2&3) ] 0","hypothesis":"Reba can now know whether David can know whether Enrique's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":3,"label":1,"names":["David","Reba","Enrique"],"index":33355,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.9992769361,"difficulty":0.0007230639}
-{"premise":"There are four persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Natalie does not know whether or not everyone's forehead is muddy.","smcdel_problem":"VARS 1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] Agentc knows whether (Agentd knows whether (1&2&3&4))","n_announcements":1,"pbcheck":"VARS 0,1,2,3,4 LAW Top OBS Agenta:2,3,4 Agentb:1,3,4 Agentc:1,2,4 Agentd:1,2,3 VALID? [ ! (1|2|3|4) ] [ ! ~(Agentb knows whether (1&2&3&4)) ] 0","hypothesis":"Daniel can now know whether Angie can know whether or not everyone's forehead is muddy.","setup":"forehead","hypothesis_depth":1,"n_agents":4,"label":1,"names":["Susan","Natalie","Daniel","Angie"],"index":52360,"s-l":"forehead-1","deberta_pred":1,"deberta_confidence":0.8874572515,"difficulty":0.1125427485}
-{"premise":"There are three persons. Everyone is visible to others. It is publicly announced that someone's forehead is muddy. It is publicly announced that Gloria does not know whether Gloria's forehead is muddy.","smcdel_problem":"VARS 1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] (Agenta knows that 3)","n_announcements":1,"pbcheck":"VARS 0,1,2,3 LAW Top OBS Agenta:2,3 Agentb:1,3 Agentc:1,2 VALID? [ ! (1|2|3) ] [ ! ~(Agentc knows whether 3) ] 0","hypothesis":"James can now know that Gloria's forehead is muddy.","setup":"forehead","hypothesis_depth":0,"n_agents":3,"label":0,"names":["James","Michael","Gloria"],"index":61642,"s-l":"forehead-0","deberta_pred":0,"deberta_confidence":0.9931609631,"difficulty":0.0068390369}